1988 AMC 8 Problem 24
Attempt Problem 24 of the 1988 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 1988 AMC 8 solutions, or check the answer key.
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24.
The square in the first diagram “rolls” clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram
Answer: A
Small hint:
Each time the square rolls over one edge of the hexagon it pivots about a shared corner and turns clockwise
Big hint:
Going from the top edge to the bottom edge is rolls, a total of which is one full turn plus an extra quarter turn clockwise
Solution:
Each roll of the square over one edge of the hexagon turns it clockwise. (At the pivot corner the square turns through minus the square’s own corner minus the hexagon’s interior angle, which leaves )
From the top of the hexagon to the bottom is rolls, for a total of That is one complete revolution () plus an extra clockwise.
The triangle starts pointing straight up, so after the extra quarter turn clockwise it points to the right.
Thus, the correct answer is A .
Problem 24 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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