# 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?

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