8.4. Four boys and three girls went to the forest to pick mushrooms. Each found several mushrooms, in total they collected 70. No two girls collected the same amount, and any three boys together brought no fewer than 43 mushrooms. The number of mushrooms collected by any two children differed by no more than 5 times. Masha collected the most among the girls. How many mushrooms did she bring?
Answer: 5 mushrooms.

Solution. Any three boys collected at least 43 mushrooms together, so there is a boy who collected no less than 15 mushrooms (since $14 \cdot 3 < 43$). Therefore, this boy and the other three collected no less than $15 + 43 = 58$ pieces.

If there is a boy who collected no less than 15 pieces, then any girl collected no less than $15 \div 5 = 3$ mushrooms. Therefore, the girls collected different numbers of mushrooms, meaning they collected at least $3 + 4 + 5 = 12$ pieces together.

Since $58 + 12 = 70$ is the total number of mushrooms collected, the girls must have collected 3, 4, and 5 mushrooms, so Masha brought 5 pieces.