Here is an ancient puzzle that has always perplexed some people. Two market women were selling their apples, one at three for a penny and the other at two for a penny. One day they were both called away when each had thirty apples unsold: these they handed to a friend to sell at five for 2¢. It will be seen that if they had sold their apples separately they would have fetched 25¢, but when they were sold together they fetched only 24¢.
“Now,” people ask, “what in the world has become of that missing penny?” because, it is said, three for l¢ and two for l¢ is surely exactly the same as five for 2¢.
Can you explain the little mystery?

A grocer in a small business had managed to put aside (apart from his legitimate profits) little sum in dollar bills, half dollars, and quarters, which he kept in eight bags, there being the same number of dollar bills and of each kind of coin in every bag. One night he decided to put the money into only seven bags, again with the same number of each kind of currency in every bag. And the following night he further reduced the number of bags to six, again putting the same number of each kind of currency in every bag. The next night the poor demented miser tried to do the same with five bags, but after hours of trial he utterly failed, had a fit, and died, greatly respected by his neighbors. What is the smallest possible amount of money he had put aside?