Puzzle 2.
Find a perfectly played, 5-move sequence leading to this position. Blue is on roll. The cube is centered.
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| 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.
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| 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