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Puzzle: can this position be reached?

Posted By: Nack Ballard
Date: Monday, 25 July 2011, at 7:42 a.m.

In Response To: Puzzle: can this position be reached? (Nack Ballard)

Money game, Blue on roll

PUZZLE: Is it possible to reach the above position with strongly played moves (or to prove that it is impossible)?

Indeed, it is possible. Below is a reconstructed game sequence that originates with the opening move. I'll walk you through it.

The first goal (more difficult to accomplish at a later stage, given best play restrictions) is to crack Blue’s board to resemble that of the target position (shown above). To this end, we’ll block Blue’s aces everywhere except on the low points, and in support of the cause, we’ll give White her 2pt.

Opening: 51S-41K-F-42P-1-62U-61H-F-65P

Blue has no more checkers in the zone than when he started; in fact he has one fewer. By moving all seven near-side checkers into his inner board, we can hasten its breakdown. What follows is the “setup” phase.

…51-52S-53P-42U-31L-53@-62@

Next comes the execution phase. In rolling four double aces in a row, poor Blue must weaken his board and kill a spare. In the process, White is able to get in a proper double (thanks to the improved placement of a recycled 6pt spare), just in time not to lose her market.

…41H-11I-32U-11I-65S-11I-C-66B-11P-21T

[The first 20 checker plays of my original game sequence were 64P-64P-52S-32K-1-61U-F-42@-52V-32K-5-42P-41@-11I-43T-11I-C-66B-11P-41D-51. However, I was uncertain of White’s cubing and of her 41D play (H might be better). To better ensure perfect play criteria, I recirculated a White checker, thereby adding 6 rolls to length of the game score.]

We need to halt Blue’s forward progress. How can we put a Blue checker on the roof (through proper play) without losing his goalkeeper on the 24pt? Here goes:

…51D-54D-32r-61H-F-64L-F

Next, White rolls 62 eight times in a row, bearing (in and) off the majority of her checkers:

…62J-F-62J-F-62J-F-62J-F-620-F-620-F-620-F-620-F

How do we get rid of White’s pesky 2pt? Her best play with 62 is NOT to bear off a checker on the 2pt. So, we assign her a roll of 21 instead, leading to

…21h-F-610-F-21i

Blue has too few back checkers, so we’ll send White back to fetch a couple more:

…31-61U-51H-51U

In the process of bringing White back around, we can sneak blots onto Blue’s 6pt and 5pt, like so:

…52H-32U-53H-43H-F-53H-F-640-42

This is the final combination:

…52K-51-32E-(63)

Below is the entire 70-roll sequence, starting with a White play and ending with a Blue play on each 10-roll line. (Red typeface identifies the last play made to reach each of the above diagrams.)

51S-41K-F-42P-1-62U-61H-F-65P-51-
52S-53P-42U-31L-53@-62@-41H-11I-32U-11I-
65S-11I-C-66B-11P-21T-51D-54D-32r-61H-F-
64L-F-62J-F-62J-F-62J-F-62J-F-
620-F-620-F-620-F-620-F-21h-F-
610-F-21i-31-61U-51H-51U-52H-32U-53H-
43H-F-53H-F-640-42-52K-51-32E-63

The end position (introduced here as a checker play problem) is shown in the first and last diagram of this post.

Nack

Messages In This Thread

• Puzzle: can this position be reached?
  Nack Ballard -- Friday, 22 July 2011, at 11:58 p.m.
  • Puzzle: can this position be reached?
    Nack Ballard -- Monday, 25 July 2011, at 7:42 a.m.
    • Bravo Nack! *NM*
      Casper van der Tak -- Monday, 25 July 2011, at 7:51 a.m.
    • Puzzle: can this position be reached?
      Turz -- Monday, 25 July 2011, at 8:46 a.m.
      • Puzzle: can this position be reached?
        Nack Ballard -- Monday, 25 July 2011, at 6:16 p.m.