[Retros] a chess-related math puzzle
Mark Tilford
ralphmerridew at gmail.com
Sun Mar 23 23:13:50 EDT 2008
On Sun, Mar 23, 2008 at 10:04 PM, andrew buchanan <andrew at anselan.com> wrote:
> Hi,
>
> 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.
>
> Best,
> Andy.
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Hmm... Am I missing something:
WK at (0,0)
w_1 at (1,0)
b_1 at (2,0)
BK at (3,0)
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