How about an extreme version of the sort problem.  Suppose x is a vector of
bits (such as they have in APL).  How do you sort x?

This would have been one way to solve the sorting small integers problem:
figure out how to sort 0-1 vectors and then work your way up from that.  I
once posed the 88 Hats
Problem<http://www.jsoftware.com/jwiki/Essays/88_Hats>to a very smart
and very persistent intern.  He solved it by generalizing a
solution to the 2 Hats problem.
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