MathDB

179

Part of 1973 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 179 All Soviet Union MO 1973 1024 sportmen in tennis tournament

Source:

7/4/2019
The tennis federation has assigned numbers to 10241024 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 512512 participants, in the third -- 256256, 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 22 always win that whose number is less. What is the greatest possible number of the winner?
combinatoricsTournament