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BGonline.org Forums
"An impuzzle"
Posted By: 6stones In Response To: "An uncommon position" (6stones)
Date: Monday, 26 October 2009, at 10:14 p.m.
Yes, this concocted position is impossible, it could not have resulted
from a legal move (, according to the standard rules of backgammon). How
could the white checker have been hit if blue is on bar, no matter how
many turns she dances? Obviously, if there were a blue blot on white's
ace point, then it would have been possible (after hitting the white
checker on entering from bar with another). Similarly with a white blot
on either of blue's open points.
Another impossible position would be the case when both are on bar and
the both boards are closed.
Any others? How about in other variants of backgammon?
The question of impossible positions (ie. those that could not have
resulted from a legal move) has a bearing on solving backgammon: if we
were to find the optimal continuation in every possible configuration of
checkers (plus cube position and match score), how big would be the class
of those positions that are actually impossible and could thus be ruled
out? Probably marginal, and I am not suggesting that it would
make the daunting task much easier, but it would be interesting to know,
whether there are any other types of such positions. Or maybe there simply aren't any...
Thank you Mr. Koca, a very good puzzle (how can I have missed those puzzles at Galore?)
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