Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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