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| − | Each square in a <math>3\times3</math> grid of squares is colored red, white, blue, or green so that every <math>2\times2</math> square contains one square of each color. One such coloring is shown on the right below. How many different colorings are possible?
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| − | ==Solution 1==
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| − | We first have <math>4!=24</math> possible ways to fill out the top left square. We then fill out the bottom right tile (let a "tile" denote a <math>1\times1</math> square and "square" refer to <math>2\times2</math>). In the bottom right square, we already have one corner filled out (from our initial coloring), and we now have <math>3</math> options left to pick from.
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| − | We then look at the right middle tile. It is part of two squares: the top right and top left. Among these squares, <math>3</math> colors have already been used, so we only have one more option for it. Similarly, every other square only has one more option, so we have a total of <math>3\cdot4!=72</math> ways.
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| − | ~Technodoggo
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