{
"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": [
"Executed operation: SETUP_CONSTANTS()"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
":constants"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Executed operation: INITIALISATION()"
]
},
"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"
]
}
],
"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"
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},
"nbformat": 4,
"nbformat_minor": 2
}