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{\bf Noam D. Elkies}
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{\bf New Directions in Enumerative Chess Problems}
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Normally a chess problem must have a unique solution, and is deemed
unsound even if there are alternatives that differ only in the order
in which the same moves are played. In an enumerative chess problem,
the set of moves in the solution is (usually) unique but the order is
not, and the task is to count the feasible permutations via an
isomorphic problem in enumerative combinatorics. Almost all
enumerative chess problems have been ``series-movers''$\!$, in which
one side plays an uninterrupted series of moves, unanswered except
possibly for one move by the opponent at the end. This can be
convenient for setting up enumeration problems, but we show that other
problem genres also lend themselves to composing enumerative problems.
Some of the resulting enumerations cannot be shown (or have not yet
been shown) in series-movers.
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