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 socks of the same color?
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Solution:
It is possible for the Martian to pull out at most red, white and blue socks without having a matched set. The next sock it pulls out must be red, white or blue, which gives a matched set. So the Martian must select socks to be guaranteed a matched set of five socks.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions