Difference between revisions of "2005 AMC 8 Problems/Problem 16"

(Created page with "==Problem== 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...")
 
(Solution)
 
(2 intermediate revisions by 2 users not shown)
Line 9: Line 9:
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2005|num-b=15|num-a=17}}
 
{{AMC8 box|year=2005|num-b=15|num-a=17}}
 +
{{MAA Notice}}

Latest revision as of 23:25, 29 December 2023

Problem

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 5 socks of the same color?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15$

Solution

The Martian can pull out $12$ socks, $4$ of each color, without having $5$ of the same kind yet. However, the next one he pulls out must be the fifth of one of the colors so he must remove $\boxed{\textbf{(D)}\ 13}$ socks.

See Also

2005 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png