## 8. Gold Coins

Ante, Branimir, Celestin, and Dubravko are sitting around a round table (in that order). Together, they have 1600 gold coins. First, Ante divides half of his gold coins into two equal parts and gives one part to his left neighbor and the other part to his right neighbor, while keeping the other half for himself. Then, Branimir does the same, followed by Celestin, and finally Dubravko. In the end, all four of them have an equal number of gold coins. How many gold coins did Branimir have at the beginning?

Result: $\quad 575$
Solution, first method.

Solving backwards:

|  | Ante | Branimir | Celestin | Dubravko |
| :--- | :---: | :---: | :---: | :---: |
| number of gold coins at the end | 400 | 400 | 400 | 400 |
| number of gold coins after 3rd step | 200 | 400 | 200 | 800 |
| number of gold coins after 2nd step | 200 | 300 | 400 | 700 |
| number of gold coins after 1st step | 50 | 600 | 250 | 700 |
| number of gold coins at the beginning | 100 | 575 | 250 | 675 |

Solution, second method. Solving backwards:
![](https://cdn.mathpix.com/cropped/2024_05_30_97e0360945497c9bac66g-6.jpg?height=714&width=1402&top_left_y=1914&top_left_x=218)

Branimir had 575 gold coins at the beginning.