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MathNet 2019-part-03 — 184 problems (EN–VI) Question 149

Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)

Question 149

In Alice's drawer there are 30 socks of 5 colors: 6 white, 6 yellow, 6 red, 6 green and 6 light blue. Her mischievous little brother takes 10 black envelopes and puts into each envelope three socks (taken from the drawer) of three different colors. Now Alice has to go to Cesenatico and must have in her suitcase at least three pairs of socks of three different colors (the two socks of each pair must be of the same color). What is the minimum number of envelopes Alice must take to be sure of having all the socks she needs?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6