2005 AMC 8 Problem 16
Attempt Problem 16 of the 2005 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 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be socks of the same color?
Answer: D
Small hint:
In the worst case, the Martian gets only socks of each color first.
Big hint:
The next sock must make five of some color.
Solution:
Note that the Martian can pull out socks of each color without drawing of the same color. The th sock, however, must be the th sock of some color.
Thus, D is the correct answer.
Problem 16 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
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- 1998 AMC 8
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