Puzzles

Forum Archive : Puzzles

 Returning to the start

 From: Nack Ballard Address: nack2000@sbcglobal.net Date: 3 May 2010 Subject: Re-reaching the starting position -- Solutions Forum: BGonline.org Forums

```What are the fewest number of rolls to re-reach the starting position?

The answer to the above question is five (or four if doubles are allowed on
the first roll). However, to make it easier in one way but more difficult
in another, I divided the problem into three parts:  In each case, you are
to find the start-position-repeat sequences that meet the conditions below.

(a) Six rolls, if played well throughout.

(b) Five rolls, if all but one roll are played well.

(c) Four rolls, if doubles now legal on first roll.

----------

Part (a): Six rolls are played well throughout. My solution is

6-2: 24/18, 13/11         4-1: 24/20, 8/7*
4-3: bar/18*              6-1: bar/24, 20/14*
5-1: bar/24, 18/13        5-1: 14/8

The second and sixth plays are errors of only .003 and .013 according to
Snowie evals, or .005 (full) and .019 (trunc) according to rollouts. The
fifth play is almost exactly tied. The other plays -- first, third and
fourth -- are clearly best. (The 4-3, which hits bar/18*, can just as well
be 5-2 or 6-1.)

Here is the six-roll sequence in full diagram illustration:

----------

Part (b): Five rolls, one big error allowed. My solution is

6-1: 24/18, 8/7           6-2: 24/18*, 13/11
4-1: bar/24, 18/14*       5-1: bar/24, 18/13
5-1: 14/8

My allowed big error is on the first play. The other plays are played
"well." According to Snowie eval, the second play is -.002 and the fifth is
-.013.

----------

Part (c): Four rolls, with doubles legal on first roll. I found only one
solution.

4-4: 24/16, 13/5          2-2: 24/20*/18, 13/11
1-1: bar/24, 16/14*/13    5-1: bar/24, 18/13
```

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