Solving the Game No. CrunchTM Leads to Word Length in Sn for n Even and n ≥ 6
The game No. CrunchTM was made by the company Binary ArtsŪ, but is no longer in production. It consists of 20 discs or tokens, numbered 1 through 20, which can move independently on an oval track. Part of the track includes a turntable which can be rotated so that arrangement of four adjacent discs is reversed. The goal is to arrange the numbered discs into a certain order. This talk will describe a systematic way to solve this game. This analysis will lead to a discussion of word length in the symmetric group S20 and more generally to word length in Sn for n even and n ≥ 6.
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