At the fair, Kate found a strange machine with a sign on it labeled, “Enter a number.” When she pushed the number $15$, the machine displayed $9$. When she entered $23$, the machine displayed $17$. Perplexed, she tried $100$, and the machine displayed $94$. 

1. What is the machine doing?

   Hint (a):

   Find a pattern.

   More Help (a):

   $15→9$
   $23→17$
   $100→94$

   Answer (a):

   For every number entered into the machine, it subtracts $6$.

2. What would the machine display if she entered $77$?

   Hint (b):

   Use the pattern you found in part (a).