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(7): Brian's solution by SilverKnight)

I was thinking about this a bit this morning. While my comments about Larry's solution aren't rigorous, they can be made so. I CAN prove (and will if you want) that the set I called "white" in R^6 has measure 0.

DJ's problem is equivalent to proving there exists a "black" point in R^6.

It seems to me that this does address the problem, since all non-white points are black.

Posted by Brian Wainscott on 2003-12-09 12:36:11