MathNet 2020 — Math Olympiad Vault — Part 05 Question 132

Determine the numbers $\overline{abc}$, with $a \lt b \lt c$, knowing that the remainders of divisions of the numbers $\overline{abc}, \overline{bca}, \overline{cab}$ by 27 belong to the set $\{1, 2, 3, 4, 5\}$.