2017 AMC 8 Problem 15
Attempt Problem 15 of the 2017 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
In the arrangement of letters and numerals below, by how many different paths can one spell ? Beginning at the in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.
Answer: D
Small hint:
Count choices one step at a time from the central .
Big hint:
From each , count adjacent ’s, then from each , count adjacent ’s.
Video solution:
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Written solution:
Starting from there are ways to reach an From each there are ways to reach a From each there are ways to reach an Multiplying all these possibilities, we get
Thus, D is the correct answer.
Problem 15 in other years
- 1985 AMC 8
- 1986 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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- 1998 AMC 8
- 1999 AMC 8
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