## Task B-2.5.

The sum of two five-digit numbers that match in the first three digits is 123422. The last two digits of one number are 1,2, and of the other 1,0 in that order. Determine these numbers.
## First solution.

The numbers are of the form $\overline{a b c 12}$ and $\overline{a b c 10}$

$\overline{a b c 12}=\overline{a b c 00}+12$.

$\overline{a b c 10}=\overline{a b c 00}+10$.

Since the sum of these numbers is 123422, it follows that:

$\overline{a b c 12}+\overline{a b c 10}=123422$

$\overline{a b c 00}+12+\overline{a b c 00}+10=123422$,

$2 \cdot \overline{a b c 00}+22=123422$. From this,

$\overline{a b c 00}=61700$.

1 point

It follows that $a=6, b=1, c=7$, 1 point

thus the desired numbers are 61712 and 61710.