Reducing the problem.

One day a mathematician decides that he is sick of math. So, he walks down to the fire department and announces that he wants to become a fireman.

The fire chief says, �Well, you look like a good guy. I�d be glad to hire you, but first I have to give you a little test.�

The fire chief takes the mathematician to the alley behind the fire department which contains a dumpster, a spigot, and a hose. The chief then says, �OK, you�re walking in the alley and you see the dumpster here is on fire. What do you do?�

The mathematician replies, �Well, I hook up the hose to the spigot, turn the water on, and put out the fire.�

The chief says, �That�s great� perfect. Now I have to ask you just one more question. What do you do if you�re walking down the alley and you see the dumpster is not on fire?�

The mathematician puzzles over the question for a while and he finally says, �I light the dumpster on fire.�

The chief yells, �What? That�s horrible! Why would you light the dumpster on fire?�

The mathematician replies, �Well, that way I reduce the problem to one I�ve already solved.