[Retros] a chess-related math puzzle

[Mark Tilford]

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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>  Retros at janko.at

>  http://www.pairlist.net/mailman/listinfo/retros

>


Hmm... Am I missing something:




WK at (0,0)
w_1 at (1,0)
b_1 at (2,0)
BK at (3,0)