1. A group of schoolchildren heading to a school camp was to be seated in buses so that each bus had the same number of passengers. Initially, 22 people were to be seated in each bus, but it turned out that three schoolchildren could not be seated. When one bus left empty, all the schoolchildren were able to sit evenly in the remaining buses. How many schoolchildren were in the group, given that no more than 18 buses were allocated for transporting the schoolchildren, and no more than 36 people can fit in each bus? Provide the answer as a number without specifying the unit.

$(2$ points)
Solution. Let $\mathrm{n}$ be the number of buses, $\mathrm{m}$ be the number of schoolchildren in each bus, and $\mathrm{S}$ be the total number of schoolchildren.

We have

$$
S=22 n+3, \quad S=(n-1) m, n \leq 10, m \leq 36, \quad 22 n+3=(n-1) m, \quad n=1+\frac{25}{m-22}
$$

Considering the constraints on $\mathrm{n}$ and $\mathrm{m}$, we get the only possible case: $m=27, \quad n=6, \quad S=135$.

Answer: 135.