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number sum equals all digit sum (Posted on 2021-01-13) Difficulty: 4 of 5
Show that one can find 50 distinct positive integers such that the sum of each number and its digits is the same.

No Solution Yet Submitted by Danish Ahmed Khan    
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more thoughts Comment 2 of 2 |
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
  Posted by Steven Lord on 2021-01-14 02:36:04

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