2024 AMC 8 Problem 13
Attempt Problem 13 of the 2024 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 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)
Answer: B
Small hint:
The sequence must have three up hops and three down hops
Big hint:
Buzz can never have more down hops than up hops at any point
Video solution:
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Written solution:
We can deduce from the choices that it is possible to exhaust all possible cases for this problem. Note that all sequences must start with up and end with down , and that it should not be possible to go down more times than Buzz has gone up so far. Keeping this in mind, we can arrive at the following possible cases: which is a total of five possible sequences.
Thus, B is the correct answer.
Problem 13 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
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2026 AMC 8