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x + y Backgammon Puzzle -- Solution

Posted By: Nack Ballard
Date: Saturday, 4 September 2010, at 4:29 a.m.

In Response To: x + y Backgammon Puzzle -- Solution (pierrez)

The "extra features" (restrictions) you propose are:

  • all wins are bargammons
  • same Blue starting position for minimum and maximum pipcount difference
  • same sequence of dice for both sides in both configurations.

Given that you didn't state otherwise, though, I'm assuming that the primary goal is still to minimize x + y. In the solution you just posted, x + y = 18. Below is a min/max pip-diff. solution (that obeys your three extra features) where x + y = 16:

White wins a Bar-G in 5 + 4 = 9 rolls39


eX ' ' ' ' ' ' ' ' ' ' '

'eO '1O ' ' ' ' ' ' ' '

Blue wins a Bar-G in 4 + 3 = 7 rolls32
White wins a Bar-G in 5 + 4 = 9 rolls99


2X ' ' ' 'cX ' ' ' ' ' '

2OcO '1O ' ' ' ' ' ' ' '

Blue wins a Bar-G in 4 + 3 = 7 rolls30


The bar-gammoning sequences are the same in both diagrams (Blue's rolls are underlined):

Blue on roll: 22-22-22-22-22-22-22
White on roll: 44-11-66-11-66-11-66-11-66

If you would like to impose an additional restriction/feature that x + y can be any value, or that x + y is exactly 18, or that it must be x = 9 and y = 9, let me know which and I'll treat it as a new problem. :)

Nack

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