## 231. Math Puzzle $8 / 84$

In a summer camp, there are a lot of pioneers. There are more than 300 but less than 400.

The camp leader wants to line them up for the morning assembly so that they form a rectangle. He tries it with rows of 2, 3, 4, 5, and 6, but there is always one child left over! Only with rows of 7 does it work.

How many pioneers are in the summer camp?
The smallest number (the least common multiple) in which the numbers 2, 3, 4, 5, and 6 divide evenly is 60. The desired number is a multiple of 60 plus the one child who always remains. And it must also be divisible by 7.

$$
60 a+1=7 b
$$

Divisibility by 7 is first met for \( a=5 \): \( 60 \cdot 5+1=7 \cdot 43 \). Therefore, there are 301 pioneers in the camp.