A riddle of ice and fire dragons - Henri Picciotto
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You can find more map coloring puzzles, and some teacher notes for a classroom activity leading to the two color theorem on Henri Picciotto’s Math Education Page.
Mathematicians have long known that any map can be colored with four or fewer colors, so that each region contains a single color, and regions that share more than one boundary point have different colors. The four color theorem was proved in 1976 by analyzing hundreds of maps with the help of a computer. This riddle gets you to think about maps that can be colored in two or three colors.
You can read about the four color theorem, its history, and its place in mathematics on Wikipedia: Four Color Theorem.
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