Problem

Source: OMEC Ecuador National Olympiad Final Round 2023 N3 P4 day 2

Tags: national olympiad, combinatorics



A number is additive if it has three digits, all of them are different and the sum of two of the digits is equal to the remaining one. (For example, $123 (1+2=3), 945 (4+5=9)$). Find the sum of all additive numbers.