Created
March 27, 2020 03:07
-
-
Save jbergknoff/c3153850d5e1df2e178b1f82aa766c2d to your computer and use it in GitHub Desktop.
Solving the Five Squared puzzle (חמש בריבוע)
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# Solving the Five Squared puzzle | |
# seven 3-pieces, two 2-pieces | |
# A = vortex | |
# B = star | |
# C = pentagon | |
# D = bullseye | |
# E = triangle | |
three_pieces = [ | |
['A', 'B', 'C'], | |
['A', 'C', 'B'], | |
['A', 'C', 'D'], | |
['A', 'E', 'C'], | |
['B', 'A', 'D'], | |
['B', 'D', 'E'], | |
['D', 'C', 'E'], | |
] | |
two_pieces = [ | |
['B', 'E'], | |
['D', 'E'], | |
] | |
# cf. https://stackoverflow.com/a/6473724/349427 | |
def transpose(list_of_lists): | |
return list(map(list, zip(*list_of_lists))) | |
five_by_three_layouts = [ | |
# [ 0 ] | |
# [ 1 ] | |
# [ 2 ] | |
# [ 3 ] | |
# [ 4 ] | |
lambda five_threes: transpose(five_threes), | |
# [ 0 ] | |
# [ 1 ] | |
# [ ][ ][ ] | |
# [2][3][4] | |
# [ ][ ][ ] | |
lambda five_threes: transpose(five_threes[:2] + transpose(five_threes[2:5])), | |
# [ 0 ] | |
# [ ][ ][ ] | |
# [2][3][4] | |
# [ ][ ][ ] | |
# [ 1 ] | |
lambda five_threes: transpose([five_threes[0]] + transpose(five_threes[2:5]) + [five_threes[1]]), | |
] | |
layouts = [] | |
# layout A | |
# two solutions: | |
# [bullseye, triangle] [pentagon, star, vortex] | |
# [triangle, pentagon, bullseye] [vortex] [star] | |
# [vortex] [star] [triangle] [pentagon] [bullseye] | |
# [pentagon] [vortex] [star] [bullseye] [triangle] | |
# [star] [bullseye] [vortex, triangle, pentagon] | |
# | |
# and, very similarly, | |
# [bullseye, triangle] [vortex, star, pentagon] | |
# [triangle, pentagon, bullseye] [vortex] [star] | |
# [vortex] [star] [triangle] [pentagon] [bullseye] | |
# [pentagon] [vortex] [star] [bullseye] [triangle] | |
# [star] [bullseye] [pentagon, triangle, vortex] | |
def layoutA(threes, twos): | |
return [ | |
twos[0] + threes[0], | |
threes[1] + [threes[2][0], threes[3][0]], | |
[threes[4][0], threes[5][0], twos[1][0], threes[2][1], threes[3][1]], | |
[threes[4][1], threes[5][1], twos[1][1], threes[2][2], threes[3][2]], | |
[threes[4][2], threes[5][2]] + threes[6], | |
] | |
# layout B | |
# two solutions: | |
# [bullseye, triangle] [pentagon, star, vortex] | |
# [star] [bullseye] [vortex, triangle, pentagon] | |
# [pentagon] [vortex] [star] [bullseye] [triangle] | |
# [vortex] [star] [triangle] [pentagon] [bullseye] | |
# [triangle, pentagon, bullseye] [vortex] [star] | |
# | |
# and, very similarly: | |
# [bullseye, triangle] [vortex, star, pentagon] | |
# [star] [bullseye] [pentagon, triangle, vortex] | |
# [pentagon] [vortex] [star] [bullseye] [triangle] | |
# [vortex] [star] [triangle] [pentagon] [bullseye] | |
# [triangle, pentagon, bullseye] [vortex] [star] | |
def layoutB(threes, twos): | |
return [ | |
twos[0] + threes[0], | |
[threes[1][0], threes[2][0]] + threes[3], | |
[threes[1][1], threes[2][1], twos[1][0], threes[4][0], threes[5][0]], | |
[threes[1][2], threes[2][2], twos[1][1], threes[4][1], threes[5][1]], | |
threes[6] + [threes[4][2], threes[5][2]], | |
] | |
# layout C | |
def layoutC(threes, twos): | |
return [ | |
twos[0] + threes[0], | |
[threes[1][0], threes[2][0], threes[3][0]] + twos[1], | |
[threes[1][1], threes[2][1], threes[3][1], threes[4][0], threes[5][0]], | |
[threes[1][2], threes[2][2], threes[3][2], threes[4][1], threes[5][1]], | |
threes[6] + [threes[4][2], threes[5][2]], | |
] | |
# layout D | |
def layoutD(threes, twos): | |
return [ | |
[threes[0][0], twos[0][0]] + threes[1], | |
[threes[0][1], twos[0][1]] + threes[2], | |
[threes[0][2]] + twos[1] + [threes[3][0], threes[4][0]], | |
threes[5] + [threes[3][1], threes[4][1]], | |
threes[6] + [threes[3][2], threes[4][2]], | |
] | |
# layout E | |
def layoutE(threes, twos): | |
return [ | |
[threes[0][0], twos[0][0]] + threes[1], | |
