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## Thursday, December 12, 2013

### A > B > C > A

In time for the new year perhaps.…

You may be able to order a set of James Grime "nontransitive dice" (earlier sold out, but being re-supplied):

http://mathsgear.co.uk/collections/all-products/products/non-transitive-grime-dice

Nontransitive dice (also known as "Efron Dice" after one of the inventors) have probably regained some attention since being mentioned in Simon Singh's recent book, "The Simpsons and Their Mathematical Secrets." Several different nontransitive combinations are actually possible, but the set mentioned in Singh's book, include "Die A" with sides, 3,3,5,5,7,7, "Die B" with sides 2,2,4,4,9,9, and "Die C" composed of sides 1,1,6,6,8,8.  On average, a throw of Die A will beat (56% of the time) a throw of Die B, and a throw of Die B will beat (56% of the time) Die C… YET, Die C, on average, will beat out Die A (56% of the time)… How cool is THAT! or as, Singh writes, "Nontransitive relationships are absurd and defy common sense, which is probably why they fascinate mathematicians."

Wikipedia covers the subject here:

http://en.wikipedia.org/wiki/Nontransitive_dice

But of course James Grime is far more entertaining here:

http://singingbanana.com/dice/article.htm

Fans of the simple competitive game "Rock, paper, scissors," may recognize that it too operates on the basis of nontransitivity.

On a sidenote, the current post over at MathTango contains some puzzle fun, including my re-tell of an old favorite from Raymond Smullyan:

http://mathtango.blogspot.com/2013/12/puzzles-puzzles.html

AND finally, a reminder that Sunday will be the last day of the sparsely-entered :-( caption contest over at MathTango:

http://mathtango.blogspot.com/2013/11/caption-contest.html