## Task 3 - 270523

In an Olympiad class, exactly half of all participants were awarded a prize. There were only first, second, and third prizes. Exactly one eighth of all participants received a first prize. Exactly one sixth of all participants received a second prize. In this Olympiad class, there were at least 20 but fewer than 30 participants in total.

How many participants were there exactly in this Olympiad class?

How many first, second, and third prizes were there?

Explain how you find these exact numbers from the given information!
The number of participants was one of the numbers 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. Exactly one eighth of them received a first prize, so the number had to be divisible by 8.

This uniquely implies: The number of participants was 24.

Since $24: 2=12$, exactly 12 participants received a prize.

Since $24: 8=3$, exactly 3 participants received a first prize.

Since $24: 6=4$, exactly 4 participants received a second prize.

Since 12 - 3 - $4=5$, exactly 5 participants received a third prize.