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Jemimah plays Nackgammon ... not! - Solution

by Stein Kulseth

194








194

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0123456bar789101112
Harvey



vanilla
backgammon



Jemimah
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 re-enter. 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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