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(4): Brian's solution by Larry Settle)

I beg to differ Larry.

By your argument, if I have a stamp that covers the whole plane except the centered point, and I stamped it on the origin, I would cover the whole plane (--since the probability that a random point is the origin, definitely countable, would be zero).

But the probability is not at issue. The "point" is: there exists a point that is not covered. So, while I believe Brian has a correct ANSWER (I think)... Brian has not give a true SOLUTION.

Posted by SilverKnight on 2003-12-08 17:28:25