There are some piles of stones.
Two players move in turn. One can remove a stone from a pile or merge two piles in a move. The player that removes the last stone wins.
With the number of stones in each pile given, how to know who will win?
2026-03-31 08:42:13.1774946533
A combinatorial game about stones
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Hint: Only by taking a pile which consists of a single stone can a player change the parity (see Brian's hint). Is there a strategy for a player who is winning on parity which avoids either player taking a single stone until the last move?
What happens when the initial position has a single pile of size 1?
What happens when there are several piles of size 1 in the initial position?