Three numbers

We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers?

Result

a =  1
b =  2
c =  4

Solution:

$1554=2 \times 3 \times 7 \times 37=3 \times 518=6 \times 259 \ \\ abc + acb + bca + bac + cba + cab=1554 \ \\ 124+142+241 + 214 + 421+ 412=1554 \ \\ a=1$

$b=2$

$c=4$

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