the travelling salesman and the four color map theorem

The map-colourer's new client wanted a map in which the same colour was not to be used for any two adjacent regions sharing a common border. The map colourer's problem was that he only had three colours, and he didn't want to start colouring in and then find he needed more colours to satisfy the client's request. So he called the travelling salesman who was the only source of pigment in the area.

"Hey Jack," he said, "how soon can you get here? I need more colours, real bad, real quick."

"Well Joe," replied the Salesman, "I've got a bit of a problem myself. I can't start my deliveries until I figure out the quickest cheapest route to deliver all the orders and return to head office."

"So what's the problem, Jack, can't you work out your route like you've always done before?"

"I wish I could," responded the Salesman, "but the thing is I need a new map: my dog ate the last one."

First published December 2008.
Image: (political) map of the world in four colours, Wikipedia 30/10/2014, mouseover for copyright and attribution.

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