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Jeff Ward's 'Magic Triangle'

Posted By: Albert Steg
Date: Thursday, 10 March 2016, at 9:28 p.m.

A long time ago I picked up a nifty mnemonic from Jeff Ward's book 'Winning is More Fun'. In Problem #49 (p.104) he looks at situations where you have a choice as to where to leave two checkers left in your home board. He draws a little triangle of the numerals 0 1 2 3 4 5 with 0 at bottom left and the number 1 2 3 ascending to the Apex (3) and then 4 5 descending on the other side. Reading top to bottom, left to right, you get the preference order of how far apart you should leave the checkers: 3-2-4-1-5-0 (with a 0 gap the checkers are on the same point, the least appealing option.

So, I was surprised today to see Mochy address the same topic in Slide 19 of his lecture "Bear Off Cube Action":

. . . where he gives the 'Magic Number' 31524(0) - - so, he has 1 and 5 preferable to 2 and 4. Neither of his examples force the question of which sequence is 'right' - - - and I guess now I'm wondering whether for some reason one is never faced with a choice between say 2 and 5 or 4 and 1? My head is starting to hurt.

In other words, can both sequences work equally well in practice -- or is Mochy maybe mistaken for this somehow? (I'm pretty sure Ward's sequence works properly).

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