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?

Correct answer:

a =  1
b =  2
c =  4

Step-by-step explanation:

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

$b=2$

$c=4$

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