Wednesday, June 20, 2007

Technological Advances in Balancing Problems

This problem I got from a fellow named Johnny Card:
Our collector has three bags of silver ingots. Well, two bags of silver, and one bag of pyrite, which looks like silver, but isn't. A pyrite ingot weighs one-tenth (0.1) of a gram more than a silver ingot. Our collector has finally purchased a digital scale, one which can measure weight to the tenth of a gram, but it is barely working (thanks to a recent incident involving weighing a chili cheese dog). The scale will certainly work once, but after that it might short out, so the collector would like to determine the fake bag as quickly as possible. How can he determine the bag of pyrite in just one weighing?

Edited to Add: Oops! I should mention that a single ingot weighs a whole number of grams - say, 100 grams. Answer in the comments.


J. Bowman said...

If he labels the bags as A, B, and C, the collector places on the scale one ingot from bag A, two ingots from bag B, and three ingots from bag C. The number in the tenths place on the scale will indicate which bag contains the pyrite.

Leo said...

You are killing me with these. Seriously. Killing me.