A bucket full of milk weighed $35 \mathrm{~kg}$. The same bucket with half the amount of milk weighed $18 \mathrm{~kg}$.

How much does the empty bucket weigh?

(L. Hozová)
The difference in weights $35-18=17(\mathrm{~kg})$ corresponds to half the milk without the pot. All the milk without the pot weighs $2 \cdot 17=34(\mathrm{~kg})$.

Thus, the difference $35-34=1$ (kg) corresponds to the empty pot. The empty pot weighs $1 \mathrm{~kg}$.

Another solution. The pot with half the amount of milk weighs $18 \mathrm{~kg}$. Therefore, $2 \cdot 18=36(\mathrm{~kg})$ corresponds to the weight of the full amount of milk and two pots.

The difference $36-35=1$ (kg) corresponds to the empty pot. The empty pot weighs 1 kg.

Evaluation. 4 points for auxiliary calculations and reasoning (e.g., 2 points each for the weights of half the milk and all the milk without the pot in the first solution); 2 points for solving the problem and the result.