There are 10 balls which come in two possible weights. Using a balance scale at most 3 times, determine whether all the balls are the same weight or not.
Notes: I got this riddle from this Mathoverflow page of riddles. A few coworkers and I have tried to solve it; we can do 8 balls pretty easily, but even 9 doesn't seem possible.
Unfortunately the page doesn't contain the answer, the riddle doesn't exist anywhere else on the Internet, and the original author is no longer active. So, I don't know the answer.
[Edit] I've asked about the more general case on math.SE