Drum God

05-07-2006, 02:53 PM

On today's episode, shown on the Hallmark Channel, Lt. Columbo is, of course, investigating a murder. In the course of his investigation, a logic puzzle comes up. He solves the puzzle, but I think an important point was left out.

The puzzle: You are presented with bags of gold. One of the bags has "fake" gold in it. The fake gold is heavier than real gold. You have a penny scale and only one penny with which to purchase a weighing. You cannot add or remove pieces during the weighing -- one penny = one reading. How do you identify the bag with the fake gold?

Columbo's solution: Take one piece from bag 1, two pieces from bag 2, and three pieces from bag 3 (and so on). Weigh the six pieces. Suppose the real gold weighed one pound and the fake gold weighed one pound and one ounce. If all the gold pieces were real (and we know this is not true), the scale would read six pounds. If it reads six pounds and one ounce, bag 1 has the fake gold; if six pounds and two ounces, bag 2 has the fake gold; if six pounds and three ounces, bag 3 has the fake gold, and so on.

My problem: Columbo's supposition of each real piece weighing one pound and each fake piece weighing one pound and one ounce is not in the original question. In order for Columbo's method to work, wouldn't you need to know the correct weights of the real and fake pieces? Since you can only weigh one time, it is not possible to make this determination.

So, how do you solve the puzzle?

The puzzle: You are presented with bags of gold. One of the bags has "fake" gold in it. The fake gold is heavier than real gold. You have a penny scale and only one penny with which to purchase a weighing. You cannot add or remove pieces during the weighing -- one penny = one reading. How do you identify the bag with the fake gold?

Columbo's solution: Take one piece from bag 1, two pieces from bag 2, and three pieces from bag 3 (and so on). Weigh the six pieces. Suppose the real gold weighed one pound and the fake gold weighed one pound and one ounce. If all the gold pieces were real (and we know this is not true), the scale would read six pounds. If it reads six pounds and one ounce, bag 1 has the fake gold; if six pounds and two ounces, bag 2 has the fake gold; if six pounds and three ounces, bag 3 has the fake gold, and so on.

My problem: Columbo's supposition of each real piece weighing one pound and each fake piece weighing one pound and one ounce is not in the original question. In order for Columbo's method to work, wouldn't you need to know the correct weights of the real and fake pieces? Since you can only weigh one time, it is not possible to make this determination.

So, how do you solve the puzzle?