2. Antea, Borna, Cvita, and Damir collect postage stamps. The number of Antea's stamps is exactly half the number of the other three children's stamps. The number of Borna's stamps is a third of the number of the other three children's stamps. The number of Cvita's stamps is a quarter of the number of the other three children's stamps. If Damir collected more than 160 but fewer than 180 stamps, how many stamps did they collect in total?
## First Solution.

Since Antea collected half the number of marbles the other three children collected, she collected a third of all the marbles.

| ANTEA | OTHERS |
| :--- | :--- | :--- |

Similarly, we conclude that Borna collected a quarter, and Cvita a fifth of all the marbles. Therefore, the total number of marbles must be divisible by 3, 4, and 5, meaning it must be a multiple of all three numbers. The smallest such number is 60.

Let's graphically represent the conditions of the problem by using 60 squares to represent the total number of marbles:
![](https://cdn.mathpix.com/cropped/2024_05_30_586c721b23ba4254274fg-2.jpg?height=534&width=1372&top_left_y=832&top_left_x=203)

After isolating Antea's, Borna's, and Cvita's marbles, 13 squares remain, representing the number of Damir's marbles. We know that Damir has between 160 and 180 marbles. Since

$160 \div 13 = 12$ with a remainder of 4,

$180 \div 13 = 13$ with a remainder of 11,

we conclude that the only number between 160 and 180 that can be divided by 13 without a remainder is $13 \cdot 13 = 169$.

Each square represents 13 marbles. Together, they collected $13 \cdot 60 = 780$ marbles.