Problem #PRU-100544

Problem

Integer numbers $a,b$ and $c$ are such that the sum of digits of a number $a+b$ is less than $5$, the sum of digits of a number $b+c$ is less than $5$, the sum of digits of a number $a+c$ is less than $5$, but the sum of digits of a number $a+b+c$ is greater than $50$. Can you find such three numbers $a,b$ and $c$?