Show that one can find 50 distinct positive integers such that the sum of each number and its digits is the same.

All numbers that end in ...92 to ...99 have a single pairing with a number 9 larger. Additionally numbers that have "9" in the hundreds place have a longer list of single pairings, each 18 larger, running from ...983 to ...999

e.g. 983, 1001

I think that describes all the pairings possible.

*Edited on ***January 14, 2021, 2:44 am**