<![CDATA[Alternate solution]]>An observant student sent us this alternate solution to the main question. 🙂

\( 9+8+7+6+5+\textcolor{red}{43}+ \textcolor{red}{21} = 99,\) so the largest number is \(43\) and its sum of digits for is \(4 + 3 = \boxed{7}\).

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