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

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Starting Position

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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

Show game

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

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