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x + y Backgammon Puzzle

Posted By: Nack Ballard
Date: Tuesday, 31 August 2010, at 5:44 a.m.

In a position that you construct: If Blue is on roll, he can win a backgammon (i.e., triple game) in x rolls. If White is on roll, he can win a backgammon in y rolls. (Sequence "Blue-White" counts as 2 rolls, not 1.)

Conditions: Blue never rolls larger than a deuce on either die. White never rolls smaller than a deuce on either die.

What is the minimum value of x + y?

Extra Credit: From the set of positions that satisfy that minimum value, what is (a) the minimum pipcount difference, and (b) the maximum pipcount difference?

Nack

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