2004 AMC 8 Problem 18
Attempt Problem 18 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual’s score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers through Each throw hits the target in a region with a different value. The scores are: Alice points, Ben points, Cindy points, Dave points, and Ellen points. Who hits the region worth points?
Alice
Ben
Cindy
Dave
Ellen
Answer: A
Small hint:
Ben’s score of has only one possible pair of distinct positive scores.
Big hint:
Use each forced pair to eliminate numbers from the remaining scores.
Solution:
The only way to get Ben’s score of is with a and since he can’t hit twice.
Cindy can achieve her score with Ben already hit and so Cindy must have hit and
Similarly, Dave must have hit and Finally, since is already used, Alice is forced to have hit and with Ellen hitting and
Thus, A is the correct answer.
Problem 18 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
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