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2018 AMC 10A Problem 20

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2018 AMC 10A Problem 20AMC 10 Step by Step
Name:                             Date: September 13, 2026
Paths & Grids · difficulty 4 of 5 · about 6 min · position P16-20

A scanning code consists of a 7×77 \times 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 color in this grid of 4949 squares. A scanning code is called symmetric\textit{symmetric} if its look does not change when the entire square is rotated by a multiple of 90∘90 ^{\circ} 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?

  1. A)

     510\text{ 510}

  2. B)

     1022\text{ 1022}

  3. C)

     8190\text{ 8190}

  4. D)

     8192\text{ 8192}

  5. E)

     65,534\text{ 65,534}

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