You have an ink stamp that is so amazingly precise that, when inked and pressed down on the plane, it makes every circle whose radius is an irrational number (centered at the center of the stamp) black.

Is it possible to use the stamp three times and make every point in the plane black?

If it is possible, where would you center the three stamps?

(In reply to re: Brian's solution by SilverKnight)

SK, Not that I'm agreeing with Larry but,

Brians ABC does work if x is chosen as transcendental - your example uses x=1. Where the three equidistant colinear points are centered is irrelevant, it is the distance between them that is labelled "x"

and

If you calculate the probability of choosing (0,1),(0,2) and (0,3) by choosing points from the entire plane at random, is this not zero (1/an infinite number of three point selections)?

Of course there are many sets of three points that will not work, so I am not happy with Larrys continuation either...

Posted by Cory Taylor on 2003-12-08 12:09:11