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| XGID=aB-Ba-C-A--BeC---c-e----B-:0:0:1:00:0:0:3:0:10 | |||||
Target Position | |||||
The inspiration for this puzzle came from Igor's reference position, shown above, which is a borderline (1.001) take/pass for White.
PART 1 of the puzzle is to reach the position (from the opening position) in EIGHT rolls that are perfectly played (according to XGR++ evaluation). As far as I know, the only perfect eight-move sequence is:
........62S-64H-21H-F-43P-F-55A-4
[The traditional notation is: 1) 62: 24/18 13/11, 64: 24/14*; 2) 21: bar/24 13/11*, 66: Fan; 3) 43: 18/11, 66: Fan; 4) 55: 8/3(2) 6/1*(2), 64: bar/21.]
Note that 43P (marked in blue) can be replaced by 52P. It's the same move (18/11) but with a different roll. If a different roll is considered to be a distinct element of an otherwise identical move, then there are two solutions to part 1. To be clear, I count one but won't quibble with someone who counts two.
As White's final roll can be 43 or 41 instead of 64 (fanning with a 3 or 1 instead of a 6), one might even argue that there are six solutions, but I believe that's going too far. Fans and partial fans are forced moves.
PART 2 of the puzzle is to reach the same position in FIVE rolls legally (no restriction on quality of play), and either side may end up on roll. Although there are many distinct solutions, finding even one is more difficult than it might appear, because (as is frequently the case with puzzles) some moves are weak backgammon-wise and/or counterintuitive.
Robert found what is probably the most straightforward solution.
It starts out with Blue rolling opening 53 and playing P (Point, 8/3 5/3), and in reply White rolls 21 and plays U (Up, 24/21), leading to this third-roll position:
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| XGID=-a-Ba-D-B---eE---c-e----B-:0:0:1:22:0:0:3:0:10 | |||||
After 53P-21U, Blue with 22 to play | |||||
Blue rolls 22 and plays N (Near, 13/11(2) 3/1*(2)). Blue has stronger moves, even within the same N family (13/11(2) 6/4*(2), and 13/9 6/4*(2)); however, the object is not to play well but rather to reach the target position!
After that, White fans, and Blue remakes the 3pt with 53. Mission accomplished.
A close cousin of Robert's solution is for Blue (with 22) to play the bizarre D (Down, 13/11(2) 8/6 3/1*), followed by using his 53 to cover both inside points, with I (Inside, 6/3 6/1).
By my count, there are 31 possible solutions for Part 2, or 40 if you count different rolls playing the same (unforced) move, all listed below. The nine doppelganger solutions are each marked with an asterisk.
Key: & = double slot (8/7 6/3), 4 = 4pt (8/4), o = outer (13/11 8/4),
..........J = Jump (8/5 8/3), P = Point (8/3 6/3). ......Nactation tutorial
The above is a Nactation key for Blue's first move of each sequence. For subsequent moves, you can consult the tutorial, though I doubt you'll need it. The rolls plus logic will probably suffice. Just keep in mind that White never hits Blue (or it cannot work) and remember your goal -- to reach the position diagrammed at the top of this post, also repeated below.
That said, if you get stuck on a sequence, just ask and I (or Mike or someone) will be glad to translate.
........31&-21u-33a-4-22N
........31&-31U-33a-4-22N
........31&-43U-33a-4-22N
........31&-53R-33a-42R-22N
........31&-54R-33a-41R-22N
........31&-63r-33a-41R-22N *
........314-31u-33A.-4-22N
........314-42V-33A.-4-22N
........314-42R-33A.-22R-22N
........314-51R-33A.-22R-22N *
........314-22V-33A.-22R-22N
........314-62U-33A.-22R-22N *
........314-22R-33A.-42R-22N
........314-62R-33A.-42R-22N *
........314-54R-33A.-41R-22N
........314-63r-33A.-41R-22N *
........314-64U-33A.-22R-22N
........42o-31u-33A.-4-42N
........42o-42V-33A.-4-42N
........53J-21u-22N-F-53I
........53J-21u-53I-F-22N
........53J-51R-53I-22R-22N
........53J-53R-53I-42R-22N
........53J-62r-53I-42R-22N *
........53J-63R-53I-41R-22N
........53J-64r-22N-4-53I
........53P-21U-22d-F-53I
........53P-21U-22N-F-53P (Robert's solution)
........53P-21U-53A-F-22N
........53P-31U-53K-4-22N
........53P-42R-53A-22R-22N
........53P-51R-53A-22R-22N *
........53P-43U-53A-F-22N
........53P-53R-53A-42R-22N
........53P-62R-53A-42R-22N *
........53P-54R-53A-41R-22N
........53P-63R-53A-41R-22N *
........53P-64R-22d-4-53I
........53P-64R-22N-4-53P
........53P-64U-53A-22R-22N
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| XGID=aB-Ba-C-A--BeC---c-e----B-:0:0:1:00:0:0:3:0:10 | |||||
Target Position | |||||