2019 AMC 8 Problem 25
Attempt Problem 25 of the 2019 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 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Alice has apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?
Answer: C
Small hint:
Give each person apples first
Big hint:
Distribute the remaining apples with two dividers
Video solution:
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Written solution:
Let us assign everybody apples. This leaves us with apples.
Then, we want to solve where and are the additional apples given to Alice, Becky, and Chris.
Note that these are all nonnegative, since we already satisfied the only condition we needed to.
We can use stars and bars to get the number of solutions as
Thus, the correct answer is C.
Problem 25 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
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- 1998 AMC 8
- 1999 AMC 8
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