A number is written this way : 12345678910111213.......201520162017, what is the remainder when this number is divided by 11?
What I've thought of is discuss them in group.
So I got
1~9:odd digits sum:25, even digits sum:20
10~99: odd digits:45*9, even digits:45*10
100~999: observe that each hundred digit and tenth digit of each three digit number can be eliminated.
Then I am stuck here. Cause there are thousands of four-digit numbers behind and they can not be eliminated. Is there any other more convenient way to solve this question? Any help is appreciated.