A hardware shop owner is setting up his store before opening and hangs a sign advertising: 1 for 10 cents, 15 for 20 cents and 110 for 30 cents. What is he selling?

The sign is obviously referring to a computerized vending machine near the door, selling base-ten logarithms in bunches of ten for ten cents each.

If you want one bunch of ten, you pay ten cents for it (log(10)=1 × 10 is 10¢).
If you want fifteen bunches of ten, you pay twenty cents (log(150=2.176 × 10 is 21.7¢) but since the vending machine only takes dimes, you can just give it 20¢).
Similarly, you can buy 110 ten bunches of ten (the base-ten logarithm of 1100 is 3.041, at ten cents each, but 30.4¢ to the machine is just three dimes).

The problem arises when you want to buy 316 of these little bundles of joy, and the simplistic mechanism inside the machine computes log(3160) in two different ways as 3.49 and 3.50 and doesn't know whether to charge you three dimes or four.

Posted by DJ on 2003-12-01 12:23:45