## Task 3 - 030733

The number $30 \star 0 \star 03$ should be divisible by 13. The $\star$ should each be replaced by one of the digits from 0 to 9. (The same digit does not necessarily have to be used for both stars.)

Give all the numbers that have the required property!
The number

$$
30 \star 0 \star 03=3000003+10000 \cdot x+100 \cdot y
$$

is exactly divisible by 13 with the digits $x$ and $y$ if $6+3 \cdot x+9 \cdot y$ is divisible by 13, because it holds that

$$
3000003+10000 \cdot x+100 \cdot y=13 \cdot(230769+769 \cdot x+7 \cdot y)+6+3 \cdot x+9 \cdot y
$$

By systematically testing $3 \cdot(2+3 \cdot y+x)$ for divisibility by 13, one quickly finds the solutions $(x, y)$ to be $(8,1),(5,2),(2,3),(9,5),(6,6),(3,7)$, and $(0,8)$.

Thus, the following numbers satisfy the required properties:

$3000803 ; \quad 3020303 ; \quad 3030703 ; \quad 3050203 ; \quad 3060603 ; \quad 3080103 ; \quad 3090503$[^5]

How many convex quadrilaterals are contained in the figure? Specify exactly how you determined this number.