MathDB

4#

Part of 2020 Junior Balkan Team Selection Tests-Serbia

Problems(1)

Combinatorics

Source: Serbia JBMO TST 2020 P4

9/5/2020
One hundred tennis players took part in a tournament where they played with each other exactly one game, with no draws. At the end of the tournament a table (ranking) is formed depending on the number of victories. It is known that one tennis player finished the tournament on kk-th place and is the only one with that number of victories, and he has beaten every tennis player who is placed above him in the table and lost to anyone ranked weaker than him on the table. Find the smallest value of kk.
combinatorics