This one’s an old one, but a good one. Some of you may have seen it before.
You are given twelve cricket balls.
(For readers on the other side of the Pond, cricket is the finest of all sports, and you really don’t know what you’re missing. But let us not digress.)
You are given 12 cricket balls, which look identical, but one of them is a bit different from the other eleven. Although it looks like the other eleven, it doesn’t weigh the same. It could be lighter, or it could be heavier. You don’t know.
The other eleven balls all weigh the same as each other.
And you also have one of those old-fashioned scales. You can put as many balls as you like on either side of the scales, and you will know whether the two sides are equal in weight, or whether one side is heavier than the other. And that is all.
You are allowed to use these scales three times, and three times only. And from that, you must identify the ball that doesn’t weigh the same as the others. And you must be able to say whether it is heavier or lighter than the others.
Over to you. (Answer some time next week.)
(Hint: don’t start with weighing 6 balls on one side against 6 on the other: all that will tell you is that either one of the balls on the lighter side is light, or that one of the balls on the heavier side is heavy. And that doesn’t really get you too far.)