CGT BQM1

   

blubb:

Is every game exactly reconstructable from the set of occuring board positions?

Problem

Consider two board positions A and B and a path of arbitrarily colored moves connecting them. Each position is allowed to occcur at most once, that is, the path, including start and end, has to comply with positional superko. Let's call the set of positions which are hit thereby the "footprint" of that path.

  1. Can two different paths between A and B have the same footprint, at all?
  2. If so, do they necessarily have the same move tally? In other words: Is it possible to calculate a path's move tally from its footprint alone?

Remarks

  • "board position" here does not refer to any particular board point but to the state of the game
  • "arbitrarily colored moves" implies that repeated moves by one color are allowed, like, W W B W B B B W B B ...
  • In a path, each position must be connected to the next one by a single move. That is, compared to its predecessor, a position has to contain exactly one more stone of one color and an unchanged or (in case of captures) smaller number of the other. Hence usually, most permutations of a legal path's footprint give an illegal path.
  • I am mainly interested in the case that the starting and ending positions are fixed, so all we have to care about is the order of intermediate positions. However, if someone finds a more general solution, I wouldn't be angry, either. :)

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(OC) 2007 the Authors, published under the OpenContent License V1.0.
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