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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: 324150 (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":
http://www.slideshare.net/masayukimochizuki1/bearoffcubeaction
. . . 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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