This article originally appeared in the July 2000 issue of GammOnLine. Thank you to Kit Woolsey for his kind permission to reproduce it here.

## Solution to Jemimah Plays Nackgammon

By Stein Kulseth
 ``` ``` Starting Position ``` ``` Current Position

Minimal number of moves.
The difference between Jemimah's dice decreased by 1 each roll.
How did the game go?

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

It is clear that both players must also hit in their own boards on moves 3 or 4. If the hitting man from moves 2 or 3 is left on the 3,4 or 5 points it can not go backwards in the last move to form the double anchor, so it must be hit to reenter. If it is on the 2 point it will necessarily be hit as the last blot must be left there so that we may hit and tidy up on the last moves. (Actually, the 1 point is also a contender for placing the last blot, but I've checked that there are no variations where this work).

This means that moves 4 and 5 must be doubles. Then we can already deduce that Jemimah was player A moving first, and that her dice differed by 2, 1 and 0 respectively.

To be able to enter two blots and hit and blot on the 2-point the 4th roll must be 22, and this move must be either bar/23*(2) 6/2* or bar/23*(2) 6/4*/2, meaning that Jemimah entered in move 3 with a 2 or a 4. This means that her number that hit and left the blot on the 2-point must have been odd, so she cannot have moved from the 6- or 8-points. The only possibility is that she moved with a 5 from the 7-point, again meaning that she must have moved 13/7 in her first move.

Putting it all together the game played went:

 Jemimah Harvey 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

The following table shows all the other variations that go from backgammon to Nackgammon in 6 moves:

 Player 1, roll 1 Player 2, roll 1 Player 1, roll 2 Player 2, roll 2 Player 1, roll 3 Player 2, roll 3 a 63/54: 13/4 43: 24/21* 8/4 22: b/21* 6/4*/2 22: b/23*(2) 6/4*/2 11: b/23*(2) 51: b/24 13/8 b 63/54: 13/4 63: 24/21* 8/2 22: b/23*/21 6/4*/2 22: b/23*(2) 6/4*/2 11: b/23*(2) 51: b/24 13/8 c 63/54: 13/4 33: 24/21* 13/10 8/2 22: b/23*/21 6/4*/2 22: b/23*(2) 6/4*/2 11: b/23*(2) 21: b/24 10/8 d 65: 13/2 41: 24/23* 8/4 22: b/21* 6/2* 22: b/23*(2) 6/4*/2 11: b/23*(2) 51: b/24 13/8 e 65: 13/2 61: 24/23* 8/2 22: b/23*/21 6/2* 22: b/23*(2) 6/4*/2 11: b/23*(2) 51: b/24 13/8 f 65: 13/2 61: 24/23* 8/2 42: b/23* 6/2* 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 g 43: 13/10 8/4 63: 24/21* 8/2 22: b/23* 10/8 6/4*/2 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 h 43: 13/10 8/4 33: 24/21* 13/10 8/2 22: b/23* 10/8 6/4*/2 22: b/23*(2) 6/2* 11: b/23*(2) 21: b/24 10/8 i 63: 13/10 8/2 61: 24/23* 8/2 22: b/23* 10/8 6/2* 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 j 32: 13/10 6/4 43: 24/21* 8/4 22: b/21* 6/4*/2 22: b/23*(2) 6/4*/2 22: b/23*(2) 10/6 51: b/24 13/8 k 32: 13/10 6/4 63: 24/21* 8/2 22: b/23*/21 6/4*/2 22: b/23*(2) 6/4*/2 22: b/23*(2) 10/6 51: b/24 13/8 l 32: 13/10 6/4 33: 24/21* 13/10 8/2 22: b/23*/21 6/4*/2 22: b/23*(2) 6/4*/2 22: b/23*(2) 10/6 21: b/24 10/8 m 43: 13/10 6/2 41: 24/23* 8/4 22: b/21* 6/2* 22: b/23*(2) 6/4*/2 22: b/23*(2) 10/6 51: b/24 13/8 n 43: 13/10 6/2 61: 24/23* 8/2 22: b/23*/21 6/2* 22: b/23*(2) 6/4*/2 22: b/23*(2) 10/6 51: b/24 13/8 o 54: 13/8 6/2 61: 24/23* 8/2 62: b/23*  8/2* 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 p 54: 13/8 6/2 41: 24/23* 8/4 64: b/21*  8/2* 22: b/23*(2) 6/4*/2 11: b/23*(2) 51: b/24 13/8 q 54: 13/8 6/2 61: 24/23* 8/2 22: b/23*  8/2* 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 r 64: 13/7 6/2 61: 24/23* 8/2 52: b/23*  7/2* 22: b/23*(2) 6/2* 11: b/23*(2) 51: b/24 13/8 s 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