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Sally Simplewit's mother wants to tile the bathroom. Having no taste, she has decided to do a multicolored pattern of square tiles around the tub, and she wishes to do so in such a way that no tile shares an edge with another tile of the same color, and so that each tile shares an edge with no more than one tile of any given color.
Sally (scientist in training) is given the job of determining the minimum number of different colors to accomplish this, so that her mother can place the order for the tiles. She is aware of the four-color theorem, which states that four colors suffice to color any map so that no two neighboring countries are the same color, but this is clearly a little different.
Today's challenge: Can you help Sally determine the minimum number of colors required for her mother's decorating plans?

HINT


Solution to yesterday's challenge



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