Sunday Times Teaser 2742 – Hymns Bored

by David Buontempo

Three three-digit hymn numbers are chosen from a hymnal containing 500 hymns.

The sums of the digits for each of the three hymn numbers are the same and, among them, they use nine different digits.  One of them is also the average of the other two.

What are the three hymn numbers (in increasing order)?