Sep 29, 2003
RAY: This week's puzzler is a prelude to next week's puzzler. You are going to learn a mechanism that I hope will help you solve next week's puzzler.
Here it is:
You have eight coins, all of which look, feel and smell identical. One of the coins is heavier than the other seven. You also have a balance scale, on which you can put coins on each side and compare their weights.
TOM: You could obviously do this with four or five weighings.
RAY: But, the question is, how can you take eight coins, and determine which is the bogus, heavier coin, with just two weighings?
RAY: Here's how you do it. You take the eight coins, and you make two piles of three and one pile of two. If the two piles of three balance, you put those aside because you know --
TOM: It's one of the other two coins!
RAY: Right. In the second weighing, you're going to put one coin in each side --
TOM: And it's going to tell you which one is heavier, immediately.
RAY: Right. Now, let's go back a step. If, in fact, the first time you put two piles of three on the scale, you get a result that shows that one side is heavier than the other, then you take those three heavier coins and put one on each side of the balance. If they are equal, then it's the coin that you didn't weigh, and if they're not then you know the answer.
TOM: Pretty darn nice.
RAY: So who's our winner, man?
TOM: The winner is Chanda, no last name given.