# Problem A. 763. (November 2019)

**A. 763.** Let \(\displaystyle k\ge 2\) be an integer. We want to determine the weight of \(\displaystyle n\) balls. One try consists of choosing two balls, and we are given the sum of the weights of the two chosen balls. We know that at most \(\displaystyle k\) of the answers can be wrong. Let \(\displaystyle f_k(n)\) denote the smallest number for which it is true that we can always find the weights of the balls with \(\displaystyle f_k(n)\) tries (the tries don't have to be decided in advance). Prove that there exist numbers \(\displaystyle a_k\) and \(\displaystyle b_k\) for which \(\displaystyle \big|f_k(n)-a_kn\big|\le b_k\) holds.

Proposed by *Surányi László,* Budapest and *Bálint Virág,* Toronto

(7 pont)

**Deadline expired on December 10, 2019.**

### Statistics:

1 student sent a solution. 0 point: 1 student.

Problems in Mathematics of KöMaL, November 2019