In a chess tournament, sports masters and candidates for masters are participating. What is the smallest number of people that can participate in this tournament if it is known that among them, masters are less than half, but more than $45 \%$.

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Let $n$ chess players participate in a tournament, and $k$ of them are masters. According to the condition, $0.9 n2 k$ $-n>0.2 k-n$ is an integer, so it is at least 1. Therefore, $0.1 n>1, n>10$.

The case $n=11$ works: in the tournament, 5 masters and 6 candidates can play.

## Answer

11.