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Sunday, May 10, 2009

Sunday May 10, 2009

Filed under: General,Geometry — m759 @ 6:29 PM
Mother’s Day
at MAA

Rick’s Tricky Six Puzzle:
S5 Sits Specially in S6
by Alex Fink and Richard Guy

Abstract. Rick Wilson identified a sliding block puzzle, the Tricky Six puzzle, in which a uniquely small fraction of the possible scrambled arrangements of the six moving pieces can be restored to the solved state. The permutations one can perform form the abstract group S5, the symmetric group on five letters, but surprisingly they aren’t any of the “obvious” copies of S5 in S6 that fix a single point and allow the other five to be permuted arbitrarily. This special S5 comes from the outer automorphism of S6, a remarkable group-theoretic map whose presence is felt in several combinatorial objects. We track down this outer automorphism in the Tricky Six puzzle as well as the projective plane of order 4, the Hoffman-Singleton graph, the Steiner system S(5,6,12), and a couple of error-correcting codes.

Meanwhile:

'Wizard of Id,' Mother's Day 2009-- Royal carriage with 'FINK ON BOARD' sign

Click to enlarge.

Background:

A pair of matronly women
gave readings of
bad mathematical poetry
on April 28 at

Carriage House Conference Center of the Mathematical Association of American in Washington, D.C

the MAA’s Carriage House
Conference Center in
Washington, D.C.

1 Comment

  1. happy mothers day

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    Comment by KatieStiller — Thursday, May 14, 2009 @ 2:39 AM

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