You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it’s the counterfeit. If they’re equal weight, the third coin is the counterfeit.
The next number in the series counts the previous numbers. Thus the first number is 1, which is one 1, or 11. To describe 11, you have two 1’s, or 21. Now you have one 2 and one 1, so the next number is 1211. The solution is to continue describing the previous number using only numbers.
One evening a man is walking home from work and an insect flies into his ear. He tries to pry it out but it doesn’t work. Shaking his head isn’t successful either. Finally he managed to get it out. How did he do it?