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Maximal number of matches for the winner of the tournament.

Source:

February 19, 2011
combinatorics unsolvedcombinatorics

Problem Statement

In a tournament with 5555 participants, one match is played at a time, with the loser dropping out. In each match, the numbers of wins so far of the two participants differ by not more than 11. What is the maximal number of matches for the winner of the tournament?