8.4. In the record $*+*+*+*+*+*+*+*=* *$, replace the asterisks with different digits so that the equality is true. Justify that the given example is unique up to the order of the addends in the left part of the equation.
Answer. $1+2+4+5+7+8+9+0=36$, the example is unique up to the order of the addends on the left side of the equation.

Solution. $1+2+4+5+7+8+9+0=36$.

Note that the given example is unique up to the order of the addends on the left side of the equation. Indeed, let the number on the right side be $\overline{a b}$. Since the sum of ten different digits is 45, the given equation can be written as $45-a-b=10 a+b$. Simplifying it, we get: $11 a+2 b=45$.

A simple enumeration shows that $a=3, b=6$.

## Criteria.

5 points. A correct example is provided (without justification).

$\mathbf{0}$ points. An incorrect example is provided (in particular, with repeating digits)