1986 AMC 8 Problem 21
Attempt Problem 21 of the 1986 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 1986 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Suppose one of the eight lettered identical squares is included with the four shaded squares in the T-shaped figure shown. How many of the resulting figures can be folded into a topless cubical box?
Answer: E
Small hint:
A topless box has faces, so the four shaded squares plus the one added square must fold into a cube missing its top
Big hint:
Try each lettered square as the fifth face; a placement fails when folding would force two faces into the same spot
Solution:
The four shaded squares fold into four faces of an open box, and the added square supplies the fifth face. Picturing the folds, the squares and each complete a valid topless box.
The squares and do not work, because folding would force four faces to meet at a single corner. That leaves valid figures.
Thus, the correct answer is E .
Problem 21 in other years
- 1985 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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