Difference between revisions of "2005 AMC 8 Problems/Problem 16"
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<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15 </math> | <math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15 </math> | ||
| − | == | + | ==Solution== |
The Martian can pull out <math>12</math> socks, <math>4</math> of each color, without having <math>5</math> 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 <math>\boxed{\textbf{(D)}\ 13}</math> socks. | The Martian can pull out <math>12</math> socks, <math>4</math> of each color, without having <math>5</math> 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 <math>\boxed{\textbf{(D)}\ 13}</math> socks. | ||
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?
Solution
The Martian can pull out 
socks, 
of each color, without having 
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 
socks.
See Also
| 2005 AMC 8 (Problems • Answer Key • Resources) | ||
| 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. 
