A 100 Streak Goal

Daniel wants to get a 100-day streak on Brilliant.org. He plans to do so in the following manner:

On the first day, he does 11 problem. On the second day, he does 22 problems. On the third day, he does 33 problems. This pattern continues on until the 1010th day. On the 1010 th day, he does 1+0=11+0=1 problem. On the 1111th day, he does 1+1=21+1=2 problems. In general, on the ab\overline{ab}th day, he does a+ba+b problems. Finally, on the 100100th day, he does 1+0+0=11+0+0=1 problem, completing his streak.

In total, how many problems did he do?

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