maths:The digital sum of a no.

　　　１　　２　　３　　４　　５　　６　　７　　８　　９　０
１　　２　　３　　４　　５　　６　　７　　８　　９　１０　１
２　　３　　４　　５　　６　　７　　８　　９　１０　１１　２
３　　４　　５　　６　　７　　８　　９　１０　１１　１２　３
４　　５　　６　　７　　８　　９　１０　１１　１２　１３　４
５　　６　　７　　８　　９　１０　１１　１２　１３　１４　５
６　　７　　８　　９　１０　１１　１２　１３　１４　１５　６
７　　８　　９　１０　１１　１２　１３　１４　１５　１６　７
８　　９　１０　１１　１２　１３　１４　１５　１６　１７　８
９　１０　１１　１２　１３　１４　１５　１６　１７　１８　９

The above table shows that the digital sum of two-digit number is either
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 (totally 18 posibilities)

Thus, by pigeon-hole principle,
among 19 different two-digit numbers, there should be at least 2 numbers that they have the same digital sum, and
among 37 different two-digit numbers, there should be at least 3 numbers that they have the same digital sum.

So, the proposition is correct!