<p>Each vertex of a regular dodecagon (<img alt="$12$" height="12" src="https://latex.artofproblemsolving.com/e/d/f/edf074831eb5bc9e61d6d6e09f525a86e3068f6a.png" width="17" />-gon) is to be colored either red or blue, and thus there are <img alt="$2^{12}$" height="15" src="https://latex.artofproblemsolving.com/7/d/3/7d30984e684d8dc3985cd42961a0ca3b95687eba.png" width="21" /> possible colorings. Find the number of these colorings with the property that no four vertices colored the same color are the four vertices of a rectangle.</p>

Question No: 397

Each vertex of a regular dodecagon ( $12$ -gon) is to be colored either red or blue, and thus there are $2^{12}$ possible colorings. Find the number of these colorings with the property that no four vertices colored the same color are the four vertices of a rectangle.

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Tags: Combinatorics Geometry

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