Dr. Steve Gadbois recently took a trip to Ireland to do a statistical analysis of the relative "number-of-leaves" vs. "luckiness" of clovers, and he chanced to take a picture of some authentic native leprechauns. Despite being a mathematician, he failed to take a count of exactly how many leprechauns were in the picture.
As he was biking back from Ireland (his DoD grant was running out), he accidentally dropped the picture, and it was cut into three pieces by the wheel spokes. Unfortunately, when he tried to put the pieces back together, he was not sure how.
Putting them together one way gave this image ...
While switching the top two pieces gave this image ...
Notice the difference? The top image has 14 little men, while the bottom image has 15 little men!
Where did the extra man come from or where did he go?!
Dr. Gadbois wondered what was going on! He analyzed the photo all the ways he knew how. He took averages, found standard deviations, did regressions, analyzed covariance. And, above all, he counted and recounted. All to no avail! Even Maple didn't help!!
Finally, he thought maybe mathematics wasn't enough. Maybe it was a problem of physics. Matter-antimatter annihilation? Destructive matter-wave interference? Quantum tunneling? Worm holes?