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Three-by-Five Problem 3, Solution

Posted By: Nack Ballard
Date: Thursday, 10 July 2014, at 12:53 p.m.

In Response To: Another three-by-five problem (Nack Ballard)

Three-by-five retro-problems

Problems 1 and 2
Solutions to Problem 1
Solutions to Problem 2

Problem 3
Solution to Problem 3: below





White is Player 2

score: 0
pip: 105
Unlimited Game
Jacoby Beaver
pip: 213
score: 0

Blue is Player 1
XGID=-----DB------C---eee---BD-:0:0:1:00:0:0:3:0:10

Reach this position in seven rolls.
The opening play is a standard one.


Of the three "three-by-five" retro-problems (see links at the beginning of the post), problem 3 (diagrammed above), which employs vacancy themes and a double-replacement theme, and which has the aesthetic touch of repeated six-checker pattern in the inner boards, is the best.

As rolls of 66 66 55 total 68 pips and White has moved only 62 pips. Blue's ownership of White's 2pt is a distraction to make the solver wonder if the fourth 6 of one of her double 6s is blocked, but actually, as in the first two problems, the way to slow White down by 6 pips is for Blue to hit on his own 6pt (after vacating it).

In problem 3, the additional trick is to find a way to get six Blue checkers (i.e., four more) sent back. To accomplish this, White hits on Blue's 12pt (after vacating it herself), on his 11pt, and twice on his 6pt.

I don't know how many people worked on this problem, but Stein was the only person to solve it.

Below is the unique solution, diagram by diagram. [If your widen your window (or use Ctrl- to zoom out), Blue's moves will be on the left and White's on the right.]





White is Player 2

score: 0
pip: 167
Unlimited Game
Jacoby Beaver
pip: 164
score: 0

Blue is Player 1
XGID=-b---AD-C--AeD---c-e----B-:0:0:1:00:0:0:3:0:10

Blue rolled 21 and played 13/11 6/5
White is Player 2

score: 0
pip: 143
Unlimited Game
Jacoby Beaver
pip: 164
score: 0

Blue is Player 1
XGID=-b---AD-C--AaD---cde----B-:0:0:1:00:0:0:3:0:10

White rolled 66 and played 13/7(4)
White is Player 2

score: 0
pip: 143
Unlimited Game
Jacoby Beaver
pip: 160
score: 0

Blue is Player 1
XGID=-b---DAAB--AaD---cde----B-:0:0:1:00:0:0:3:0:10

Blue rolled 11 and played 8/7 6/5(3)
White is Player 2

score: 0
pip: 123
Unlimited Game
Jacoby Beaver
pip: 193
score: 0

Blue is Player 1
XGID=-----DaAB--a-D---dde----BB:0:0:1:00:0:0:3:0:10

White rolled 55 and played 24/19* 24/14* 13/8
White is Player 2

score: 0
pip: 129
Unlimited Game
Jacoby Beaver
pip: 189
score: 0

Blue is Player 1
XGID=a----DA-B--aAC---dde----D-:0:0:1:00:0:0:3:0:10

Blue rolled 11 and played bar/24(2) 13/12 7/6*
White is Player 2

score: 0
pip: 105
Unlimited Game
Jacoby Beaver
pip: 221
score: 0

Blue is Player 1
XGID=-----D--B----C---eee----DB:0:0:1:00:0:0:3:0:10

White rolled 66 and played bar/19*/13*/7 14/8
White is Player 2

score: 0
pip: 105
Unlimited Game
Jacoby Beaver
pip: 213
score: 0

Blue is Player 1
XGID=-----DB------C---eee---BD-:0:0:1:00:0:0:3:0:10

Blue rolled 22 and played bar/23(2) 8/6(2)

The Nactation sequence is:

21$-66D-11N.-55s-11F-66B-22C

Initially, I noticed a twin solution with Blue's first two moves being 13/11 8/7 and 6/5(4). This is why I added the condition that the opening play (13/11 6/5) is a standard one. For puzzle-solvers who know only the rules of backgammon, the condition could instead be stated as follows: "The destination points for the two halves of the opening play are in different quadrants."

Nack

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