6. The brothers found a treasure of gold and silver. They divided it so that each received 100 kg. The eldest received the most gold - 30 kg - and one fifth of all the silver. How much gold was in the treasure
Solution. 1) The elder brother received 70 kg of silver, which is one fifth of the total amount; therefore, the total mass of silver is 350 kg.

2) The others received more silver than the elder brother, i.e., each received more than 70 kg. If there are at least five brothers, then in total they would receive more than 350 kg; therefore, there are no more than four brothers.
3) But there must be at least four of them, since the mass of silver exceeds 300 kg. Therefore, there are four brothers.
4) The total mass of the treasure is 400 kg, so the mass of gold is 400-350=50 kg.

## Criteria.

If it is not proven (but simply assumed out of the blue) that there are exactly four brothers, the problem is not solved (no more than 3 points).

Errors. In addition to the correct answer, the participant suggests the variant "five brothers, each received 30 kg of gold" - deduct 1 point.

Progress. "The total mass of silver is 350 kg" - 1 point.

"Brothers are no more than four" with reasoning close to the correct one - 2 points.

Only an example is provided (without proving that the answer cannot be different) — 1 point.