# Is it possible to go from a Backgammon opening position to a Nackgammon opening position in 6 moves?

Is it possible to go from a Backgammon opening position (left picture) to a Nackgammon opening position (right picture) in 6 moves? And if not, how many turns would it take?

• This seems more like a puzzle question than an appropriate one for card and board games, which is more about rules questions and strategy. Jul 29, 2018 at 11:38
• @JKreft. Actually the question is on topic. The 'puzzles' tag fit perfectly: Questions that present some scenario, and asks you to provide a solution that satisfies some requirement. Apr 21 at 19:15

Yes, it is possible to do it in 6 moves.

This is a problem posted by Stein Kulseth in the year 2000. He also gives the solution and describes all the minimum-length games that produce Nackgammon's opening position.

It is fairly easy to see that 5 moves are not enough, but there are a number of 6-move solutions. In order to have 4 men sent back these must follow this general outline:

1. Player A leaves a forward blot
2. Player B hits from the 24-point and also leaves a forward blot
3. A hits B's forward blot when entering and again hits in his own board while leaving another forward blot on the 2 point
4. B hits A's forward blot when entering his 2 men and again hits in his own board while leaving yet another forward blot on the 2 point
5. A enters 2 men, hits and tidies up
6. B enters and tidies up
• This answer would be better if it answered the question. Can you do it in 6 moves?
– Zags
Apr 18 at 17:08

I don't have a lower bound on number of turns. However, 6 is not enough. (I'm assuming you meant 6 total turns, not 6 turns each.)

You can work backward just from the second player finishing their cleanup. Assuming WLOG that the second player is red.

Red's final move both have to be to 23 or 24 from Bar or 24, and can't take any white pieces. White's final moves both have to be to 1 or 2 from Bar or 1. So, in its first two moves, red has to take a minimum of two white pieces in the white home board while moving a piece from 13 to 2 and a piece from 6 into a takeable position. If done as part of the second move, that takeable position has to be 1 or 2.

Every combination I can find that allows red to do this in two moves leaves white unable to fulfill its similar conditions on turn 2.

• The other answer show a solution in 6 turns, so this answer is wrong. Apr 21 at 8:52