Problem
COM-B1-M11-P008 Pile \(34\)
#8
★★☆☆☆ Level 2 of 5
There are \(34\) stones. In one move, a player may take from \(1\) to \(4\) stones. The last move wins. Who wins?
Control positions are multiples of \(5\).
Multiples of \(5\) are losing. Since \(34\equiv4\pmod5\), the first player takes \(4\) stones and leaves \(30\). Then the first player complements the opponent’s move to \(5\).
The game is recognized by repeated move range.