2020 AMC 12A Problem 6
Attempt Problem 6 of the 2020 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 12A solutions, or check the answer key.
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6.
In the plane figure shown below, of the unit squares have been shaded. What is the least number of additional unit squares that must be shaded so that the resulting figure has two lines of symmetry?
Answer: D
Solution:
For both symmetries, the lines must be the vertical and horizontal center lines of the -by- grid. Every shaded square then forces the squares obtained by reflecting it across each line.
The top square lies off-center, so its reflection group has squares, requiring more. The middle square sits on the central column, so its group has squares, requiring more. The bottom-right square again has a group of requiring more.
The least number of additional squares is
Thus, D is the correct answer.
Problem 6 in Other Years
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