## Task 2 - 110512

Rolf claims that an addition problem with a sum of 1000 can be formed, where all addends are natural numbers, and in their decimal representation, only the digit 8 appears, and exactly 8 times in total.

Determine whether Rolf's claim is correct!

If it is, provide all such addition problems and order the addends from largest to smallest!
The result of the addition problem must end in zero, which is only possible if at least 5 addends end in 8. According to the problem statement, 10 or more addends are not allowed.

To fit 8 digits of 8 into 5 addends, 3 digits of 8 must appear as tens, hundreds, or thousands. This gives the following possibilities:

\[
\begin{aligned}
& 88+88+88+8+8=280 \\
& 888+88+8+8+8=1000 \\
& 8888+8+8+8+8=8920
\end{aligned}
\]

Only (2) results in a sum of 1000 and is thus the only possible solution. Rolf is right; there is such an addition problem, and there is exactly one.