Hi! I have a backgammon puzzle and am not sure how to go about solving it. You must go from A) standard starting board to B) Dack starting board layout in 6 moves (3 each player). We are told that the difference between player 1's dice decreases by one each turn. So player 1 could roll 5-3 (difference of two), and then 6-5 (difference of one), and then maybe 3-3 (difference of zero) for example. We also know rolls 4 and 5 are doubles and there is a rumor that also in roll 4, 2 checkers come back on the board. (I'm not sure if that's true)

I take it this means player 1's first roll has to be either:13,35,24,or 46;
second roll:12, 23, 34, 45, or 56, and third roll is a double that is probably double 1's? Is my logic flawed? The final roll 6 is also probably double 1's or 12? Is 16 or 26 an option? I'm not a very good player and have no idea how this is possible or how to go about figuring it out. I have seen a solution with 11 moves total but not 6. Can anyone help?

For anyone reading this post it's supposed to read Nackgammon, a variant of Backgammon by Nack Ballard. It is the same as the regular game, except that each player starts with two additional back checkers.

Setup: The setup is the same as in backgammon except that one checker from each player's six-point and mid-point are moved to the opponent's two-point. The players start with four back checkers rather than the usual two. bkgm.com/variants/Nackgammon.html

64: 13/7 6/2 .............41: 24/23* 8/4
54: b/21* 7/2*..........22: b/23*(2) 6/4*/2
11: b/23*(2)...............51: b/24 13/8