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Wolfgang Haken: 2 puzzles worth knowing

2 puzzles from Wolfgang Haken, each explained in a minute and credited to the original work. Free on Savvy.

• Color any map so neighbors never match — how few colors do you need?

  Take any flat map divided into regions — countries, counties, anything — where neighboring regions share a real border, not just a single point. Color every region so no two neighb…

  — Kenneth Appel and Wolfgang Haken, Four color theorem

• Try to draw a map that needs a fifth color. Mapmakers couldn't either

  Take any map divided into regions, like countries or counties, and color each region so that no two regions sharing a border have the same color. Mapmakers had long noticed four co…

  — Kenneth Appel and Wolfgang Haken, Every Planar Map is Four Colorable

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