Question 108
Vladimir chose three digits $a, b$ and $c$ such that $a \gt b \gt c \gt 0$ and with them he formed the numbers $abc$, $cba$ and $cab$. Note that $abc$ is not the product of $a, b$ and $c$, but the number of digits $a, b$ and $c$. For example, if $a = 1$, $b = 2$ and $c = 3$, $abc$ will be number 123. After choosing these three digits $a, b$ and $c$, Vladimir realized that one of the numbers formed was equal to the sum of the other two. Find the numbers formed by Vladimir.