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| XGID=-b----F-D---aD---cbcbb--A-:0:0:1:00:0:0:3:0:10 | |||||
Each side played twice | |||||
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| XGID=-b----E-E---aD---cbcbb--A-:0:0:1:00:0:0:3:0:10 | |||||
Each side played twice | |||||
For each of the above two problems:
From the standard opening position, each side (legally) moved twice. How is this possible?
Congratulations to Kevin McDonough, Brian Lonergan, Roberto Litzenberger, Pat Fusco, Casper, and Bulent Bahar, for solving problem #1, and to Kevin McDonough, Brian Lonergan, Roberto Litzenberger, Pat Fusco and Casper, for solving problem #2 of the Five-prime Mystery!
Here is the sequence for Problem #1:
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| XGID=-b----F-B---cEb--c-c-b-AA-:0:0:1:55:0:0:3:0:10 | |||||
Problem #1: Halfway position | |||||
Technically, there are three (similar) solutions for problem #1. In the above diagram, Blue played 21C (Cross, 24/23, 8/6), which no respondent chose. Most found instead the mainstream opening play 21S (Split, 24/23 13/11) and there was no reason to look for the diagrammed alternative above. Please verify for yourself, though, that after Blue's next roll, he will converge on the target position.
(There is even a third way to play 21 that works, which I'll reveal later.)
In response to Blue's 21 play, White played 22N (Near, 13/11(2) 6/4(2)), a strong and familiar move.
Next, Blue rolls 55 and plays B (Both up and down), running one checker from 23pt to 13pt, and bringing two down from 13pt to 8pt. Then White makes a five-point prime with a roll of 66, reaching the target/final position diagrammed below.
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| XGID=-b----F-D---aD---cbcbb--A-:0:0:1:00:0:0:3:0:10 | |||||
Problem #1: Final position | |||||
I assume most readers were already aware that the player rolling second in backgammon can make a five-point prime with 22 followed by 66 (and those are the only two rolls that work). However, I also figured that many readers would NOT have been previously aware that one can make the same prime by rolling 66 first and then 22, because it is necessary to "misplay" 66 in order to make it work.
That brings us to Problem #2:
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| XGID=-b----E-C---aEA--cde----A-:0:0:1:65:0:0:3:0:10 | |||||
Problem #2: Halfway position | |||||
In problem #1, Blue needed 23 pips, and is able to reach his target position with rolls of 21 and 55. In essence, he had an extra 8/6 to play.
In problem #2, Blue needs only 21 pips (i.e., 24/8 and 13/8). If we could give Blue a roll of 01 (zero, one) played 24/23, followed by 55, we could solve as we did in problem #1. But it is not possible to roll 01.
How else can we divide up 21 pips? One way is a 5-pip roll (played 13/8) followed by 44. However, that doesn't work because White's midpoint blocks Blue's 24/8. The other way to divide up 21 pips is 54 plus 33. However, if Blue starts with 24/20 13/8, White's 17pt blocks 20/8.
The 21-pip combo that uniquely works for Blue is 64 + 65.
If Blue starts with 65R (24/13), then he can't play 13/8(2) with 64, even though it's the right number of pips. Starting instead with 65S (24/18 13/8) looks promising, but the hitch is that after White's 22N (13/11(2) 6/4(2)), Blue's intended follow-up of 18/8 is inconveniently blocked by White's 11pt and 13pt.
Contrary to what one might suspect is coming next, the solution involves Blue running first with 64R (24/14). This is where White reveals the alternate way of making her five-prime, which involves rolling 66 first and playing four checkers down. See diagram above.
From here, I trust you can visualize the rest: Blue rolls 65 and plays T (sTack/Tower, 14/8 13/8); then White rolls 22 and plays A (Attack, 7/5(2) 6/4(2)), thereby reaching the final position (below).
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| XGID=-b----E-E---aD---cbcbb--A-:0:0:1:00:0:0:3:0:10 | |||||
Problem #2: Final position | |||||
Going back to problem #1, the third solution (submitted by Kevin and Casper) is for Blue to open with 21U (Up, 24/21), White plays 66D (13/7(4)), Blue plays 55G (1:2:1 Glasses, 21/6 13/8), and White finishes with 22A. Note that in the other two problem #1 solutions, White had to start with 22 (as 66 would block the 23pt checker), but in the third solution she must start with 66 (because 22N would point on Blue, who started with 21A).
Nack