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SMITH and JONES: Two puzzles -- SOLUTIONS

Posted By: Nack Ballard
Date: Thursday, 16 March 2017, at 8:16 p.m.

In Response To: SMITH and JONES: Two puzzles (Nack Ballard)

		White score: 0 pip: 166 Unlimited Game pip: 166 score: 0 Blue
XGID=aa-a-ADACA--bB--acada-A-AA:0:0:1:00:0:0:3:0:10
Puzzle Position

...Puzzle #1: From the opening position (first roll must be non-doublets), reach the above position in fewer than 26 rolls.

...Puzzle #2: From the above position, re-reach the opening position in fewer than 20 rolls.

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Puzzle #1: The shortest solution I found is seven rolls:

		White score: 0 pip: 151 Unlimited Game pip: 180 score: 0 Blue
XGID=-a---aD-C---cE--acAea---AA:0:0:1:33:0:0:2:0:10
Blue to play 33 61W-44g_33

Blue's opening roll was 61 and he played 24/18 6/5. In reply, White rolled 44 and played 24/20* 13/9 13/5. Now Blue rolls 33 and will play bar/22 13/7 8/5*.

		White score: 0 pip: 156 Unlimited Game pip: 168 score: 0 Blue
XGID=aa---ADAB---cD--acAea-A-A-:0:0:1:54:0:0:2:0:10
Blue to play 54 61W-44g_33g_F-54

After Blue played bar/22 13/7 8/5* from the previous diagram, White fanned, and now Blue rolls 54. He will play 13/9 13/8.

		White score: 0 pip: 156 Unlimited Game pip: 159 score: 0 Blue
XGID=aa---ADACA--cB--acAea-A-A-:0:0:-1:33:0:0:2:0:10
White to play 33 61W-44g_33g_F-54D-33

After Blue played 13/9 13/8 from the previous diagram, White rolls 33. He will play bar/22 13/7* 6/3*.

		White score: 0 pip: 144 Unlimited Game pip: 169 score: 0 Blue
XGID=-a-a-ADACA--bB--acada-a-AB:0:0:1:63:0:0:2:0:10
Blue to play 63 61W-44g_33g_F-54D-33G-3

After White played bar/22 13/7* 6/3* from the previous diagram, Blue rolls 63, thereby entering one checker with a 3 (hitting) and fanning with the other. The completion of this play produces the symmetrical puzzle position -- Smith's and Jones' FARE position, each player having one checker on the roof. (See the next diagram, which is the end position for Puzzle 1 and the starting position for Puzzle 2.)

In a very similar alternate solution, Blue's first two turns involve a transposition. Replace his 61W with 61&, and his 33c_ with 33g_, which means that for 6 of the pips, his initial 24/18 becomes 13/7, and his next turn's 13/7 becomes 24/18.

		White score: 0 pip: 166 Unlimited Game pip: 166 score: 0 Blue
XGID=aa-a-ADACA--bB--acada-A-AA:0:0:1:00:0:0:2:0:10
Puzzle position

Puzzle 2 (Re-reach the opening position): The shortest solution I found is eight rolls.

In this position, White (the far-side player) rolls 11. He will play bar/24 22/20* 7/6.

[In the original post, I suggested that Blue roll first in both (independent) puzzles, because Blue's and White's positions are exactly symmetrical and I wanted potential uniformity in presenting respondent's solutions. However, as nobody responded, I'm having White go first for Puzzle 2, so that if desired the solutions for both puzzles together can be played through as a continuous sequence.]

		White score: 0 pip: 162 Unlimited Game pip: 186 score: 0 Blue
XGID=-b---aDACA--bB--ac-ea-A-AB:0:0:1:11:0:0:2:0:10
Blue to play 11 11C_11

After White played bar/24 22/20* 7/6 from the previous diagram, Blue rolls 11. He will play bar/24 bar/23 7/6.

		White score: 0 pip: 162 Unlimited Game pip: 182 score: 0 Blue
XGID=-b---aE-CA--bB--ac-ea-AAB-:0:0:-1:43:0:0:2:0:10
White to play 43 11C_11c_43

After Blue played bar/24 bar/23 7/6 from the previous diagram, White rolls 43. He will play 20/16*/13.

		White score: 0 pip: 155 Unlimited Game pip: 198 score: 0 Blue
XGID=-b----E-C---cB--ac-ea-AABA:0:0:1:22:0:0:2:0:10
Blue to play 22 11C_11c_43R-22

After White played 20/16*/13 from the previous diagram, Blue rolls 22. He will play bar/23 22/20*/16*.

		White score: 0 pip: 191 Unlimited Game pip: 190 score: 0 Blue
XGID=bb----E-C---cB--Ac-e---BB-:0:0:-1:11:0:0:2:0:10
White to play 11 11C_11c_43R-22K-11

After Blue played bar/23 22/20*/16* from the previous diagram, White rolls 11. She will play bar/23(2).

		White score: 0 pip: 187 Unlimited Game pip: 187 score: 0 Blue
XGID=-bb---E-C---cC---c-e---BB-:0:0:-1:55:0:0:2:0:10
White to play 55 11C_11c_43R-22K-11@-21R-55

After White played bar/23(2) from the previous diagram, Blue rolled 21 and ran his blot to the midpoint with 16/13.

Curiously, we have reached a familiar-looking position. If, for both sides, we move a 6pt spare back to the midpoint, we have the opening position of Nackgammon!

White now rolls 55 and will play 23/13(2). After that, Blue will also roll 55 and play 23/13(2). I trust you can visualize that with these moves the opening position is restored.

Recap of Solutions:

Puzzle 1 (7 rolls): 61W-44g_33c_F-54D-33G-3
Puzzle 2 (8 rolls): 11C_11c_43R-22K-11@-21R-55R-55R

Nack

Messages In This Thread

• SMITH and JONES: Two puzzles
  Nack Ballard -- Tuesday, 14 March 2017, at 10:25 p.m.
  • SMITH and JONES: Two puzzles -- SOLUTIONS
    Nack Ballard -- Thursday, 16 March 2017, at 8:16 p.m.