MathNet 1974 — Part 01 Question 11

Find all three-digit decimal numbers $a_1a_2a_3$ which equal the mean of the six numbers $a_1a_2a_3$, $a_1a_3a_2$, $a_2a_1a_3$, $a_2a_3a_1$, $a_3a_1a_2$, $a_3a_2a_1$.