21. Baron Münchhausen told a story. "A whole crowd gathered. We reached a crossroads. Then half of our group turned left, a third - right, and a fifth - straight ahead." "But excuse me," the duke noticed, - the sum of a half, a third, and a fifth is not equal to one, so you are lying!" The baron objected: "I am not lying, I am rounding. For example, 17 people are walking. I say that a third turned. According to you, should one of the people split? No, with rounding, it turns out that six turned. After all, the closest whole number to the fraction $17 / 3$ is 6. And if I say that half of 17 people turned - that means 8 or 9 people." It is known that Baron Münchhausen never lies. What is the largest number of people that could have been in the crowd?

## 7th grade
21. Answer: 37 (18 to the left, 12 to the right, 7 straight).

Evaluation: $\frac{1}{2}+\frac{1}{3}+\frac{1}{5}=\frac{31}{30}$. If there were a total of people, then $\frac{1}{30} \cdot$ is the error. Let's calculate the maximum error (in fractions of a person): $\frac{1}{2}+\frac{1}{3}+\frac{2}{5}=\frac{37}{30}$. Therefore, $\frac{37}{30} \geqslant \frac{1}{30}$, from which $x \leqslant 37$.

## 7th grade