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Different best play in seven positions

Posted By: Nack Ballard
Date: Wednesday, 14 November 2018, at 7:23 p.m.

In Response To: 32 from the bar -- Six problem VARIANTS (Nack Ballard)

As nobody has yet responded, I'm restructuring this post.

The position shown below is uniquely amazing. (It was originally posted by benf with two checkers on Blue's 11pt, but I have modified it.)

 White is Player 2 score: 0 pip: 101 Unlimited GameJacoby Beaver pip: ? score: 0 Blue is Player 1
XGID=--aBBBBbB----B-----bcb-bcA:1:-1:1:32:0:0:3:0:10

Put the two Blue checkers on a vacant point and play 32

There are thirteen Blue checkers on the board. Take the two checkers currently sitting in Blue's bearoff tray and put them on the board on any vacant point that is not in the opponent's outer board. There are six choices: The 22pt, 12pt, 11pt, 10pt, 9pt and 1pt.

A seventh position is created by (a) moving White's 5pt spare to one of the other occupied points in her board and (b) putting the two Blue checkers on one of the above six points. There is only one combination of "a" and "b" (which you need to guess/find) that will satisfy the condition set forth in the bold-face sentence below.

Blue has a 32 to play. His 3 is forced (bar/22). With the 2, he can move from one of his seven occupied points (except one of the 2s is blocked in the case of owning the 22pt, 9pt or 1pt). In other words, Blue has seven legal options with his deuce: 13/11, 8/6, 6/4, 5/3, 4/2*, 3/1, and from the floating point.

Every legal deuce is the best play for one and only one of each of the seven positions!

.....Position: 22pt, 12pt, 11pt, 10pt, 9pt, 1pt, a+b
.....Deuce: 13/11, 8/6, 6/4, 5/3, 4/2*, 3/1, from floating point.

Your objective is to match the position (on the first line above) with its best deuce (on the second line above).

If you don't consult XG, please feel free to reply with any or all of your seven guesses.

If you DO consult XG, you can privately marvel at the diverse deuces (and size of the margins) but please limit your public reply to reporting the correct combination of "a" and "b."

Good luck!

Nack

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