Week of 11-10-98:

A farmer has a rock that weighs exactly 40 lbs. He uses it on a balance scale to weigh grain. I guess he sells it in 40 lb amounts, or something.  Anyway, one day his neighbor borrows his rock.  He returns the next day, very sorry, and tells the farmer that he accidentally dropped the rock and it broke into 4 pieces. But the farmer tells him that he's actually done him a favor! The farmer says that he can now weigh any weight from 1 to 40 lbs in 1 lb increments.

Your mission:  what is the weight of each of these 4 pieces, and how does he use them?

Good Luck.

The answer to this question is amazing. You probably guessed that you'd need a one pound rock. That let's you weigh one pound of grain. If you also have a three pound rock, then you can weigh 2, 3, and 4 pounds, too. You have 4 pounds of rock used up now, and you want to be able to do 5. What can you take 4 pounds away from to get 5? 9 pounds, of course. Now you can weigh 5, 6, 7, 8, 9, 10, 11, 12, and 13 pounds of grain. You only have one piece left to make now, which is of course 27 pounds. Notice anything about those rocks? 1, 3, 9, and 27 pounds? They're all powers of three! Pretty cool, huh?