# Fooling around with factorials -- part 2 -- with thanks to Alisa Meier

**Number Theory**Level 4

Let \(S(n)\) denote the number of digits of \(n\). Then find the sum of all \(n\)'s that satisfy the following equation:

\[\large S(n!) + 1 = n\]

Let \(S(n)\) denote the number of digits of \(n\). Then find the sum of all \(n\)'s that satisfy the following equation:

\[\large S(n!) + 1 = n\]

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