# [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.

> _______________________________________________

> Retros mailing list

> 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)