Problem
COM-B1-M08-P006 Thirty-Seven Stones
#6
★★☆☆☆ Level 2 of 5
There are \(37\) stones. In one move, a player may take from \(1\) to \(4\) stones. The last move wins. Find a winning strategy.
Multiples of \(5\) are losing.
Since one may take from \(1\) to \(4\), the losing positions are multiples of \(5\). The number \(37\) has residue \(2\) modulo \(5\). The first player takes \(2\) stones and leaves \(35\). After that, if the opponent takes \(a\), the first player takes \(5-a\), again leaving a multiple of \(5\).
Standard task with full strategy.