If You Beg For Money, You Might End Up Doing Math

Yesterday I was walking around with my friend in a market hall. Two girls of age 15 asked us whether we could give them 40 euro cents. It is about \$0.6. We asked them what could we gain in response. They didn’t figure anything out (and the girls refused to sing for us), we proposed that they should solve some mathematical problem. Our mistake was probably that we didn’t invent a problem that would suit the girl’s level (*). I suppose first we gave a bit too hard a problem and then maybe a too easy one. They solved the easy one and we gave them the money. I regret a bit about (*) and that we didn’t keep them thinking a bit longer. Maybe that was the only chance to think in their lives. That is why I decided to write down some classical problems that are simple enough to be understood by someone who is 15 and has low mathematical self-esteem. The last of the following problems is the one that the girls were able to solve.

1. On the one side of a river there is a man with a wolf a goat and a cabbage. The man has a boat which fits at most one of those three items (the wolf, the goat or the cabbage) and the man wants to deliver all of them to the other coast. The problem is that he cannot leave the wolf with goat alone, because then the wolf will eat the goat and he cannot leave the cabbage with the goat, since the goat will eat the cabbage. What should the man do in order to complete his task?

Pictures are from Wikipedia: wolf and cabbage are GNU-guys, goat is Creative Commons, author Axpd..

2. There are 24 coins one of which is fake. The fake coin weights less than a normal coin and the normal coins weight equally much. Suppose you have a weighing scale that can always tell which one of two collections of coins is lighter. How to figure out which coin is false making use of the scale only three times?

3. How much is 379 + 623?
4. There are six glasses on the table in a row. The first three are full of water and the last three are empty. So the sequence is full-full-full-empty-empty-empty. By moving only one glass make the sequence to be alternating: full-empty-full-empty-full-empty.