[Retros] a chess-related math puzzle

andrew buchanan andrew at anselan.com
Sun Mar 23 22:04:44 EDT 2008


Inspired by Bernd's recent matrix, here is a little
math puzzle which I hope is chessish enough to be
interesting here. (And no DR unlike this morning heh.)

Suppose that W & B (the kings) are distinct points in
the plane, and we can choose the location of other
distinct points w_1,...,w_k, (white points) &
b_1,...,b_l (black points).

Say a white point w_i is *pinned* if there exists j
such that w_i lies on the line segment between b_j &
W. Similarly define pinning for the black points b_j.

Can there exist a non-empty set of white & black
points all of which are pinned? If yes show one, if
not prove it.


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