Solve the no connection puzzle
You are given a box with eight holes labelled A-to-H, connected by fifteen straight lines in the pattern as shown
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H
You are also given eight pegs numbered 1-to-8. The idea is to place the pegs in the holes so that the (absolute) difference between any two numbers connected by any line is greater than one.
For example, in this attempt:
4 7
/|\ /|\
/ | X | \
/ |/ \| \
8 - 1 - 6 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 5
Note that 7 and 6 are connected and have a difference of 1 so it is not a solution.
The task is to produce and show here one solution to the puzzle.
- Reference
No Connection Puzzle (Video).
Python
A brute force search solution. <lang python>from __future__ import print_function from itertools import permutations
connections = ((0, 2), (0, 3), (0, 4),
(1, 3), (1, 4), (1, 5),
(6, 2), (6, 3), (6, 4),
(7, 3), (7, 4), (7, 5),
(2, 3), (3, 4), (4, 5))
def ok(conn, perm):
"""Connected numbers ok?""" this, that = conn return abs(perm[this] - perm[that]) != 1
def solve():
return [perm for perm in permutations(range(1, 9))
if all(ok(conn, perm) for conn in connections)]
if __name__ == '__main__':
solutions = solve()
print("A, B, C, D, E, F, G, H =", ', '.join(str(i) for i in solutions[0]))</lang>
- Output:
A, B, C, D, E, F, G, H = 3, 4, 7, 1, 8, 2, 5, 6
- All solutions pretty printed
Add the following code after that above: <lang python>def pp(solution):
"""Prettyprint a solution"""
boardformat = r"""
A B
/|\ /|\
/ | X | \
/ |/ \| \
C - D - E - F
\ |\ /| /
\ | X | /
\|/ \|/
G H"""
for letter, number in zip("ABCDEFGH", solution):
boardformat = boardformat.replace(letter, str(number))
print(boardformat)
if __name__ == '__main__':
for i, s in enumerate(solutions, 1):
print("\nSolution", i, end=)
pp(s)</lang>
- Extra output
Solution 1
3 4
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
5 6
Solution 2
3 5
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
4 6
Solution 3
3 6
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
4 5
Solution 4
3 6
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
5 4
Solution 5
4 3
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
6 5
Solution 6
4 5
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
6 3
Solution 7
4 5
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 6
Solution 8
4 6
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 5
Solution 9
5 3
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
6 4
Solution 10
5 4
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
6 3
Solution 11
5 4
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 6
Solution 12
5 6
/|\ /|\
/ | X | \
/ |/ \| \
7 - 1 - 8 - 2
\ |\ /| /
\ | X | /
\|/ \|/
3 4
Solution 13
6 3
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
4 5
Solution 14
6 3
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
5 4
Solution 15
6 4
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
5 3
Solution 16
6 5
/|\ /|\
/ | X | \
/ |/ \| \
2 - 8 - 1 - 7
\ |\ /| /
\ | X | /
\|/ \|/
4 3