Problem A. 417. (January 2007)

A. 417. n3 people runs several rounds of race without any tie. Denote by f(n) the smallest possible number of rounds such that for any three people, all their six possible orders occur. Prove that ln n<f(n)<20ln n.

(By Péter Pál Pach and Anna Puskás)

(5 pont)

Deadline expired on February 15, 2007.

Statistics:

10 students sent a solution.
5 points:	Gyenizse Gergő, Kisfaludi-Bak Sándor, Nagy 224 Csaba, Nagy 235 János, Tomon István.
4 points:	Hujter Bálint.
2 points:	4 students.

Problems in Mathematics of KöMaL, January 2007