3. In Alice's drawer, there are 30 socks in 5 colors: 6 white, 6 yellow, 6 red, 6 green, and 6 blue. Her mischievous little brother takes 10 black envelopes and puts three socks (taken from the drawer) of three different colors in each envelope. Now Alice needs to go to Cesenatico and must have at least three pairs of socks of three different colors in her suitcase (the two socks of each pair must be the same color). How many envelopes does Alice need to take, at a minimum, to be sure she has all the socks she needs?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
3. The answer is $\mathbf{( C )}$. We observe that if Alice takes 3 envelopes, she cannot be sure to have the 3 pairs of socks she needs: for example, the first envelope might contain a white sock, a yellow one, and a red one, the second a white, a yellow, and a green one, and the third a white, a yellow, and a blue one, and there would only be two well-matched pairs (one white and one yellow).

If Alice takes 4 envelopes, we see that in any case she finds the 3 pairs she needs. Let's call the three (distinct) colors of the socks in the first envelope $A, B$, and $C$; let's call $D$ and $E$ the two colors that do not appear in the first envelope. The second envelope must have at least one color in common with the first, say $A$, so we have the pair of that color. If it does not have other colors in common, its colors are $A, D$, and $E$, so with the third envelope we get the other two pairs (at least two socks are not $A$ and therefore pair with non-$A$ socks found previously). If the second envelope has at least one other color in common, say $B$, we have the pair of that color as well. It remains to find the third pair: noting that each of the 4 envelopes contains at least one sock of a color different from $A$ and $B$, among these socks there must be two of the same color (there are only 3 colors available, namely $C, D$, and $E$), and then these socks will be the third pair. The minimum number of envelopes required is therefore 4.