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Twin PUZZLES: Prime versus Blot-prime -- SOLUTIONS

Posted By: Nack Ballard
Date: Thursday, 18 February 2016, at 4:13 p.m.

In Response To: Twin PUZZLES: Prime versus Blot-prime (Nack Ballard)

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 168 score: 0 Blue is Player 1
XGID=-b---BB-D---eE---c-cb---AA:0:0:1:00:0:0:3:0:10
32S-52H-F-65R-54R-F-65R-65H-F-32H-41-32K-5-41P-11E (perfectly played)

BLUE is on roll. Each side plays FOUR moves.

Noting the caption above, here is a recap of the puzzle goals stated in the original post:

Problem 1: Blue gets a FULL BLOT PRIME, and White a SEVEN-point PRIME.

Problem 2: Blue gets a SIX-point PRIME, and White a FULL BLOT PRIME (blots on fifteen consecutive points).

For each problem: What is the move sequence?

This puzzle pair is an improvement on the blot-prime sublime problem, which was to create a blot-prime for only one side, without a goal for the other player's position. Also, no additional restrictions are imposed here. (Hitting and duplicate rolls are permitted.)

Problem 1: Blue gets a FULL BLOT PRIME, and White a SEVEN-point PRIME.

Starting with the position diagrammed above, Blue rolls 33 and plays it as shown below.

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-b---BB-D-B-eC---c-cbAA---:0:0:-1:66:0:0:3:0:10

White to play 66

Blue rolled 33 and played bar/22 24/21 13/10(2).

White now has 66 to play

 White is Player 2 score: 0 pip: 141 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-----BBbD-B-cC---cbcbAA---:0:0:1:66:0:0:3:0:10

Blue to play 66

White rolled 66 and played 24/18(2) 13/7(2).

Blue now rolls his own 66.

 White is Player 2 score: 0 pip: 141 Unlimited GameJacoby Beaver pip: 132 score: 0 Blue is Player 1
XGID=--B--BBbB-B-cC-AAcbcb-----:0:0:-1:55:0:0:3:0:10

White to play 55

Blue rolled 66 and played 22/16 21/15 8/2(2).

White now rolls 55.

 White is Player 2 score: 0 pip: 121 Unlimited GameJacoby Beaver pip: 132 score: 0 Blue is Player 1
XGID=--B--BB-B-B-dC-AAcbcb-a---:0:0:1:22:0:0:3:0:10

Blue to play 22

White rolled 55 and played 18/13(2) 13/8 8/3. (With the fourth 3, it also works to play 13/8 or 6/1.)

Blue now rolls 22.

 White is Player 2 score: 0 pip: 121 Unlimited GameJacoby Beaver pip: 124 score: 0 Blue is Player 1

White to play 44

Blue rolled 22 and played 16/14 13/11 6/4 5/3.

White now rolls 44.

 White is Player 2 score: 0 pip: 105 Unlimited GameJacoby Beaver pip: 124 score: 0 Blue is Player 1

Blue to play 11

White rolled 44 and played 13/9(4).

Blue now rolls 11.

 White is Player 2 score: 0 pip: 105 Unlimited GameJacoby Beaver pip: 120 score: 0 Blue is Player 1

White to play 55

Blue rolled 11 and played 13/12 10/9 8/7 2/1, thereby achieving his full blot-prime.

Lastly, White rolls 55.

 White is Player 2 score: 0 pip: 85 Unlimited GameJacoby Beaver pip: 120 score: 0 Blue is Player 1
XGID=-AAAAAAAAAAAAAAAbbbbbbb-a-:0:0:1:00:0:0:3:0:10

Problem 1: FINAL Position

White rolled 55 and played 9/4(2) 8/3 6/1, thereby achieving her seven-point prime.

Problem 2: Blue gets a SIX-point PRIME, and White a FULL BLOT PRIME

The original position is repeated below.

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 168 score: 0 Blue is Player 1
XGID=-b---BB-D---eE---c-cb---AA:0:0:1:33:0:0:3:0:10

Blue to play 33

Blue again starts with a roll of 33, but he makes a different move.

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-b---BB-D---eE-A-c-cb-A---:0:0:-1:44:0:0:3:0:10

White to play 44

Blue rolled 33 and played bar/22 24/15.

White now rolls 44.

 White is Player 2 score: 0 pip: 149 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-b---BB-D---dE-Aab-baaAaa-:0:0:1:66:0:0:3:0:10

Blue to play 66

White rolled 44 and played 13/9 8/4 6/2 5/1.

Blue now rolls 66.

 White is Player 2 score: 0 pip: 149 Unlimited GameJacoby Beaver pip: 132 score: 0 Blue is Player 1
XGID=-b---BBDD---dA-Aab-baaAaa-:0:0:-1:22:0:0:3:0:10

White to play 22

Blue rolled 66 and played 13/7(4).

White now rolls 22

 White is Player 2 score: 0 pip: 141 Unlimited GameJacoby Beaver pip: 132 score: 0 Blue is Player 1
XGID=-a-a-BBDD---bAbAab-aabAaa-:0:0:1:22:0:0:3:0:10

Blue to play 22

White rolled 22 and played 24/22 13/11(2) 6/4.

Blue now rolls his own 22.

 White is Player 2 score: 0 pip: 144 Unlimited GameJacoby Beaver pip: 124 score: 0 Blue is Player 1
XGID=aa-BB--DD---bAbAab-aabAaa-:0:0:-1:55:0:0:3:0:10

White to play 55

Blue rolled 22 and played 6/4(2) 5/3*(2).

White now rolls 55.

 White is Player 2 score: 0 pip: 124 Unlimited GameJacoby Beaver pip: 124 score: 0 Blue is Player 1
XGID=---BB--DD-aabAbAab-aabAaa-:0:0:1:22:0:0:3:0:10

Blue to play 22

White rolled 55 and played bar/15 24/14.

Blue now rolls another 22.

 White is Player 2 score: 0 pip: 124 Unlimited GameJacoby Beaver pip: 116 score: 0 Blue is Player 1
XGID=---BBBBBB-aabAbAab-aabAaa-:0:0:-1:11:0:0:3:0:10

White to play 11

Blue rolled 22 and played 8/6(2) 7/5(2), thereby achieving his six-point prime.

Lastly, White rolls 11.

 White is Player 2 score: 0 pip: 120 Unlimited GameJacoby Beaver pip: 141 score: 0 Blue is Player 1
XGID=---BBBBBB-aaaaaaaaaaaaaaaC:0:0:1:00:0:0:3:0:10

Problem 2: FINAL Position

White rolled 11 and played 13/12* 11/10* 8/7 4/3*, thereby achieving her full blot-prime.

The roll order for the problem 2 solution "filmed" was 33-44-66-22-22-55-22-11. It is equally possible to replace the second- to sixth-roll order with 22-66-44-22-55 or 22-22-55-66-44, though the checker plays are the same.

For details on how puzzle solutions can be deduced, ask me specific questions, and/or read the analysis of the original blot-prime problem.

Nack

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