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Five-point Mystery -- Solution

Posted By: Nack Ballard
Date: Thursday, 14 March 2019, at 12:03 a.m.

In Response To: Five-point Mystery (Nack Ballard)

		White is Player 2 score: 0 pip: 163 Unlimited Game Jacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=-b---BD-B---eE---b-db---B-:0:0:1:00:0:0:3:0:10
Each side played twice

From the standard opening position, each side (legally) moved twice, neither having played to the other's 5pt. How is this possible?

ANSWER

Congratulations to John O'Hagan for finding the unique solution!

As the final position is symmetrical, it makes no difference which color wins the opening roll. Let's assume Blue goes first:

		White is Player 2 score: 0 pip: 167 Unlimited Game Jacoby Beaver pip: 160 score: 0 Blue is Player 1
XGID=-b---AD-C---eE---cAe----A-:0:0:-1:61:0:0:3:0:10
Blue played 61W

With his opening 61, Blue played W (Wild, 24/18 6/5).

White replies with her own roll of 61, and...

		White is Player 2 score: 0 pip: 160 Unlimited Game Jacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-a---ADaC---eE---bae----AA:0:0:1:11:0:0:3:0:10
White played 61X

With her reply roll of 61, White played X (hit-and-split, 24/18 8/7*).

Blue rolls 11 now, and...

		White is Player 2 score: 0 pip: 167 Unlimited Game Jacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=aa---BD-B---eE---bae----B-:0:0:-1:11:0:0:3:0:10
Blue played 11Q

With his roll of 11, Blue played 11Q (Quarters, bar/24 8/7*/5).

White rolls her own 11 now, and similarly plays Q:

		White is Player 2 score: 0 pip: 163 Unlimited Game Jacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=-b---BD-B---eE---b-db---B-:0:0:1:00:0:0:3:0:10
Final Position (61W-61X-11Q-11Q)

Let's revisit the original conditions:

From the standard opening position, each side (legally) moved twice, neither having played to the other's 5pt. How is this possible?

If the clause in red typeface is omitted, there are five additional solutions (six altogether):

.....61W-61X-11Q-11Q (original solution)
.....61B-41X-11Q-11Q
.....41W-61X-11Q-11Q
.....41W-61X-11Q-31C
.....41B-41X-11Q-11Q
.....41B-41X-11Q-31C

(I do not count the six symmetrical sequences generated if White goes first instead of Blue.)

Nack

Messages In This Thread

• Five-point Mystery
  Nack Ballard -- Wednesday, 13 March 2019, at 10:00 a.m.
  • Five-point Mystery
    John O'Hagan -- Wednesday, 13 March 2019, at 7:10 p.m.
  • Five-point Mystery -- Solution
    Nack Ballard -- Thursday, 14 March 2019, at 12:03 a.m.
    • Five-point Mystery
      David Rockwell -- Thursday, 14 March 2019, at 2:08 a.m.
      • Five-point Mystery
        Nack Ballard -- Thursday, 14 March 2019, at 7:58 a.m.