2016_09_ChessDance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "Oq1xibzMT1Wl"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import time\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import ListedColormap\n",
    "import matplotlib.pyplot as plt\n",
    "import requests\n",
    "from bs4 import BeautifulSoup\n",
    "import itertools\n",
    "from copy import deepcopy as dcopy,copy\n",
    "\n",
    "from z3 import *\n",
    "from IPython.display import Markdown, display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "ICTfvjZUT1Wr"
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "**Chess Dance**\n",
       "\n",
       "Five chess pieces are placed on a chessboard:  a Q ueen, K ing, R ook, B ishop, and k N ight, as shown. They all move simultaneously, and finish at squares that we’ll label Q1, K1, B1, R1, and N1.  They continue moving, and no square is ever visited more than once, for a total of 8 moves .  (So in total, 45 squares will be labeled:  Q0 through Q8, K0 through K8, etc.) Pieces move according to the same rules as chess (e.g. a Rook can move anywhere along its row or column).  After each move, no piece is allowed to be under attack from any other piece. The numbers along the rows and columns presented here are the products of the non-zero numbers that were visible after only 7 moves After all 8 moves are finished, the 8 row products and the 8 column products are recalculated (non-zero numbers only). The answer to this month’s puzzle is the largest possible sum for these 16 products."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "url='https://www.janestreet.com/puzzles/chess-dance/'\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "y =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "display(Markdown(\"**\"+y[6]+\"**\\n\\n\"+str(\" \".join(y[7:26]))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "source": [
    "<img src=\"https://www.janestreet.com/puzzles/wp-content/uploads/2016/09/sep16_puzzle.png\" width=350>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [],
   "source": [
    "col_tot = [2744,36,375,336,108,240,20,504]\n",
    "row_tot = [7,1890,8,10080,20,840,144,1260]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "844RhDFpT1Wu"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved in 559.27 seconds\n",
      "The sum of products is 62,943\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 324x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "start = time.time()\n",
    "s = Optimize()\n",
    "\n",
    "#set up the variables\n",
    "Q = [Int(\"Q_%s\" % (i+1)) for i in range(9) ]\n",
    "K = [Int(\"K_%s\" % (i+1)) for i in range(9) ]\n",
    "R = [Int(\"R_%s\" % (i+1)) for i in range(9) ]\n",
    "N = [Int(\"N_%s\" % (i+1)) for i in range(9) ]\n",
    "B = [Int(\"B_%s\" % (i+1)) for i in range(9) ]\n",
    "\n",
    "# add the objective\n",
    "s.maximize(Sum([Product([If(i % 8==x,y,1) for y in range(1,9) for i in [Q[y],K[y],R[y],N[y],B[y]]]) +\n",
    "               Product([If(i / 8==x,y,1) for y in range(1,9) for i in [Q[y],K[y],R[y],N[y],B[y]]])\n",
    "               for x in range(8)]))\n",
    "\n",
    "#fixed\n",
    "s += Q[0] == 8\n",
    "s += Q[8] == 49 #doesn't seem to like putting this in the optimum spot !\n",
    "s += K[0] == 57\n",
    "s += R[0] == 36\n",
    "s += N[0] == 6\n",
    "s += B[0] == 55\n",
    "\n",
    "#distinct placements on the board \n",
    "pieces = Q+K+R+N+B\n",
    " \n",
    "s += Distinct([i for i in pieces])\n",
    "s += [And(i>-1,i<64) for i in pieces]\n",
    "\n",
    "# valid moves\n",
    "a = [(i,j) for i,j in itertools.product((1, -1),(2,-2))]\n",
    "n_moves = [f(i,j) for i,j in itertools.product([1, -1],[2,-2]) for f in [lambda i,j:(i,j),lambda i,j:(j,i)]]\n",
    "r_moves = [f(i) for i in range(1,8) for f in [lambda x:(x,0),lambda x:(0,x),lambda x:(0,-x),lambda x:(-x,0)]]\n",
    "k_moves = [(i,j) for (i,j) in itertools.product([-1,0,1],[-1,0,1]) if (i,j) != (0,0)]\n",
    "b_moves = [f(i) for i in range(1,8) for f in [lambda x:(x,x),lambda x:(-x,x),lambda x:(x,-x),lambda x:(-x,-x)]]\n",
    "q_moves = b_moves+r_moves\n",
    "\n",
    "s += [Or([And(Q[i]%8 - Q[i-1]%8 == x,Q[i]/8 - Q[i-1]/8 == y) for x,y in q_moves]) for i in range(1,9)]\n",
