Forum Archive :
Puzzles
Replace the missing checkers
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In case I ever get in trouble for posting off-topics articles to
r.g.b., I could steal somebody else's puzzle and tack it on the
end of my post. This one is by Bob Koca (what happened to him,
anyway? I haven't heard from him in months) from the August '96
GAMES magazine:
+13-14-15-16-17-18-------19-20-21-22-23-24-+
| X O X | | X X X X X |
| | | |
| | X | |
| | | |
X | | | |
v| |BAR| |
X | | | |
| | | | OOO
| | | | OOO
| | | O | OOO
| X X X X X | | O | OOO
+12-11-10--9--8--7--------6--5--4--3--2--1-+
O (moving anticlockwise) has borne off 12 chequers. Two X's have been
removed from the game, either from the playing field, the bar, or the
bear-off tray. Where must these two pieces go in order to create the
only possible position that could have resulted from legal moves?
(Answer to be posted in a few days if nobody gets it.)
Cheers,
Gary.
--
Gary Wong, Department of Computer Science, University of Arizona
gary@cs.arizona.edu http://www.cs.arizona.edu/~gary/
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Gary Wong writes:
Congratulations to Matt Reklaitis, for correctly deducing the answer to
Bob's puzzle:
Best I came up with is that they must be on the 10 and 11 points, O just
having rolled a 6-1, with no legal 6 to play used the 1 to hit X on 16.
The prize for the second question ("Where is Bob"?) is split between Matt
and Chuck :-)
Hope you enjoyed the puzzle! (It was too hard for me, I had to give up and
peek at the answers.)
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Puzzles
- 13 blots (Timothy Chow+, Aug 2009)
Alice, who is not on the bar, discovers that however she plays she ends up with 13 blots. What is her position and roll?
- All-time best roll (Kit Woolsey+, Dec 1997)
What position and roll give the greatest gain in equity?
- All-time worst roll (Tim Chow+, Feb 2009)
Find a position that goes from White being too good to double to Black being too good to double.
- All-time worst roll (Michael J. Zehr, Jan 1998)
What position and roll give the greatest loss in equity?
- Back to Nack (Zorba+, Oct 2005)
How can you go from the backgammon starting position to Nackgammon?
- Cube ownership determines correct play (Kit Woolsey, Jan 1995)
Find a position and roll where the correct play depends on who owns the cube.
- Highest possible gammon rate (Robert-Jan Veldhuizen+, May 2004)
What is the highest possible gammon rate in an undecided game?
- Infinite loops (Timothy Chow, Mar 2013)
- Is this position reachable? (Timothy Chow+, Feb 2013)
- Janowski Paradox (Robert-Jan Veldhuizen+, Nov 2000)
Position that's a redouble but not a double?
- Least shots on a blot within direct range (Raymond Kershaw, Dec 1998)
Find a position with no men on bar that has the least number of shots out of 36 to hit a blot within direct range.
- Legal but not likely (David desJardins, July 2000)
Find a position that can be legally reached but never through optimum play.
- Lowest probability of winning (masque de Z+, Apr 2012)
What is the smallest win probability in backgammon, greater than zero.
- Mirror puzzle (Nack Ballard, Apr 2010)
Go from the starting position to the mirror position (colors reversed)
- Most checkers on the bar (Tommy K., May 1997)
What is the maximum total possible checkers on the bar?
- Most possible plays (Kees van den Doel+, May 2002)
Find the position and dice roll which have the most possible plays.
- Not-so-greedy bearoff (Kit Woolsey, Mar 1997)
Find a no-contact position where it is better to move a checker than bear one off.
- Not-so-greedy bearoff (Walter Trice, Dec 1994)
Find a no-contact position where it is better to move a checker than bear one off.
- Priming puzzle (Gregg Cattanach+, May 2005)
From the starting position, form a full 6-prime in three rolls.
- Pruce's paradox (Alan Pruce+, Dec 2012)
- Quiz (Martin Krainer, Oct 2003)
- Replace the missing checkers (Gary Wong+, Oct 1998)
- Returning to the start (Nack Ballard, May 2010)
What is the least number of rolls that can return a game to the starting position?
- Returning to the start (Tom Keith+, Nov 1996)
What is the least number of rolls that can return a game to the starting position?
- Shortest game (Stephen Turner+, Jan 1996)
What is the shortest (cubeless) game in which both players play reasonably?
- Small chance of ending in doubles (Walter Trice, Dec 1999)
Find a position where the probability of the game ending in doubles is less than 1/6.
- Three-cube position (Timothy Chow+, Sept 2011)
Find a position and roll for which three different checker plays are best, depending on the location of the cube.
- Trivia question (Walter Trice, Dec 1998)
What is the symmetric bearoff with the smallest pip count that is not an initial double?
- Worst possible checker play (Gregg Cattanach+, June 2004)
What position and roll have the largest difference between best and worst play?
- Worst possible opening move (Gregg Cattanach, June 2004)
What is the worst possible first move given any choice of dice?
- Worst symmetric bearoff of 8 checkers (Gregg Cattanach+, Jan 2004)
What symmetric arrangement of 8 checkers in each player's home board gives roller least chance to win?
- Worst takable position (Christopher Yep, Jan 1994)
What position has lowest chance of winning but is a correct take if doubled?
- Zero equity positions (Kit Woolsey, Apr 1995)
Find a position with exactly zero equity in (1) money play or (2) cubeless.
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