add version of N-Queens with visualization

d11cb81e · Michael Leuschel · 4c968736 · d11cb81e · d11cb81e · d11cb81e
Commit d11cb81e authored Oct 9, 2019 by Michael Leuschel
--- a/notebooks/models/NQueens_Puzzle.ipynb
+++ b/notebooks/models/NQueens_Puzzle.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## N-Queens Puzzle\n",
+    "\n",
+    "The N-Queens is a famous constraint solving benchmark puzzle.\n",
+    "It is a generalisation of the original eight queens puzzle, where the goal is to place eight queens on a 8*8 chessboard so that no two queens attach each other.\n",
+    "\n",
+    "We now write a B machine with constants\n",
+    "* n: the size of the chess board\n",
+    "* queens: a partial function from 1..n to 1..n, stating in which row the queen on any given column is placed\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Loaded machine: Queens"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "::load\n",
+    "MACHINE Queens\n",
+    "CONSTANTS n, queens\n",
+    "PROPERTIES\n",
+    " n>0 & n<120 &\n",
+    " queens : (1..n) +-> (1..n)\n",
+    " \n",
+    "DEFINITIONS\n",
+    "      ANIMATION_FUNCTION_DEFAULT == ( {r,c,i|r:1..n & c:1..n & i=(r+c) mod 2 }  );\n",
+    "      ANIMATION_FUNCTION == ( {r,c,i|c:1..n & c|->r:queens & i=2+((r+c) mod 2) }  );\n",
+    "\n",
+    "      ANIMATION_IMG0 == \"images/ChessPieces/Chess_emptyl45.gif\";\n",
+    "      ANIMATION_IMG1 == \"images/ChessPieces/Chess_emptyd45.gif\";\n",
+    "      ANIMATION_IMG2 == \"images/ChessPieces/Chess_qll45.gif\";\n",
+    "      ANIMATION_IMG3 == \"images/ChessPieces/Chess_qld45.gif\";\n",
+    "      \n",
+    "      no_attack(q1,q2,board) == no_attack_pos(q1,board(q1),q2,board(q2));\n",
+    "      no_attack_pos(q1,q1row,q2,q2row) == (q1row+q2-q1 /= q2row & q1row-q2+q1 /= q2row);\n",
+    "      Solution(board) == (\n",
+    "         board :  perm(1..n) /* for each column the row in which the queen is in */\n",
+    "         &\n",
+    "         !(q1,q2).(q1:1..n & q2:2..n & q2>q1 => no_attack(q1,q2,board) )\n",
+    "        )\n",
+    "END"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine constants set up using operation 0: $setup_constants()"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":constants"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine initialised using operation 1: $initialise_machine()"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":init"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the PROPERTIES we have not stated any constraint of our puzzle. Hence the default solution is n=1 and an empty board:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "$\\renewcommand{\\emptyset}{\\mathord\\varnothing}(\\emptyset\\mapsto 1)$"
+      ],
+      "text/plain": [
+       "(∅↦1)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(queens,n)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let us now slowly tighten the constraints. We can use the ```:find``` command to find\n",
+    "states which satisfy the PROPERTIES and some additional predicate.\n",
+    "Let us first require that every queen is really placed.\n",
+    "We also impose an 8 by 8 board."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Found a matching state and made it current state"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":find queens : 1..8 --> 1..8"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "$\\{(1\\mapsto 1),(2\\mapsto 1),(3\\mapsto 1),(4\\mapsto 1),(5\\mapsto 1),(6\\mapsto 1),(7\\mapsto 1),(8\\mapsto 1)\\}$"
+      ],
+      "text/plain": [
+       "{(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1)}"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "queens"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can use the graphical visualization ANIMATION_FUNCTION to display the solution:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We now also require that queens is a bijection, i.e., that no two queens are placed on the same row:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Found a matching state and made it current state"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":find queens : 1..8 >-> 1..8"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Finally, let us solve the puzzle by also respecting the diagonals.\n",
+    "We use the predefined Solutions DEFINITION in the model above."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Found a matching state and made it current state"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":find n=8 & Solution(queens)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "$\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 4)\\}$"
+      ],
+      "text/plain": [
+       "{(1↦1),(2↦5),(3↦8),(4↦6),(5↦3),(6↦7),(7↦2),(8↦4)}"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "queens"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Obviously we can solve the puzzle for other values of n:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Found a matching state and made it current state"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":find n=20 & Solution(queens)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/ChessPieces/Chess_qll45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/ChessPieces/Chess_qld45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/ChessPieces/Chess_emptyd45.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"0\" src=\"images/ChessPieces/Chess_emptyl45.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "ProB 2",
+   "language": "prob",
+   "name": "prob2"
+  },
+  "language_info": {
+   "codemirror_mode": "prob2_jupyter_repl",
+   "file_extension": ".prob",
+   "mimetype": "text/x-prob2-jupyter-repl",
+   "name": "prob"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
+%% Cell type:markdown id: tags:
+
+## N-Queens Puzzle
+
+The N-Queens is a famous constraint solving benchmark puzzle.
