## Task 3 - 100613

Let $a, b, c, d, e, f, g, h$ be pairwise distinct single-digit natural numbers not equal to zero, and let it be given that:

$$
a+b=10, \quad c+d+e=16, \quad f+g+h=14
$$

Which single-digit natural number (not equal to zero) was not used in these three equations?

Provide a possible solution for $a, b, c, d, e, f, g, h$!
There are exactly 9 single-digit natural numbers not equal to zero, namely $1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9$. The sum of all these 9 numbers is

$$
1+2+3+4+5+6+7+8+9=45
$$

According to the problem, exactly 8 of them were used.

From the given equations, by adding them up, we get:

$$
a+b+c+d+e+f+g+h=10+16+14=40
$$

Thus, the number 5 was not used. One possible solution is, for example:

$$
a=1, \quad b=9, \quad c=2, \quad d=8, \quad e=6, \quad f=3, \quad g=7, \quad h=4
$$