$[$ Classical combinatorics (miscellaneous).]

In a dark room, on a shelf, there are four pairs of socks of two different sizes and two different colors lying in a random order. What is the smallest number of socks that need to be moved from the shelf to a suitcase, without leaving the room, to ensure that the suitcase contains two pairs of different sizes and colors?

#
First, note that seven socks are sufficient. Indeed, only one sock is not taken, which means all pairs of socks except one are taken. Therefore, in the suitcase, there are two pairs of different colors and sizes, specifically the pair that differs from the one not taken only by color, and the pair that differs from the one not taken only by size.

If one sock from each of the two pairs of the same color is left on the shelf, then there will not be two pairs of different colors in the suitcase. Therefore, six socks may not be enough.

## Answer

7 socks.