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Math genius vs an outstanding player

There is an similar discussion based on Arie Bialostocki's 1998 article:

http://www.cut-the-knot.org/proofs/PegsAndGroups.shtml

Arie points out that, according to the game brochure (Milton Bradley Co., 1986), whoever succeeds in leaving the last peg in the center is a genius. Anyone who leaves a single peg elsewhere is an outstanding player. Quite a cause to stop and wonder.

Alexander Bogomolny

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