1) You have Nine balls, identical except one weights slightly
more than the other. You have a cheap balance scale that you can
use only twice. (Balance scale meaning that you can weight one
side against the other) Find the heavy ball.
2) This one is similar but a quite a bit harder. You have Twelve gems that are almost identical. You know only that one of these gems does not weight the same as the other, not heavier or lighter, just different. You have a scale similar to the one in problem one, except that you can use it three times. Find the different gem.