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Retrograde Backgammon Puzzle #2 Solution

Posted By: Taper_Mike
Date: Sunday, 8 November 2015, at 10:00 a.m.

In Response To: Retrograde Backgammon Puzzle #1 Solution (Taper_Mike)

Puzzle 2.

Find a perfectly played, 5-move sequence leading to this position. Blue is on roll. The cube is centered.





White is Player 2

score: 0
pip: 159
Unlimited Game
pip: 142
score: 0

Blue is Player 1
XGID=aB-B-aC-B---dD---d-e----B-:0:0:1:00:0:0:0:0:10
Blue on roll, cube action?

I found four different solutions for this one. In three of them, White opens 51S = 24/23, 13/8.

Next, Blue hits twice when he rolls 41. K (Kill) = 6/2*/1*.

The solutions diverge on third roll. One possibility is that White fans, leading to the position below.





White is Player 2

score: 0
pip: 164
Unlimited Game
pip: 162
score: 0

Blue is Player 1
XGID=bA----D-C---dE---d-e----B-:0:0:1:55:0:0:0:0:10
Blue to play 55

In these sequences where White opens 51S, the fourth roll is always the same. Blue rolls a devastating 55, and makes both his 1pt and 3pt. J (Jump) = 13/3, 8/3, 6/1.

The solution is complete, when White rolls either 65, 53, or 51, and enters a single checker on the 20pt.

We arrive at the same position when we allow White to enter a single checker on the third roll. If he enters on the 22pt, then he will be hit when Blue rolls 55. The fifth roll is as above.

If we let White come in on the 20pt on the third roll, then he must fan on the fifth.

Using Nactation, the three sequences are:

51S-41K-F-55J-5
51S-41K-3-55J-5
51S-41K-5-55J-F

A somewhat less obvious sequence has White opening with 52. On the second roll, Blue hits with 32N = 13/11, 6/3*. After a critical dance, it's all over for White, when Blue rolls 55.

52S-32N-F-55A-5

Mike

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