6. (7 points) If the number $A$ is written on the board, you can add any of its divisors, except 1 and $A$ itself. Can you get 1234321 from $A=4$? Answer: Yes.
Solution. Adding a divisor $n$ to a number means adding $n$ to a number of the form $k n$. The result will be a number of the form $(k+1)n$. Note that the number 1234321 is divisible by 11. Then to the number $A=4=2 \cdot 2$, we will add 2 until we get the number $2 \cdot 11$: $2 \cdot 2 \rightarrow 2 \cdot 3 \rightarrow 2 \cdot 4 \rightarrow 2 \cdot 5 \rightarrow \ldots \rightarrow 2 \cdot 11$. Then we will add 11:

$$
2 \cdot 11 \rightarrow 3 \cdot 11 \rightarrow 4 \cdot 11 \rightarrow 5 \cdot 11 \rightarrow \ldots \rightarrow 112211 \cdot 11=1234321
$$

## Grading Criteria.

- Any correct algorithm for obtaining the number - 7 points.
- There is an idea of how to obtain a number that is a multiple of a proper divisor of the number 1234321, -3 points.
- Answer "yes" without justification - 0 points.


## Maximum score for all completed tasks - 42.