The people of Wonderland are having an election. Each voter writes the names of 10 candidates on their ballot. No name can be written twice on the same ballot.
There are 11 ballot boxes in total and each box has at least one ballot inside. The March Hare, who is counting the votes, notices something:
If he takes one ballot from each box (so 11 altogether), there is always at least one candidate whose name appears on all 11 of those papers.
Prove that there is at least one ballot box and one candidate such that every ballot in that box contains the name of that candidate.