Convert a new problem into an old one

What do you do when you see a new problem? Try to convert it into an old one. Here is an example:

 

One day a mathematician decides that he is sick of math and wants to be a fireman. So, the mathematician 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 spicket, 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 spicket, 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 awhile and the 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.”

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