Task B-3.5. Let $a, b$ and $c$ be three different digits, none of which is equal to zero. From $a, b, c$ we form three-digit numbers with different digits. If the sum of all such three-digit numbers is 3552, determine the smallest among them.
Solution. From the digits $a, b$ and $c$, we can form 6 different three-digit numbers. (1 point)

$$
a b c, a c b, b a c, b c a, c a b, c b a
$$

In their sum, each digit appears twice in the hundreds, tens, and units place:

$$
(2 a+2 b+2 c) \cdot 100+(2 a+2 b+2 c) \cdot 10+(2 a+2 b+2 c) \cdot 1
$$

Then $222(a+b+c)=3552$, or $a+b+c=16$.

The smallest three-digit number with the desired property is obtained for $a=1, b=6$ and $c=9$, so the desired number is 169.

(1 point)