> For N balls, the other balls can/should be binary searched.

Interesting assertion. Can you prove that? Can you give a provably minimal search pattern?

  > It's just a little tricky when it comes to the last two.

Another interesting assertion. It seems to me that the case of exactly two balls is trivial, once the solution is found.

Sorry, can't find the link, but it was a Topcoder problem at least 5 years ago.

Well, it is trivial with two balls, once you get it, but it's tricky with respect to "just binary search".