a second game on the same tape. sixteen piles, one for each class. a pile holds one stone for every swap of that class in the window. this is plain nim, so it is solved: xor the pile sizes. if the result is zero the player to move has already lost. if it is not, the winning moves are listed below, and there is always at least one.
piles
hollow stones are the ones a winning move takes away.
pile sizes in binary
class
stones
32
16
8
4
2
1
the parity row read as a binary number is the count game value: .