Forum Archive :
Puzzles
Replace the missing checkers

In case I ever get in trouble for posting offtopics 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:
+131415161718192021222324+
 X O X   X X X X X 
   
  X  
   
X    
v BAR 
X    
    OOO
    OOO
   O  OOO
 X X X X X   O  OOO
+121110987654321+
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
bearoff 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/


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 61, 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.)




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?
 Alltime best roll (Kit Woolsey+, Dec 1997)
What position and roll give the greatest gain in equity?
 Alltime 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.
 Alltime 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 (RobertJan 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 (RobertJan 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.
 Notsogreedy bearoff (Kit Woolsey, Mar 1997)
Find a nocontact position where it is better to move a checker than bear one off.
 Notsogreedy bearoff (Walter Trice, Dec 1994)
Find a nocontact 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 6prime 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.
 Threecube 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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