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Retrograde backgammon puzzle

Posted By: benf
Date: Monday, 25 February 2013, at 12:56 a.m.

In Response To: Retrograde backgammon puzzle (Timothy Chow)

Cool puzzle.

Can the position below be reached in a legal game of backgammon? Yes

If so, can you deduce who's on roll? Blue must be on roll otherwise there would be a fourth checker in whites home board from blue being able to bring in two checkers on the last two rolls.

The sequence that makes this possible is below in both text and diagrams. From the starting position white is on roll:

(W)51: 5/off 5/4 (B)42: bar/21 bar/23

(W)41: bar/21 5/4* (B)43: bar/21 bar/22

(W)31: bar/24 24/21

Starting position:

		White is Player 2 score: 0 pip: 15 Unlimited Game Jacoby Beaver pip: 155 score: 0 Blue is Player 1
XGID=--AA----------------c----F:0:0:-1:51:0:0:3:0:10
White to play 51

eXtreme Gammon Version: 2.10.193.pre-release

Black rolls 42:

		White is Player 2 score: 0 pip: 9 Unlimited Game Jacoby Beaver pip: 155 score: 0 Blue is Player 1
XGID=--AA----------------aa---F:0:0:1:42:0:0:3:0:10
Blue to play 42

eXtreme Gammon Version: 2.10.193.pre-release

White rolls 41 playing bar/21 5/4*:

		White is Player 2 score: 0 pip: 30 Unlimited Game Jacoby Beaver pip: 149 score: 0 Blue is Player 1
XGID=a-AA----------------aA-A-D:0:0:-1:41:0:0:3:0:10
White to play 41

eXtreme Gammon Version: 2.10.193.pre-release

Black rolls 43:

		White is Player 2 score: 0 pip: 25 Unlimited Game Jacoby Beaver pip: 153 score: 0 Blue is Player 1
XGID=--AAa----------------a-A-E:0:0:1:43:0:0:3:0:10
Blue to play 43

eXtreme Gammon Version: 2.10.193.pre-release

White rolls 31:

		White is Player 2 score: 0 pip: 46 Unlimited Game Jacoby Beaver pip: 146 score: 0 Blue is Player 1
XGID=a-AAa----------------AAA-C:0:0:-1:31:0:0:3:0:10
White to play 31

eXtreme Gammon Version: 2.10.193.pre-release

Messages In This Thread

• Retrograde backgammon puzzle
  Timothy Chow -- Sunday, 24 February 2013, at 8:22 p.m.
  • Retrograde backgammon puzzle
    Smcrtorchs -- Sunday, 24 February 2013, at 11:20 p.m.
  • Retrograde backgammon puzzle
    benf -- Monday, 25 February 2013, at 12:56 a.m.
    • Retrograde backgammon puzzle
      Bob Koca -- Monday, 25 February 2013, at 5:27 p.m.
      • Retrograde backgammon puzzle
        6stones -- Monday, 25 February 2013, at 7:25 p.m.
        • Retrograde backgammon puzzle
          6stones -- Monday, 25 February 2013, at 10:29 p.m.
      • Retrograde backgammon puzzle
        Timothy Chow -- Tuesday, 26 February 2013, at 1:19 a.m.
        • Retrograde backgammon puzzle
          Matt Cohn-Geier -- Tuesday, 26 February 2013, at 4:41 a.m.
          • Retrograde backgammon puzzle
            Timothy Chow -- Tuesday, 26 February 2013, at 6:01 p.m.
            • Retrograde backgammon puzzle
              Bob Koca -- Tuesday, 26 February 2013, at 6:32 p.m.
    • Retrograde backgammon puzzle
      Timothy Chow -- Tuesday, 26 February 2013, at 1:10 a.m.
  • Retrograde backgammon puzzle
    playBunny -- Saturday, 2 March 2013, at 9:52 p.m.