The people of Wonderland are having an election. Each voter writes the names of 10 candidates on their ballot paper (they cannot write the same name twice on their ballot paper).
There are 11 ballot boxes in total and each ballot box has at least one ballot paper inside. The March Hare, who is counting the votes, notices something:
If he takes one ballot paper from each ballot box (so 11 ball together), there will always be at least one candidate whose name appears on all 11 of those papers.
Prove that there is at least one ballot box and a candidate’s name such that every ballot paper on that box contains the name of that candidate.