# Digit Extrema!

Let $$A_N$$ denote the set of digit sums of $$N$$-digit numbers. Let $$B_N$$ be the set of the digit sums of elements of $$A_N$$. Let $$b_N$$ be the largest element of $$B_N$$. Let $$a_N$$ be the largest element of $$A_N$$ which gives $$b_N$$ as a digit sum. Find $$a_{10}$$

For example, $$A_1={1, 2, 3, 4, 5,\ldots, 9}$$, and $$B_1={1,2,3,4,5,\ldots,9}$$. Thus, $$b_1=9$$, an d $$a_1=9$$

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