[threes[0][1], twos[0][1]] + threes[2], | |
[threes[0][2]] + threes[3] + [threes[4][0]], | |
threes[5] + [twos[1][0], threes[4][1]], | |
threes[6] + [twos[1][1], threes[4][2]], | |
] | |
# layout F | |
def layoutF(threes, twos): | |
return [ | |
twos[0] + [threes[0][0], threes[1][0], threes[2][0]], | |
[threes[3][0], threes[4][0], threes[0][1], threes[1][1], threes[2][1]], | |
[threes[3][1], threes[4][1], threes[0][2], threes[1][2], threes[2][2]], | |
[threes[3][2], threes[4][2]] + threes[5], | |
threes[6] + twos[1], | |
] | |
layouts += [layoutA, layoutB, layoutC, layoutD, layoutE, layoutF] | |
for five_by_three_layout in five_by_three_layouts: | |
def layoutG(threes, twos): | |
three_by_five = transpose(five_by_three_layout(threes[:5])) | |
return [ | |
twos[0] + three_by_five[0], | |
twos[1] + three_by_five[1], | |
[threes[5][0], threes[6][0]] + three_by_five[2], | |
[threes[5][1], threes[6][1]] + three_by_five[3], | |
[threes[5][2], threes[6][2]] + three_by_five[4], | |
] | |
def layoutH(threes, twos): | |
five_by_three = five_by_three_layout(threes[:5]) | |
return [ | |
twos[0] + threes[5], | |
twos[1] + threes[6], | |
five_by_three[0], | |
five_by_three[1], | |
five_by_three[2], | |
] | |
def layoutI(threes, twos): | |
five_by_three = five_by_three_layout(threes[:5]) | |
return [ | |
twos[0] + threes[5], | |
threes[6] + twos[1], | |
five_by_three[0], | |
five_by_three[1], | |
five_by_three[2], | |
] | |
def layoutJ(threes, twos): | |
three_by_five = transpose(five_by_three_layout(threes[:5])) | |
return [ | |
twos[0] + three_by_five[0], | |
[threes[5][0], threes[6][0]] + three_by_five[1], | |
[threes[5][1], threes[6][1]] + three_by_five[2], | |
[threes[5][2], threes[6][2]] + three_by_five[3], | |
twos[1] + three_by_five[4], | |
] | |
def layoutK(threes, twos): | |
five_by_three = five_by_three_layout(threes[:5]) | |
return [ | |
twos[0] + threes[5], | |
five_by_three[0], | |
five_by_three[1], | |
five_by_three[2], | |
twos[1] + threes[6], | |
] | |
def layoutL(threes, twos): | |
five_by_three = five_by_three_layout(threes[:5]) | |
return [ | |
twos[0] + threes[5], | |
five_by_three[0], | |
five_by_three[1], | |
five_by_three[2], | |
threes[6] + twos[1], | |
] | |
layouts += [layoutG, layoutH, layoutI, layoutJ, layoutK, layoutL] | |
def judge_square(square): | |
if len(square) != 5 or any([len(row) != 5 for row in square]): | |
print(f'Invalid square: {square}') | |
raise Exception('Invalid square') | |
for row in square: | |
if len(set(row)) != 5: | |
return False | |
for row in transpose(square): | |
if len(set(row)) != 5: | |
return False | |
return True | |
def generate_permutations(pieces): | |
if len(pieces) == 1: | |
yield [pieces[0]] | |
yield [pieces[0][::-1]] | |
return | |
permutation_length = len(pieces) | |
for sub_permutation in generate_permutations(pieces[1:]): | |
for index in range(permutation_length): | |
#print(f'inserting {pieces[0]} on either side of {sub_permutation[:index]} and {sub_permutation[index:]}') | |
yield sub_permutation[:index] + [pieces[0]] + sub_permutation[index:] | |
yield sub_permutation[:index] + [pieces[0][::-1]] + sub_permutation[index:] | |
def solve(): | |
three_pieces_permutations = generate_permutations(three_pieces) | |
two_pieces_permutations = list(generate_permutations(two_pieces)) | |
counter = 0 | |
for three_pieces_permutation in three_pieces_permutations: | |
for two_pieces_permutation in two_pieces_permutations: | |
counter += 1 | |
if counter % 10000 == 0: | |
print(f'Checked {counter}') | |
for layout in layouts: | |
square = layout(three_pieces_permutation, two_pieces_permutation) | |
if judge_square(square) is True: | |
print('found one') | |
print(three_pieces_permutation, two_pieces_permutation) | |
print(square) | |
print(layout) | |
if __name__ == '__main__': | |
solve() |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment