examples/notebook/contrib/labeled_dice.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Labeled dice problem in Google CP Solver.
From Jim Orlin 'Colored letters, labeled dice: a logic puzzle' http://jimorlin.wordpress.com/2009/02/17/colored-letters-labeled-dice-a-logic-puzzle/ ''' My daughter Jenn bough a puzzle book, and showed me a cute puzzle. There are 13 words as follows: BUOY, CAVE, CELT, FLUB, FORK, HEMP, JUDY, JUNK, LIMN, QUIP, SWAG, VISA, WISH.
There are 24 different letters that appear in the 13 words. The question is: can one assign the 24 letters to 4 different cubes so that the four letters of each word appears on different cubes. (There is one letter from each word on each cube.) It might be fun for you to try it. I'll give a small hint at the end of this post. The puzzle was created by Humphrey Dudley. '''
Jim Orlin's followup 'Update on Logic Puzzle': http://jimorlin.wordpress.com/2009/02/21/update-on-logic-puzzle/
Compare with the following models:
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver("Labeled dice")
#
# data
#
n = 4
m = 24
A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Y = (
list(range(m)))
letters = [
"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O",
"P", "Q", "R", "S", "T", "U", "V", "W", "Y"
]
num_words = 13
words = [[B, U, O, Y], [C, A, V, E], [C, E, L, T], [F, L, U, B], [F, O, R, K],
[H, E, M, P], [J, U, D, Y], [J, U, N, K], [L, I, M, N], [Q, U, I, P],
[S, W, A, G], [V, I, S, A], [W, I, S, H]]
#
# declare variables
#
dice = [solver.IntVar(0, n - 1, "dice[%i]" % i) for i in range(m)]
#
# constraints
#
# the letters in a word must be on a different die
for i in range(num_words):
solver.Add(solver.AllDifferent([dice[words[i][j]] for j in range(n)]))
# there must be exactly 6 letters of each die
for i in range(n):
b = [solver.IsEqualCstVar(dice[j], i) for j in range(m)]
solver.Add(solver.Sum(b) == 6)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(dice)
db = solver.Phase(dice, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)
#
# result
#
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
# print "dice:", [(letters[i],dice[i].Value()) for i in range(m)]
for d in range(n):
print("die %i:" % d, end=" ")
for i in range(m):
if dice[i].Value() == d:
print(letters[i], end=" ")
print()
print("The words with the cube label:")
for i in range(num_words):
for j in range(n):
print(
"%s (%i)" % (letters[words[i][j]], dice[words[i][j]].Value()),
end=" ")
print()
print()
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
main()