Now there is a question:
For twenty two-digit numbers, we add two digits together. (like 12 and get the result 3) Prove in these twenty numbers, there must be at least 2 same results.
Now I know I can assume the most extreme example which is adding 0,0 0,1 until 9,9, so I have at most 19 results. Therefore, the twentieth must be as same as one of the previous 19 ones.
But actually, I don't know the standard and rigorous proof of this problem. Can anyone help me with this standard proof?