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SMO 2011 Junior Round 1 Question 21

SMO · SMO 2011 Junior Round 1

Question 21

Suppose a function $M(n)$, where $n$ is a positive integer, is defined by
$$M(n)=\begin{cases}n-10,&n>100,\\M(M(n+11)),&n\le100.\end{cases}$$
How many solutions does the equation $M(n)=91$ have?