## Task 4 - 060524

Hans is participating in the training of the track and field section of his school sports community. One of the exercises consists of rhythmic walking followed by rebounding in a standing position.

The length of the exercise track is $30 \mathrm{~m}$. At the beginning and end, there are flagpoles. Hans covers the distance in the following way:

Two steps forward, rebound, then one step back, rebound, then again two steps forward ... and so on, until he reaches the second flagpole.

What is the exact number of steps he takes in total under the given conditions, if his step length is exactly $5 \mathrm{dm}$?
With every 3 steps, Hans moves forward $50 \mathrm{~cm}$. Therefore, after exactly $2 \cdot 3 \cdot 29$ steps $=174$ steps, he is $29 \mathrm{~m}$ away from the starting point.

Since he reaches the second flagpole after two more steps and then stops the exercise according to the conditions, he covers the exercise distance with exactly 176 steps.

Solutions of the II. Round 1966 taken from [5]

### 2.8 VII. Olympiad 1967

### 2.8.1 I. Round 1967, Class 5