Get a Blue Flame
Ted joined Brilliant on January 1st and solved \(1\) problem.
Starting from the following day, January 2, Ted solves a number of problems each day which is equal to the sum of the digits of the number of problems he solved so far.
For example, if he has solved \(13\) problems so far, he will solve \(1+3=4\) that day.
When he gets a Blue Flame on January 20, by getting a 20-day streak, what is the total number of problems has he solved on Brilliant?