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Three on your 5 point puzzle (read before my replies to Nack's thread)

Posted By: Nack Ballard
Date: Monday, 21 June 2010, at 4:53 p.m.

In Response To: Three on your 5 point puzzle (read before my replies to Nack's thread) (Bob Koca)

From the start of a backgammon game there have been 3 rolls and each player now has at least three checkers on his own five point.

a) What is the minimum possible difference in pipcount?
b) What is the maximum possible difference in pipcount?

I wonder (as Stick does) what you mean by "3 rolls." My usual interpretation of that would be a total of 3 rolls or 1.5 full moves (e.g., Blue, White, Blue). But Stein seems to have interpreted that you mean 3 full "moves" (i.e., 3 rolls by each player, a total of 6 rolls), so I'll tackle that one too.

My answers:

(a) Minimum pipcount difference is zero (for either interpretation).
(b) Maximum pipcount difference: For 1.5 moves (3 rolls total), I got 35, and for 3 moves (6 rolls total) I got 121.

The 1.5 move max solution is unique. The 3-move max solution is unique except for a trivial difference in the first roll that immediately transposes.

Nack

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