MathDB
Drawing socks

Source: AHSME 1986 problem 17

October 1, 2011
pigeonhole principleAMC

Problem Statement

A drawer in a darkened room contains 100100 red socks, 8080 green socks, 6060 blue socks and 4040 black socks. A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. What is the smallest number of socks that must be selected to guarantee that the selection contains at least 1010 pairs? (A pair of socks is two socks of the same color. No sock may be counted in more than one pair.)
<spanclass=latexbold>(A)</span> 21<spanclass=latexbold>(B)</span> 23<spanclass=latexbold>(C)</span> 24<spanclass=latexbold>(D)</span> 30<spanclass=latexbold>(E)</span> 50 <span class='latex-bold'>(A)</span>\ 21\qquad<span class='latex-bold'>(B)</span>\ 23\qquad<span class='latex-bold'>(C)</span>\ 24\qquad<span class='latex-bold'>(D)</span>\ 30\qquad<span class='latex-bold'>(E)</span>\ 50