A Sticky Problem

Dr. John Henry Steelman
Mathematics Department

The following problem appeared in the June-July issue of the American Mathematical Monthly.

A game starts with one stick of length 1 and four sticks of length 4.  The two players move alternately.  A move consists of breaking a stick of length at least 2 into two sticks of shorter integer lengths or removing n sticks of length n for some n in {1,2,3,4}.  The player who makes the last move wins.  Which player can force a win and how?
The talk will discuss how standard problem-solving techniques can be used to attack this question.  The intended audience comprises students who have had some introduction to proof.  The solution that will be developed involves the concepts of induction and basic modular arithmetic.

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