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While tidying up the children's room before the guests arrived, mom found nine socks. Among any four of these socks, at least two belonged to one child, and among any five, no more than three had the same owner. How many children could there have been, and how many socks could have belonged to each child?
Since among any four socks, at least two belonged to one child, there are no more than three children. No child can own more than three socks (otherwise, there would be five socks, among which more than three belong to one owner).

The mother found a total of nine socks, so there cannot be fewer than three children. Therefore, there are three children in the room, and each of them owns exactly three of the found socks.

## Answer

Three children, each of whom owned exactly three socks.