1992 AMC 12 Problem 8
Attempt Problem 8 of the 1992 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 1992 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
8.
A square floor is tiled with congruent square tiles. The tiles on the two diagonals of the floor are black. The rest of the tiles are white. If there are black tiles, then the total number of tiles is
Answer: E
Small hint:
If the floor has tiles on a side, count the tiles on both diagonals
Big hint:
Because the total number of black tiles is odd, the two diagonals share one center tile
Solution:
For an odd each diagonal contains tiles and the two diagonals share only the center tile. Hence so The floor therefore contains tiles.
Thus the correct answer is E.
Problem 8 in other years
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