5. Three Thieves, Bingo, Bunko, and Balko, robbed a bank and carried away 22 bags of banknotes. They placed them in a row so that the first bag contained the least amount of money, and each subsequent bag contained one more stack of banknotes than the previous one. Chief Bingo divided the stolen bags of money according to the principle: the first one for me (Bingo), the second one for you (Bunko), the third one for me (Bingo), the fourth one for you (Balko), the fifth one for me (Bingo), the sixth one for you (Bunko)... Then they counted the money. Bunko and Balko found that together they had a whopping total of 6710000 SIT. They were also delighted to find that together they had 110000 SIT more than their chief. Your task is to determine how much money was in the first bag. Write down the answer.[^3]

## Solutions to the Problems and Scoring

 A contestant who arrives at the solution by any correct method (even if the scoring does not provide for it) receives all possible points.

For a correct method, any procedure that

- sensibly takes into account the wording of the problem,
- leads to the solution of the problem,
- is mathematically correct and complete.

A contestant who has only partially solved the problem, from otherwise correct solving procedures but does not show the way to the final solution of the problem, cannot receive more than half of the possible points.

## First Year


5. Šopi šefa: $x+(x+2)+\cdots+(x+20)=\frac{6600000}{k}$ ..... 1 point
Šopi Bunka in Balka: $(x+1)+(x+3)+\cdots+(x+21)=\frac{6710000}{k}$ ..... 1 point
Rearrangement of both equations: ..... 1 point

$$
\begin{aligned}
& 11(x+10)=\frac{6600000}{k} \quad \text { and } \\
& 11(x+11)=\frac{6710000}{k}
\end{aligned}
$$

Solution of the system $x=50$ ..... 1 point
$k=10000$ ..... 1 point
Answer: In the first bag, there are $x \cdot k=500000$ SIT. ..... 1 point

[^0]:    Solve the problems independently on the provided paper, and each problem on a separate page.

    Do not sign the sheets, write only your code.

    Write your answers with a pen clearly and neatly. The solution to each problem will be graded from 0 to 6 points.

    You have 120 min available for solving.

    THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

[^1]:    Solve the problems independently on the provided paper, and each problem on a separate page.

    Do not sign the sheets, write only your code.

    Write your answers with a pen clearly and neatly. The solution to each problem will be graded from 0 to 6 points.

    You have 120 min available for solving.

    THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

[^2]:    Solve the problems independently on the provided paper, and each problem on a separate page.

    Do not sign the sheets, write only your code.

    Write your answers with a pen clearly and neatly. The solution to each problem will be graded from 0 to 6 points.

    You have 120 min available for solving.

    THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.

[^3]:    Solve the problems independently on the provided paper, and each problem on a separate page.

    Do not sign the sheets, write only your code.

    Write your answers with a pen clearly and neatly. The solution to each problem will be graded from 0 to 6 points.

    You have 120 min available for solving.

    THE NATIONAL COMPETITION COMMITTEE WISHES YOU GREAT SUCCESS.