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How many ways are there to achieve symmetry in a grid of black and white squares? A scanning code consists of a 7×7 grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each in this grid of 49 squares. A scanning code is called symmetric if its look does not change when the entire square is rotated by a multiple of 90 degrees counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the total number of possible symmetric scanning codes? This problem is contributed by the Mathematical Association of America American Mathematical Competitions (MAA AMC) and first appeared on the 2018 AMC 10A exam. Learn more about MAA AMC Competitions. Send your solution to circles@aimath.org by February 28, 2019, March 31, 2019, for a chance to win a free MAA AMC study guide of your choice. Winners can choose between an AMC 8 Math Club Package, AMC 10/12 Math Club Package, a Math Wrangle Handbook, a CD containing past contests and solutions.

This article originally appeared in the Spring 2019 MTCircular.


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