2. On four cards, four numbers are written, the sum of which is 360. You can choose three cards with the same number written on them. There are two cards, one of which has a number three times larger than the other. What numbers could be written on the cards?
Answer: $36,108,108,108$ or $60,60,60,180$.

Solution. Let the smallest of the four numbers be x. Then the largest is 3x. The three equal numbers can be either the three larger or the three smaller, from which we get two equations: $3 x+3 x+3 x+x=360$ and $x+x+x+3 x=360$. From the first, we find $x=36$, and the numbers on the cards are $36,108,108,108$. From the second, we find $x=60$, and the numbers on the cards are $60,60,60,180$.

## Criteria.

Only one of the two options is obtained: 3 points.