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: Solution by Cory Taylor)

As a result of what Cory Taylor has said, it seems Brian Smith's proof (excellent, by the way) needs only add the constraint that not only must x be irrational, but also x². There are still many, many, such sets of points that can be found.

Posted by Charlie on 2003-12-03 14:32:02