B3. Berry has picked 756 raspberries. He distributes the raspberries among himself and his friends so that everyone gets exactly the same amount. However, three of his friends are not as hungry and each return a number of raspberries, namely exactly a quarter of their own portion. Berry, on the other hand, is quite hungry and not only eats his own portion but also the raspberries he gets back. At some point, he loses count, but he is sure that he has eaten more than 150 raspberries.

How many raspberries did Berry eat exactly?
B3. 189

Let $n$ be the number of people (including Berry). Initially, everyone gets $\frac{756}{n}$ raspberries. Three friends then each give back $\frac{1}{4} \cdot \frac{756}{n}=\frac{189}{n}$ raspberries to Berry. This implies that 189 must be divisible by $n$.

The number of friends is at least 3, so $n \geqslant 4$. Also, $n \leqslant 8$, because if $n \geqslant 9$, then everyone initially gets no more than $\frac{756}{9}=84$ raspberries, so Berry would eat no more than $84+3 \times 21=147$ in total. This contradicts the fact that he ate more than 150.

Of the options $n=4,5,6,7,8$, $n=7$ is the only possibility, because 189 is not divisible by 4, 5, 6, or 8. Therefore, everyone initially got $\frac{756}{7}=108$ raspberries, and three friends each gave back $\frac{108}{4}=27$ raspberries. Berry ate a total of $108+3 \times 27=189$ raspberries.