Reply To: Maths

That looks spot on @Astralica. Well done.

My posts may get somewhat out of order, but having attempted to simulate all possible coin positions and checked for compliance with the rules, I believe there are 92 different solutions to the puzzle, but they are grouped with up to three rotations and up to four reflections of the same basic solution and then additional reflections of each rotation. It’s looking more like nine unique solutions excluding symmetries.

For the hash function, my first though was to sum values from a symmetrical table to the hash value for any space occupied by a coin. Something like:

49 35 21 14 14 21 35 49
35 25 15 10 10 15 25 35
21 15 9 6 6 9 15 21
14 10 6 4 4 6 10 14
14 10 6 4 4 6 10 14
21 15 9 6 6 9 15 21
35 25 15 10 10 15 25 35
49 35 21 14 14 21 35 49

Obviously I want to maintain symmetry, but avoid collisions for different arrangements. Do you have any thoughts?

Thanks