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Nov 5, 1996, 3:00:00 AM11/5/96

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Is it possible that at some point in a game of backgammon, at

the end of a player's move, that the board has returned to its

original starting configuration?

What is the shortest sequence of (legal) moves that could do this?

Nov 5, 1996, 3:00:00 AM11/5/96

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I constructed a game which accomplish your goal in 3 moves:

1) 62: 13/5 64: 13/7 24/20*

2) 43: 25/18* 21: 25/24 20/18

3) 32: 18/13 32: 18/13

I believe it isn't possible in fewer moves, but maybe I just didn't

see the way to build such an opening.

Alexander (acey_deucey on FIBS)

Nov 5, 1996, 3:00:00 AM11/5/96

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Don Banks (dba...@gpu4.srv.ualberta.ca) wrote:

: Is it possible that at some point in a game of backgammon, at

: the end of a player's move, that the board has returned to its

: original starting configuration?

: What is the shortest sequence of (legal) moves that could do this?

Here is what I came up with:

12 11 10 9 8 7 6 5 4 3 2 1

0 X X 0

0 X X 0

0 X X

0 X

0 X

X 0

X 0

X 0 0

X 0 0 X

X 0 0 X

13 14 15 16 17 18 19 20 21 22 23 24

1-3 X slots 5 and splits to 21.

4-1 0 hits blot on 24.

1-6 X enters, hits 0 blot on 24, moves 21-15.

5-5 0 enters, hits on 15 and hits on 24, hitting 3 X blots.

1-1 X enters, hits 0 blot on 24, splits on 23.

5-2 0 enters on 5, runs to 7.

3-2 X runs 23 to 18

5-4 0 runs from 7 to 16.

5-3 X runs to from 18 to 10, without hitting a 0 blot.

3-4 0 moves men back to 19.

3-1 X moves man back to 5.

Nov 5, 1996, 3:00:00 AM11/5/96

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In article <55mvct$a...@pulp.ucs.ualberta.ca>, dba...@gpu4.srv.ualberta.ca

(Don Banks) wrote:

< Is it possible that at some point in a game of backgammon, at

< the end of a player's move, that the board has returned to its

< original starting configuration?

<

< What is the shortest sequence of (legal) moves that could do this?

Here's a candidate game:

2-1: 6/3 2-1: 24/22* 6/5

6-5: b/20*/14 6-1: b/24 22/16

6-2: 14/6 6-4: 16/6

Thanks,

Peter Bell (USRobots)

Nov 5, 1996, 3:00:00 AM11/5/96

to

dba...@gpu4.srv.ualberta.ca (Don Banks) writes:

> Is it possible that at some point in a game of backgammon, at

> the end of a player's move, that the board has returned to its

> original starting configuration?

>

> What is the shortest sequence of (legal) moves that could do this?

Here is a way of doing it in five moves:

1) 41: 13/9 24/23 44: 24/16* 13/5

2) 31: bar/24 23/20* 11: bar/24 16/13

3) 52: 20/13

I conjecture it cannot be done in fewer moves than that.

It is easy to see that it takes at least four moves. Calling the

players X and O, let us assume X has the first move. Both sides, on

their first move, must move forward from the starting position, so

both sides need to get at least one checker hit in order to return to

the starting position. On his first move X has no blots to hit.

Hence, starting from O's first move, at least the following events

have to happen (in some order):

(A) O sends back one of X's checkers.

(B) X reenters.

(C) X sends back one of O's checkers.

(D) O reenters.

Assuming (A) happens first (otherwise we waste too much time), the

only two events that can happen in the same move are (B) and (C).

This means it will take at least three moves for all four events to

happen, bringing the total to four moves. So fewer than four is

definitely impossible.

If someone is going to come up with a four-move solution, they will

have to find a way of doing (B) and (C) in one move that also takes

X's checkers into the starting configuration. I claim this is

impossible, but I have not worked out a proof.

(Incidentally, it _can_ be done if we allow doubles for X's first

move, but that would of course be cheating, since it is the opening

move.)

-- Ole (hoegh on fibs)

Nov 5, 1996, 3:00:00 AM11/5/96

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Don Banks wrote:

>

> Is it possible that at some point in a game of backgammon, at

> the end of a player's move, that the board has returned to its

> original starting configuration?

>

> What is the shortest sequence of (legal) moves that could do this?

The best I could do is five rolls:

--- WHITE --- --- BLACK ---

31: 13/9 44: 24/16*, 13/5

32: bar/20* 31: bar/24, 16/13

43: 20/13

Tom

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