+It is a generalisation of the original eight queens puzzle, where the goal is to place eight queens on a 8*8 chessboard so that no two queens attach each other.
+
+We now write a B machine with constants
+* n: the size of the chess board
+* queens: a partial function from 1..n to 1..n, stating in which row the queen on any given column is placed
+
+%% Cell type:code id: tags:
+
+``` prob
+::load
+MACHINE Queens
+CONSTANTS n, queens
+PROPERTIES
+ n>0 & n<120 &
+ queens : (1..n) +-> (1..n)
+
+DEFINITIONS
+      ANIMATION_FUNCTION_DEFAULT == ( {r,c,i|r:1..n & c:1..n & i=(r+c) mod 2 }  );
+      ANIMATION_FUNCTION == ( {r,c,i|c:1..n & c|->r:queens & i=2+((r+c) mod 2) }  );
+
+      ANIMATION_IMG0 == "images/ChessPieces/Chess_emptyl45.gif";
+      ANIMATION_IMG1 == "images/ChessPieces/Chess_emptyd45.gif";
+      ANIMATION_IMG2 == "images/ChessPieces/Chess_qll45.gif";
+      ANIMATION_IMG3 == "images/ChessPieces/Chess_qld45.gif";
+
+      no_attack(q1,q2,board) == no_attack_pos(q1,board(q1),q2,board(q2));
+      no_attack_pos(q1,q1row,q2,q2row) == (q1row+q2-q1 /= q2row & q1row-q2+q1 /= q2row);
+      Solution(board) == (
+         board :  perm(1..n) /* for each column the row in which the queen is in */
+         &
+         !(q1,q2).(q1:1..n & q2:2..n & q2>q1 => no_attack(q1,q2,board) )
+        )
+END
+```
+
+%% Output
+
+    Loaded machine: Queens
+
+%% Cell type:code id: tags:
+
+``` prob
+:constants
+```
+
+%% Output
+
+    Machine constants set up using operation 0: $setup_constants()
+
+%% Cell type:code id: tags:
+
+``` prob
+:init
+```
+
+%% Output
+
+    Machine initialised using operation 1: $initialise_machine()
+
+%% Cell type:markdown id: tags:
+
+In the PROPERTIES we have not stated any constraint of our puzzle. Hence the default solution is n=1 and an empty board:
+
+%% Cell type:code id: tags:
+
+``` prob
+(queens,n)
+```
+
+%% Output
+
+    $\renewcommand{\emptyset}{\mathord\varnothing}(\emptyset\mapsto 1)$
+    (∅↦1)
+
+%% Cell type:markdown id: tags:
+
+Let us now slowly tighten the constraints. We can use the ```:find``` command to find
+states which satisfy the PROPERTIES and some additional predicate.
+Let us first require that every queen is really placed.
+We also impose an 8 by 8 board.
