How many $9$ 's are sandwiched between $6$ and $7$ in the following sequence:
$696996676979669779667$?

A $9$ is considered "sandwiched" if it resides exactly between a $6$ and a $7$. This means we need to identify the total occurrences of triplets structured either as $(697)$ or $(796)$.
Let us scan the sequence sequentially:
$69699667697966697779667$

* First match: $\dots 67[697]9\dots$ (forward order)
* Second match: $\dots 69[796]6\dots$ (reverse order)
* Third match: $\dots 66[697]7\dots$ (forward order)
* Fourth match: $\dots 77[796]6\dots$ (reverse order)

Counting these setups yields exactly $4$ occurrences.