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magic_square_and_cards

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/magic_square_and_cards.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/examples/contrib/magic_square_and_cards.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

Magic squares and cards problem in Google CP Solver.

Martin Gardner (July 1971) ''' Allowing duplicates values, what is the largest constant sum for an order-3 magic square that can be formed with nine cards from the deck. '''

This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

python

import sys
from ortools.constraint_solver import pywrapcp


def main(n=3):
  # Create the solver.
  solver = pywrapcp.Solver("n-queens")

  #
  # data
  #
  # n = 3

  #
  # declare variables
  #
  x = {}
  for i in range(n):
    for j in range(n):
      x[(i, j)] = solver.IntVar(1, 13, "x(%i,%i)" % (i, j))
  x_flat = [x[(i, j)] for i in range(n) for j in range(n)]

  s = solver.IntVar(1, 13 * 4, "s")
  counts = [solver.IntVar(0, 4, "counts(%i)" % i) for i in range(14)]

  #
  # constraints
  #
  solver.Add(solver.Distribute(x_flat, list(range(14)), counts))

  # the standard magic square constraints (sans all_different)
  [solver.Add(solver.Sum([x[(i, j)] for j in range(n)]) == s) for i in range(n)]
  [solver.Add(solver.Sum([x[(i, j)] for i in range(n)]) == s) for j in range(n)]

  solver.Add(solver.Sum([x[(i, i)] for i in range(n)]) == s)  # diag 1
  solver.Add(solver.Sum([x[(i, n - i - 1)] for i in range(n)]) == s)  # diag 2

  # redundant constraint
  solver.Add(solver.Sum(counts) == n * n)

  # objective
  objective = solver.Maximize(s, 1)

  #
  # solution and search
  #
  solution = solver.Assignment()
  solution.Add(x_flat)
  solution.Add(s)
  solution.Add(counts)

  # db: DecisionBuilder
  db = solver.Phase(x_flat, solver.CHOOSE_FIRST_UNBOUND,
                    solver.ASSIGN_MAX_VALUE)

  solver.NewSearch(db, [objective])
  num_solutions = 0
  while solver.NextSolution():
    print("s:", s.Value())
    print("counts:", [counts[i].Value() for i in range(14)])
    for i in range(n):
      for j in range(n):
        print(x[(i, j)].Value(), end=" ")
      print()

    print()
    num_solutions += 1
  solver.EndSearch()

  print()
  print("num_solutions:", num_solutions)
  print("failures:", solver.Failures())
  print("branches:", solver.Branches())
  print("WallTime:", solver.WallTime())


n = 3
if len(sys.argv) > 1:
  n = int(sys.argv[1])
main(n)