+
+%% Cell type:code id: tags:
+
+``` prob
+:find queens : 1..8 --> 1..8
+```
+
+%% Output
+
+    Found a matching state and made it current state
+
+%% Cell type:code id: tags:
+
+``` prob
+queens
+```
+
+%% Output
+
+    $\{(1\mapsto 1),(2\mapsto 1),(3\mapsto 1),(4\mapsto 1),(5\mapsto 1),(6\mapsto 1),(7\mapsto 1),(8\mapsto 1)\}$
+    {(1↦1),(2↦1),(3↦1),(4↦1),(5↦1),(6↦1),(7↦1),(8↦1)}
+
+%% Cell type:markdown id: tags:
+
+We can use the graphical visualization ANIMATION_FUNCTION to display the solution:
+
+%% Cell type:code id: tags:
+
+``` prob
+:show
+```
+
+%% Output
+
+    <table style="font-family:monospace"><tbody>
+    <tr>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    </tbody></table>
+    <Animation function visualisation>
+
+%% Cell type:markdown id: tags:
+
+We now also require that queens is a bijection, i.e., that no two queens are placed on the same row:
+
+%% Cell type:code id: tags:
+
+``` prob
+:find queens : 1..8 >-> 1..8
+```
+
+%% Output
+
+    Found a matching state and made it current state
+
+%% Cell type:code id: tags:
+
+``` prob
+:show
+```
+
+%% Output
+
+    <table style="font-family:monospace"><tbody>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    </tr>
+    </tbody></table>
+    <Animation function visualisation>
+
+%% Cell type:markdown id: tags:
+
+Finally, let us solve the puzzle by also respecting the diagonals.
+We use the predefined Solutions DEFINITION in the model above.
+
+%% Cell type:code id: tags:
+
+``` prob
+:find n=8 & Solution(queens)
+```
+
+%% Output
+
+    Found a matching state and made it current state
+
+%% Cell type:code id: tags:
+
+``` prob
+:show
+```
+
+%% Output
+
+    <table style="font-family:monospace"><tbody>
+    <tr>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    </tbody></table>
+    <Animation function visualisation>
+
+%% Cell type:code id: tags:
+
+``` prob
+queens
+```
+
+%% Output
+
+    $\{(1\mapsto 1),(2\mapsto 5),(3\mapsto 8),(4\mapsto 6),(5\mapsto 3),(6\mapsto 7),(7\mapsto 2),(8\mapsto 4)\}$
+    {(1↦1),(2↦5),(3↦8),(4↦6),(5↦3),(6↦7),(7↦2),(8↦4)}
+
+%% Cell type:markdown id: tags:
+
+Obviously we can solve the puzzle for other values of n:
+
+%% Cell type:code id: tags:
+
+``` prob
+:find n=20 & Solution(queens)
+```
+
+%% Output
+
+    Found a matching state and made it current state
+
+%% Cell type:code id: tags:
+
+``` prob
+:show
+```
+
+%% Output
+
+    <table style="font-family:monospace"><tbody>
+    <tr>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    <tr>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="2" src="images/ChessPieces/Chess_qll45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
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+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
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+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    </tr>
+    <tr>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="3" src="images/ChessPieces/Chess_qld45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    <td style="padding:0px"><img alt="1" src="images/ChessPieces/Chess_emptyd45.gif"/></td>
+    <td style="padding:0px"><img alt="0" src="images/ChessPieces/Chess_emptyl45.gif"/></td>
+    </tr>
+    </tbody></table>
+    <Animation function visualisation>
+
+%% Cell type:code id: tags:
+
+``` prob
+```
--- a/notebooks/models/images/ChessPieces/Chess_emptyd45.gif
+++ b/notebooks/models/images/ChessPieces/Chess_emptyd45.gif
--- a/notebooks/models/images/ChessPieces/Chess_emptyl45.gif
+++ b/notebooks/models/images/ChessPieces/Chess_emptyl45.gif
--- a/notebooks/models/images/ChessPieces/Chess_qld45.gif
+++ b/notebooks/models/images/ChessPieces/Chess_qld45.gif
--- a/notebooks/models/images/ChessPieces/Chess_qll45.gif
+++ b/notebooks/models/images/ChessPieces/Chess_qll45.gif