It's possible to solve this in one weighing if you're really lucky. Put 4 on the left side of the balance, and 4 on the right. If they balance, the remaining rectagle is the odd one.
So in one sense, the least number of weighings to find the odd rectangle is one. However that's not a very good solution - probably what was meant was, find the least number of weighings in which you can guarantee a solution. This, I agree, is three.
I already know the solution with 13 balls is 3 It is? I'm familiar with a 12-ball puzzle where you need 3 weighings; I don't see how to do it for 13 balls, unless you know in advance whether the odd ball is heavier or lighter. And if you know that, then you can actually handle 27 balls in 3 weighings. Why stop at 13?
Maybe there's something different about the 13-ball problem which I'm missing.
[ February 24, 2004: Message edited by: Jim Yingst ]