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| XGID=-b----E-C---eE---c-e----B-:0:0:1:00:0:0:3:0:10 | |||||
Opening position | |||||
Super-congrats to TarHeelFan and Mike, for their solutions of 17 rolls (the minimum)!
And gratitude to Stick, for inspiring them.
From the opening position, there are 34 crossovers to the bearoff tray (two times 4 from the 24pt, five times 3 from the 13pt, three times 2 from the 8pt, and five from the 6pt).
Let's say Blue goes first. He can gain 2 crossovers on the opening roll, and 4 crossovers for each turn after (32 crossovers in 8 rolls). Thus, he can possibly bear off in 9 turns.
White, going second, can roll doublets every turn, and needs only 32 crossovers, as she does not need to bear off her last two checkers (the conditions stated that the loser may have only 13 checkers off). She therefore needs only 8 turns to achieve her part.
In short, Blue goes first and the game can last just 9 + 8 = 17 rolls (in theory, and in practice as it turns out).
Each side starts with 167 pips. Clearly, this is not divisible by 4. The slack is taken up by the opening non-doublet in Blue's case, or by the pips from the two checkers not yet borne off in White's case. The doublets + non-doublet combination must be
.....(a) 156 + 11, or
.....(b) 160 + 7, or
.....(c) 164 + 3.
Any of "a," "b" and "c" seems possible in theory. Now, practically speaking...
(1) Which (one or more) of these (a, b, c) allow bearing off in 9 turns for one side (with opponent's checkers conveniently off the board)?
(2) Are any of these possible when tried one-sided but impossible when interactive with opponent?
If you already solved the puzzle in 17 rolls, please share your solution or solutions (or at least a list of the rolls therein). In a couple of days, I will provide an overview, including any responses/opinions that I get for "1" and "2."
If you have not yet solved the puzzle, feel free to use the explanation in this post as assistance. If you need further help, you can read TarHeelFan's, Mike's and/or any others' forthcoming solutions, before finding your own variant. There is scope for creativity.
Nack