Place eight 'A's and eight 'B's in a 4x4 grid such that each 'A' is orthogonally bordered by 1 or 3 'A's and each 'B' is orthogonally bordered by 0, 2, or 4 'B's.
Can a 6x6 grid be filled with 18 'A's and 18 'B's in this manner?
Note: 'orthogonally' means horizontally or vertically
This seems to be the single possible solution.
It can be shown (in an exthaustive way) that there are no possible
solutions with a B bordered by 4 B's, with an A bordered by 3 A's, or a
B bordered by 2 B's both horizontally bordering (or both vertically).
The B's also can't form a 3x3 square, as the middle square would be an
A which has no other A's bordering. For the A's, all of them have a
single neigbouring A, so they form domino's. The only possible
configuration which follows these constraints is the solution shown