    "s += [Or([And(K[i]%8 - K[i-1]%8 == x,K[i]/8 - K[i-1]/8 == y) for x,y in k_moves]) for i in range(1,9)]\n",
    "s += [Or([And(R[i]%8 - R[i-1]%8 == x,R[i]/8 - R[i-1]/8 == y) for x,y in r_moves]) for i in range(1,9)]\n",
    "s += [Or([And(N[i]%8 - N[i-1]%8 == x,N[i]/8 - N[i-1]/8 == y) for x,y in n_moves]) for i in range(1,9)]\n",
    "s += [Or([And(B[i]%8 - B[i-1]%8 == x,B[i]/8 - B[i-1]/8 == y) for x,y in b_moves]) for i in range(1,9)]\n",
    "\n",
    "# not under attack\n",
    "s += [And([Not(And(K[i]%8 - Q[i]%8 == x,K[i]/8 - Q[i]/8 == y)) for x,y in q_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(R[i]%8 - Q[i]%8 == x,R[i]/8 - Q[i]/8 == y)) for x,y in q_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(N[i]%8 - Q[i]%8 == x,N[i]/8 - Q[i]/8 == y)) for x,y in q_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(B[i]%8 - Q[i]%8 == x,B[i]/8 - Q[i]/8 == y)) for x,y in q_moves]) for i in range(1,9)]\n",
    "\n",
    "s += [And([Not(And(Q[i]%8 - K[i]%8 == x,Q[i]/8 - K[i]/8 == y)) for x,y in k_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(R[i]%8 - K[i]%8 == x,R[i]/8 - K[i]/8 == y)) for x,y in k_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(N[i]%8 - K[i]%8 == x,N[i]/8 - K[i]/8 == y)) for x,y in k_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(B[i]%8 - K[i]%8 == x,B[i]/8 - K[i]/8 == y)) for x,y in k_moves]) for i in range(1,9)]\n",
    "\n",
    "s += [And([Not(And(Q[i]%8 - R[i]%8 == x,Q[i]/8 - R[i]/8 == y)) for x,y in r_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(K[i]%8 - R[i]%8 == x,K[i]/8 - R[i]/8 == y)) for x,y in r_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(N[i]%8 - R[i]%8 == x,N[i]/8 - R[i]/8 == y)) for x,y in r_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(B[i]%8 - R[i]%8 == x,B[i]/8 - R[i]/8 == y)) for x,y in r_moves]) for i in range(1,9)]\n",
    "\n",
    "s += [And([Not(And(Q[i]%8 - N[i]%8 == x,Q[i]/8 - N[i]/8 == y)) for x,y in n_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(K[i]%8 - N[i]%8 == x,K[i]/8 - N[i]/8 == y)) for x,y in n_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(R[i]%8 - N[i]%8 == x,R[i]/8 - N[i]/8 == y)) for x,y in n_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(B[i]%8 - N[i]%8 == x,B[i]/8 - N[i]/8 == y)) for x,y in n_moves]) for i in range(1,9)]\n",
    "\n",
    "s += [And([Not(And(Q[i]%8 - B[i]%8 == x,Q[i]/8 - B[i]/8 == y)) for x,y in b_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(K[i]%8 - B[i]%8 == x,K[i]/8 - B[i]/8 == y)) for x,y in b_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(R[i]%8 - B[i]%8 == x,R[i]/8 - B[i]/8 == y)) for x,y in b_moves]) for i in range(1,9)]\n",
    "s += [And([Not(And(N[i]%8 - B[i]%8 == x,N[i]/8 - B[i]/8 == y)) for x,y in b_moves]) for i in range(1,9)]\n",
    "\n",
    "# row_col sums\n",
    "for x in range(8):\n",
    "    s += row_tot[x] == Product([If(i % 8==x,y,1) for y in range(1,8) for i in [Q[y],K[y],R[y],N[y],B[y]]])\n",
    "    s += col_tot[x] == Product([If(i / 8==x,y,1) for y in range(1,8) for i in [Q[y],K[y],R[y],N[y],B[y]]])\n",
    "\n",
    "\n",
    "# cut down the search space by looking at divisors of the totals\n",
    "for n in range(1,8):\n",
    "    poss = [i*8+j for i in range(8) for j in range(8) if (col_tot[i] % n ==0) and (row_tot[j] % n ==0) ]\n",
    "    s += Or([Q[n]== p for p in poss])\n",
    "    s += Or([K[n]== p for p in poss])\n",
    "    s += Or([R[n]== p for p in poss])\n",
    "    s += Or([N[n]== p for p in poss])\n",
    "    s += Or([B[n]== p for p in poss])\n",
    "\n",
    "if s.check() == sat:\n",
    "    m = s.model()\n",
    "    q = [m.evaluate(Q[i]).as_long() for i in range(9)]\n",
    "    k = [m.evaluate(K[i]).as_long() for i in range(9)]\n",
    "    r = [m.evaluate(R[i]).as_long() for i in range(9)]\n",
    "    n = [m.evaluate(N[i]).as_long() for i in range(9)]\n",
    "    b = [m.evaluate(B[i]).as_long() for i in range(9)]\n",
    "    print(\"Solved in {:.2f} seconds\".format(time.time()-start))\n",
    "\n",
    "    board= [[\"\" for i in range(8)] for j in range(8)]\n",
    "    colours = np.zeros((8,8))\n",
    "    prod = np.zeros((8,8))\n",
    "    for i in range(9):\n",
    "        board[q[i] % 8][q[i] // 8] = \"Q%s\"% i\n",
