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dudeney

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

First, you must install ortools package in this colab.

python

%pip install ortools

python

# Copyright 2010 Pierre Schaus ([email protected])
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from ortools.constraint_solver import pywrapcp


def dudeney(n):
  solver = pywrapcp.Solver('Dudeney')
  x = [solver.IntVar(list(range(10)), 'x' + str(i)) for i in range(n)]
  nb = solver.IntVar(list(range(3, 10**n)), 'nb')
  s = solver.IntVar(list(range(1, 9 * n + 1)), 's')

  solver.Add(nb == s * s * s)
  solver.Add(sum([10**(n - i - 1) * x[i] for i in range(n)]) == nb)
  solver.Add(sum([x[i] for i in range(n)]) == s)

  solution = solver.Assignment()
  solution.Add(nb)
  collector = solver.AllSolutionCollector(solution)

  solver.Solve(
      solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),
      [collector])

  for i in range(collector.SolutionCount()):
    nbsol = collector.Value(i, nb)
    print(nbsol)

  print('#fails:', solver.Failures())
  print('time:', solver.WallTime(), 'ms')


dudeney(6)