The people in Wonderland are having an election. Every voter writes 10 candidate names on a bulletin and puts it in a ballot box.
There are 11 ballot boxes all together. The March Hare, who is counting the votes, is very surprised to discover that there is at least one bulletin in each ballot box. Moreover, he learned that if he takes one bulletin from each ballot box (11 bulletins all together), then there is always a candidate whose name is written in each of the 11 chosen bulletins. Prove that there is a ballot box, in which all the bulletins contain the name of the same candidate.