    "        board[k[i] % 8][k[i] // 8] = \"K%s\"% i        \n",
    "        board[r[i] % 8][r[i] // 8] = \"R%s\"% i        \n",
    "        board[n[i] % 8][n[i] // 8] = \"N%s\"% i        \n",
    "        board[b[i] % 8][b[i] // 8] = \"B%s\"% i        \n",
    "        colours[q[i] % 8][q[i] // 8] = 1\n",
    "        colours[k[i] % 8][k[i] // 8] = 2\n",
    "        colours[r[i] % 8][r[i] // 8] = 3\n",
    "        colours[n[i] % 8][n[i] // 8] = 4\n",
    "        colours[b[i] % 8][b[i] // 8] = 5\n",
    "        prod[q[i] % 8][q[i] // 8] = i\n",
    "        prod[k[i] % 8][k[i] // 8] = i\n",
    "        prod[r[i] % 8][r[i] // 8] = i\n",
    "        prod[n[i] % 8][n[i] // 8] = i\n",
    "        prod[b[i] % 8][b[i] // 8] = i    \n",
    "    \n",
    "    prod[prod==0] = 1\n",
    "    \n",
    "    soln = np.sum(np.product(prod,0))+np.sum(np.product(prod,1))\n",
    "    print(\"The sum of products is {:,.0f}\\n\".format(soln))\n",
    "        \n",
    "    fig,ax = plt.subplots(1,1,figsize=(4.5,4.5))    \n",
    "    ax =sns.heatmap(colours,annot=board,cbar=False,cmap=ListedColormap([\"w\",\"gold\",\"lime\",\"c\",\"r\",\"darkorange\"]),fmt=\"\",linewidths=1,linecolor=\"k\",annot_kws={\"size\":12,\"color\":\"k\"},alpha=.15,\n",
    "                    xticklabels=col_tot, yticklabels=row_tot)\n",
    "    ax.tick_params(left=False, bottom=False,labelleft=False, labelright=True)\n",
    "    plt.xticks(rotation=0,fontsize =10)\n",
    "    plt.yticks(rotation=0,fontsize =10)\n",
    "    plt.tight_layout()\n",
    "    plt.show()   \n",
    "else:\n",
    "    print(\"failed to solve\")  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution\n",
      "~~~~~~~~\n",
      "There’s quite a bit of logic to sift through with this month’s puzzle, but when the dust settles, this is the completed grid that maximizes the sum of the 16 products, which is 62,943 .   Congratulations to everyone who managed to crack this one! Correct Submissions:\n"
     ]
    }
   ],
   "source": [
    "url='https://www.janestreet.com/puzzles/solutions/september-2016-solution/'\n",
    "res = requests.get(url)\n",
    "soup = BeautifulSoup(res.content, 'html.parser')\n",
    "x =[text for text in soup.body.stripped_strings]\n",
    "\n",
    "print(\"Solution\")\n",
    "print(\"~~~~~~~~\")\n",
    "print(\" \".join(x[7:11]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://www.janestreet.com/puzzles/sep16_solution.png\" width=450>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[0, 1, 3, 5, 7, 24, 25, 27, 29, 31, 56, 57, 59, 61, 63]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n =7\n",
    "\n",
    "board= [[\"\" for i in range(8)] for j in range(8)]\n",
    "for i in range(64):\n",
    "    board[i % 8][i // 8] = i\n",
    "\n",
    "possible = np.array([[(col_tot[i] % n ==0) and (row_tot[j] % n ==0) for i in range(8)] for j in range(8)])\n",
    "\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(4,4))    \n",
    "ax =sns.heatmap(possible,annot=board,cbar=False,cmap='Greys',fmt=\"\",linewidths=1,linecolor=\"k\",annot_kws={\"size\":12,\"color\":\"k\"},alpha=.15,\n",
    "                    xticklabels=col_tot, yticklabels=row_tot)\n",
    "ax.tick_params(left=False, bottom=False,labelleft=False, labelright=True)\n",
    "plt.xticks(rotation=0,fontsize =10)\n",
    "plt.yticks(rotation=0,fontsize =10)\n",
    "plt.tight_layout()\n",
    "plt.show()   \n",
    "\n",
    "[i*8+j for i in range(8) for j in range(8) if (col_tot[i] % n ==0) and (row_tot[j] % n ==0) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# using some of the solutions to test\n",
    "q_solve = [8,0,7,63,61,52,59,56,49]\n",
    "k_solve = [57,50,43,35,28,21,14,5,4]\n",
    "r_solve = [36,39,38,30,46,41,47,31,29]\n",
    "n_solve = [6,12,27,17,2,19,9,3,18]\n",
    "b_solve = [55,62,26,33,51,23,37,1,10]\n",
    "\n",
    "n=3\n",
    "s+= [Q[i] == q_solve[i] for i in range(n)]\n",
    "s+= [K[i] == k_solve[i] for i in range(n)]\n",
    "s+= [R[i] == r_solve[i] for i in range(n)]\n",
    "s+= [N[i] == n_solve[i] for i in range(n)]\n",
    "s+= [B[i] == b_solve[i] for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "include_colab_link": true,
   "name": "JaneSt-Feb18.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}