January 2024 - Solution
January 2024 Solution:
There are 84 solutions in total to the original board. Of those, there are three pairs of solutions for which a solution to the bonus part can be given:
[8, 13, 5, 11, 10, 14, 1, 15, 3, 12, 2, 16, 4, 7, 9, 6] [12, 8, 9, 6, 14, 10, 2, 16, 4, 7, 1, 11, 13, 3, 5, 15] [-,-,+,+,-,+,+,+,-,+,+,-,+,+,+,+,-,-,+,+,+,+,-,-]
[15,10,8,12,13,7,1,11,3,5,2,9,14,4,6,16] [16,12,9,14,10,6,2,8,4,7,1,11,13,3,5,15] [-,-,+,+,-,-,+,-,-,-,+,-,+,+,+,+,-,-,+,-,+,-,-,+]
[13,12,6,14,5,9,4,8,1,10,7,11,2,3,16,15] [14,8,2,15,4,16,1,11,5,9,3,10,6,7,13,12] [-,+,-,+,+,+,-,+,+,-,-,-,-,+,+,+,-,+,-,-,-,-,-,+]
The straightforward method to solve the problem is using a constraint satisfaction solver. One can also attempt backtracking algorithms specifically suitable for the problem itself. However, not a single solver has managed to find a solution method suitable for a third-grade student, and it seems none exists.