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(8): Brian's solution by Brian Wainscott)

Measure 0 doesn't mean non-existant.

You must prove that there are no white points (not that they are measure zero, i.e., countable).
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And of course this stuff is provable... that's one of the reasons why DJ submitted it in the first place... again... a COOL problem. (It just doesn't involve probabilities... :-)

Posted by SilverKnight on 2003-12-09 12:55:07