# 4-pile Same-Nim

The game Same-Nim is a two player game played with piles of stones. A valid move consists of removing a positive number of stones from one of the piles, such that there is some pair of piles that contains the same number of stones. The players alternate turns to make a move. A player loses the game if they are unable to remove any stones on their turn.

A game of Same-Nim is played with 4 piles of sizes $$(30,30,a,b),$$ where $$1 \leq a, b \leq 30.$$ For how many of the $$900$$ possible ordered pairs $$(a,b)$$ does the first player have a winning strategy?

Details and assumptions

A valid move may result in more than 1 pair of piles that contain the same number of stones.

The pair of piles with the same number of stones may both have $$0$$ stones, if the piles had stones in them when the game started.

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