viernes, 6 de enero de 2017

1043. Seven colors

    One day I was talking about the four-color theorem demonstrated by K. Appel and W. Haken's computers in 1976. I commented that this theorem stated that 4 colors were enough to color a map demanding border regions have different colors. I pointed out that this theorem was true on planet Earth but not on planet Torus which was like a huge doughnut. On Torus there were maps that needed 7 colors.
    I left the subject here in the hope that some student would give some explanation... And it did happen... Pepe Chapuzas will never cease to amaze me! The next day he brought a set of dominoes. Well, there were only 21 tiles because he had removed the 7 doubles...

    Dear Teacher:
    In a rectangular world map of planet Earth, the left side and the right side represent the same meridian. In a rectangular world map of planet Torus, that happens too, but in addition, the top side and the down side represent the same parallel...
    If I arrange the tiles as follows and you imagine that this is a world map of Torus with 7 regions (from 0 to 6) that border to one another... We need 7 different colors...

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