Brain Teasers/Collection of coin questions
8 coins, 1 weighs less, balance scale
Q: You are given 8 pennies, 7 of which weigh exactly the same, but one penny weighs less than the other 7. You also have a judge scale. Find the one penny that weighs the least.
A: Break them into 3 groups. 3, 3, 2. For the group of 3, weight 1:1. If they weigh same, the other one is the lightest.
12 marbles, 1 weighs different, balance scale
Q: You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. You are asked to both identify it and determine whether it is heavy or light.