Putnam US BrainTeaser Invariant

Difficult

1995

Problem - 2804

$\textbf{Heaps of Beans}$

A game starts with four heaps of beans, containing $3$, $4$, $5$ and $6$ beans, respectively. The two players move alternately. A move consists of taking either one bean from a heap, provided at least two beans are left behind in that heap, or a complete heap of two or three beans. The player who takes the last bean wins. Does the first or second player have a winning strategy?

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