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2

Part of 2013 Flanders Math Olympiad

Problems(1)

2013 smurfs are sitting at a large round table.

Source: Flanders Math Olympiad 2013 p2

12/24/2022
20132013 smurfs are sitting at a large round table. Each of them has two tickets. on each card represents a number from {1,2,...,2013}\{1, 2, . . ., 2013\} such that each of the numbers from this set occurs exactly twice. Every smurf takes the card every minute with the smaller of the two numbers, it smurfs on to its left neighbor and receives a card from his right neighbor. Show that there will come a time when a smurf has two cards with the same number.
combinatorics