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            <h1>Geometry and Combinatorics

                

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    <p>A two-player game is played with two piles of stones, with sizes \(m,n\).  On a player's turn, that player can remove any positive integer number of stones from one pile, or the same positive integer number of stones from each pile.  A player loses when they are unable to take a stone.  If \(1 \leq m,n \leq 30\), for how many of the \(30 \times 30 = 900\) starting positions does the first player have a winning strategy?</p>

    

    

    

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