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"Distinct Move" rule
Posted By: Nack Ballard
Date: Thursday, 12 November 2015, at 4:13 a.m.
In Response To: Two Puzzles (Taper_Mike)
An identical play with an alternate roll is not considered different (e.g., 13/7* with 42 is the same as 13/7* with 51).
If this rule is omitted, I find three solutions for the first puzzle. For the second, however, only one.
You are correct, and it is clear that you solved both puzzles.
If there is not some rule of this type, the number of solutions are, for practical purposes, exaggerated. For example, for your recent Puzzle 2, we ultimately concluded that there are four (similar) solutions:
.....51S41KF55J5
.....51S41K355J5
.....51S41K555JF
.....51S41K5355JFOn the final roll, a "5" can be any of three different rolls (65 53 51), or a "F" (Fan) can be any of six different rolls (63 61 31 66 33 11). If each roll is counted separately, the total number of solutions is 18.
One could have a rule that applies just to fans and partial fans, but I think it's even better to apply it universally: to count ANY distinct move as one play, regardless of how many different rolls achieve it.
If this distinction is regarded as an automatic rule, it means that bar/20 is the same move, regardless of whether the roll is 32 or 41, and therefore your Puzzle 3 has a unique 7move solution  congratulations!
Nack

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