Try this beautiful Problem based on Number game from AMC 8 2020 Problem 22.
When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.
For example, starting with an input of $N=7$, the machine will output $3 \cdot 7+1=22$. Then if the output is repeatedly inserted into the machine five more times, the final output is 26.
$7 \rightarrow 22 \rightarrow 11 \rightarrow 34 \rightarrow 17 \rightarrow 52\\ \rightarrow 26$
When the same 6 -step process is applied to a different starting value of $N$, the final output is 1 . What is the sum of all such integers $N$ ?
$N \rightarrow \longrightarrow \rightarrow-\rightarrow \longrightarrow \rightarrow 1$
Pattern
Number series
AMC 8 2020 Problem 22
83
Try to start with the final output and work backwards.
Try to form a tree keeping in mind all the possible outcomes.
So, the sum will be,
$1+8+64+10=83$
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