4. Luka, Marko, Adrian, Filip, Ivan, and Borna were goal scorers for their school's handball team last season. The diagram shows the total number of goals each of them scored. Using the data provided, determine how many goals each of them scored.

![](https://cdn.mathpix.com/cropped/2024_06_03_6294b4e3daf24715e671g-1.jpg?height=794&width=1085&top_left_y=1616&top_left_x=517)

Marko scored two goals fewer than Luka.

Ivan scored the fewest goals.

The number of Luka's goals is equal to the number of goals scored by Filip and Adrian combined.

Filip scored twice as many goals as Borna.

The use of a pocket calculator or any reference materials is not allowed.

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4. 

![](https://cdn.mathpix.com/cropped/2024_05_30_f210cd8de88dd249b29dg-3.jpg?height=694&width=974&top_left_y=313&top_left_x=541)

From the diagram and the conditions of the problem, we conclude that Ivan achieved one goal.

1 POINT

Since Marko achieved two goals fewer than Luka, from the diagram we conclude that Marko achieved 8 or 6 or 4 goals, and Luka achieved 10 or 8 or 6 goals.

From the following condition: "The number of Luka's goals is equal to the number of goals achieved by Filip and Adrian together," and the graphical representation, we conclude that Luka achieved 10 goals (and Filip and Adrian either 4 or 6), and Marko achieved 8 goals.

2 POINTS

From the condition: "Filip achieved twice as many goals as Borna," we conclude that Filip achieved 6 goals, and Borna achieved 3 goals. Therefore, Adrian achieved 4 goals.

3 POINTS

TOTAL 6 POINTS

Note: The correct number of goals determined for each boy, and without explanation, earns 1 POINT each.