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Blotfest puzzle

Posted By: Timothy Chow
Date: Saturday, 29 August 2009, at 5:40 p.m.

At Bob Koca's suggestion, I am posting a backgammon puzzle that I came up with a few months ago.

Alice was playing backgammon. She was not on the bar. She rolled the dice and discovered that, no matter how she played the roll, she would end up with 13 blots. What was the position and the roll?

Remark: I used the word "the" but actually the solution is not unique. For extra credit: Can 13 be increased to 14 or even 15? I don't think so, but I don't have a proof.

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