A phenomenal mathematical riddle involving the axiom of choice

[Jrthedawg]

Have a look at this riddle. I've never seen anything quite like it, and I am a collector of math puzzles and brain teasers.

 

See if you can solve it without reading the solution (at the bottom of the link). I guess there is a slight hint given in the explanation, and that is that a solution involves the axiom of choice.

[imatfaal]

great puzzle - and a great discussion here

http://forums.xkcd.com/viewtopic.php?t=103672&p=3413662