[The Pigeonhole Principle (continued).]

Three people are playing table tennis in a knockout format, meaning the player who loses a match gives way to the player who did not participate in it. In the end, Nikanor played 10 matches, Filimon played 15, and Agafon played 17. Who among them lost the second match?
A total of $(10+15+17): 2=21$ games were played. Note that no one could skip two games in a row. This means that Nikanor played all the games with even numbers and only them. Since he did not play in the third game, he lost the second game.

## Answer

Nikanor.