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 \(1\) problem. On the second day, he does \(2\) problems. On the third day, he does \(3\) problems. This pattern continues on until the \(10\)th day. On the \(10\) th day, he does \(1+0=1\) problem. On the \(11\)th day, he does \(1+1=2\) problems. In general, on the \(\overline{ab}\)th day, he does \(a+b\) problems. Finally, on the \(100\)th day, he does \(1+0+0=1\) problem, completing his streak.

In total, how many problems did he do?

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