1972 AMC 12 Problem 28
Attempt Problem 28 of the 1972 AMC 12 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 1972 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
A circular disc with diameter is placed on an checkerboard with width so that the centers coincide. The number of checkerboard squares which are completely covered by the disc is:
Answer: E
Small hint:
No square touching the outside border can be completely covered
Big hint:
Among the interior squares, test the four corner squares separately
Solution:
The border squares are not fully covered. Consider the remaining interior grid and measure distances in square side lengths, so the disc has radius The four outer corners of this interior grid are at distance from the center, so those four corner squares are not fully covered. Every other interior square lies within the disc: its farthest possible corner is at distance at most Hence squares are completely covered.
Therefore, the correct answer is E.
Problem 28 in other years
- 1950 AMC 12
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