A hare is running a 2024-meter race. At the start, it pushes off with its left foot and alternates regularly between its left foot, right foot, and both feet throughout the race. When the hare pushes off with its left foot, it jumps $35 \mathrm{dm}$, when it pushes off with its right foot, it jumps $15 \mathrm{dm}$, and when it pushes off with both feet, it jumps $61 \mathrm{dm}$.

How many jumps will the hare make before reaching the finish line? And which foot will it use to push off before the final jump?

(L. Hozová)
We will calculate everything in decimeters. The race is $20240 \mathrm{dm}$ long, and the hare's triple jump measures $35+15+61=111 \mathrm{dm}$. By division with a remainder, we find that

$$
20240=182 \cdot 111+38
$$

Thus, after 182 triple jumps, the hare has $38 \mathrm{dm}$ left to the finish line.

The next jump is made with the left foot, covering $35 \mathrm{dm}$, leaving $3 \mathrm{dm}$ to the finish line. The following jump is made with the right foot, and with this jump, the hare will reliably jump past the finish line.

In total, the hare will make $182 \cdot 3+2=548$ jumps, and the jump before the final one will be made with the right foot.