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Puzzles
Is this position reachable?

Here's a puzzle I created while helping to design the 2013 MIT Mystery
Hunt. This puzzle ended up not being used but I thought some readers here
might enjoy it.
Can the position below be reached in a legal game of backgammon? If so, can
you deduce who's on roll?
12 11 10 9 8 7 6 5 4 3 2 1
++++++++++++++
   X X X  O's home
  X  
  X  
  X  
   
   
   
   O 
   O X X  X's home
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1


Benf writes:
Cool puzzle.
Can the position below be reached in a legal game of backgammon? Yes
If so, can you deduce who's on roll? X must be on roll otherwise there
would be a fourth checker in O's home board from X 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 O is on roll:
(O) 51: 5/off, 5/4 (X) 42: bar/21*, bar/23
(O) 41: bar/21, 5/4* (X) 43: bar/21*, bar/22
(O) 31: bar/24, 24/21
Starting position:
12 11 10 9 8 7 6 5 4 3 2 1
++++++++++++++
  X  O 
  X  O 
  X  O 
  X  
  X  
  X  
   
   
   X X 
++++++++++++++
13 14 15 16 17 18 19 20 21 22 23 24
(O) 51: 5/off, 5/4
13 14 15 16 17 18 19 20 21 22 23 24
++++++++++++++
  X  O O 
  X  
  X  
  X  
  X  
  X  
   
   
   X X 
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1
(X) 42: bar/21*, bar/23
12 11 10 9 8 7 6 5 4 3 2 1
++++++++++++++
   O X X 
  X  
  X  
  X  
  X  
   
  O  
   
   X X 
++++++++++++++
13 14 15 16 17 18 19 20 21 22 23 24
(O) 41: bar/21, 5/4*
13 14 15 16 17 18 19 20 21 22 23 24
++++++++++++++
  X  O X 
  X  
  X  
  X  
  X  
   
   
   
   O X X 
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1
(X) 43: bar/21*, bar/22
12 11 10 9 8 7 6 5 4 3 2 1
++++++++++++++
   X X X 
  X  
  X  
  X  
   
   
  O  
   
   O X X 
++++++++++++++
13 14 15 16 17 18 19 20 21 22 23 24
(O) 31: bar/24/21
13 14 15 16 17 18 19 20 21 22 23 24
++++++++++++++
   X X X 
  X  
  X  
  X  
   
   
   
   O 
   O X X 
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1




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