ASU 179 All Soviet Union MO 1973 1024 sportmen in tennis tournament
Source:
July 4, 2019
combinatoricsTournament
Problem Statement
The tennis federation has assigned numbers to sportsmen, participating in the tournament, according to their skill. (The tennis federation uses the olympic system of tournaments. The looser in the pair leaves, the winner meets with the winner of another pair. Thus, in the second tour remains participants, in the third -- , et.c. The winner is determined after the tenth tour.) It comes out, that in the play between the sportsmen whose numbers differ more than on always win that whose number is less. What is the greatest possible number of the winner?