## Task 1 - 090621

Klaus participated in a track race as a member of the cycling section of a company sports club. After the race, his brother Reiner asked Klaus about the outcome of the race. Klaus said:

"When I crossed the finish line, no rider was next to me; exactly one third of the participating riders had already reached the finish line, and exactly half of all participants were still behind me."

State which position Klaus finished in this race and how many riders in total participated in the race!
(I) According to the problem statement, (because $\frac{1}{3}+\frac{1}{2}=\frac{5}{6}$) all drivers except Klaus accounted for $\frac{5}{6}$ of all participating drivers. Therefore, Klaus represented $\frac{1}{5}$ of all participants.

This is only possible if the number of participants was 6.

(II) Therefore, because $\frac{1}{3} \cdot 6=2$, exactly 2 of the participants finished ahead of Klaus, so Klaus finished in 3rd place.

## Solution adopted from $[5]$