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Three-roll puzzle (new)

Posted By: Daniel Murphy
Date: Sunday, 25 April 2010, at 10:00 p.m.

In Response To: Three-roll puzzle (new) (Bob Koca)

White's position could also be obtained losing 3 pips by having two checkers hit on 23 and 24.

I thought of that, Bob, and my "therefore" assumed there's no solution to the problem from that position -- that's why I wrote "the only way for one checker to lose 3 pips..." If the solution includes one checker losing 3 pips (it does) then one of the plays must include bar/22.

White can reach the final position having been hit twice:

Blue 4-4 13/9(4) ... White 1-1 24/23 13/12*(3)
Blue 4-4 bar/21 9/1* 6/2* ... White 1-1 bar/24*(2) 13/12(2)
Blue 4-4 bar/21 9/5(3) ... White 6-6 24/12(2)

But then Blue trails in the pip count 134-155. Blue can't roll 6-6 or 5-5 the first roll and still enter, hit on 24 and hit on 23 on the second roll. And 4-4 is the best he can do on the second and third rolls, being on the bar.

From the original position White needs exactly 29 pips and exactly 9 crossovers with 3 doublets. He can lose 3 crossovers by playing 24/22 and being hit once, or 24/23 and being hit in twice, but only the first play leads to a solution.

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