1992 AMC 8 Problem 20
Attempt Problem 20 of the 1992 AMC 8 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 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Which pattern of identical squares could not be folded along the lines shown to form a cube?
Answer: D
Small hint:
A cube has faces, so each pattern has squares; try folding each one up in your mind
Big hint:
Track where each square lands as the pattern folds; a pattern fails when two squares would cover the same face
Solution:
Each of the five patterns has squares. Folding patterns (A), (B), (C), and (E) wraps the squares neatly onto the six faces of a cube.
For pattern (D), any attempt to fold forces two of the squares to land on the same face, so they overlap and no cube can be formed.
Thus, the correct answer is D .
Problem 20 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1993 AMC 8
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