Analyzing Number Series for Specific Digit Patterns

The task is to count instances of the digit $\text{7}$ in the given series that satisfy two conditions:

• The digit $\text{7}$ must be immediately preceded by the digit $\text{8}$.
• The digit $\text{7}$ must NOT be immediately followed by the digit $\text{3}$.

Series Scan for Qualifying 7s

The series is: $898762263269732872778747794$

We need to find occurrences of $\text{7}$ where the preceding digit is $\text{8}$ and the succeeding digit is not $\text{3}$.

Let's examine the series segment by segment:

• $...876...$: Here, $\text{7}$ is preceded by $\text{8}$ and followed by $\text{6}$. Since $\text{6}$ is not $\text{3}$, this instance counts. (Count = 1)
• $...73...$: Here, $\text{7}$ is followed by $\text{3}$. This does not meet the second condition. It also doesn't meet the first condition as it is preceded by $\text{7}$, not $\text{8}$.
• $...872...$: Here, $\text{7}$ is preceded by $\text{8}$ and followed by $\text{2}$. Since $\text{2}$ is not $\text{3}$, this instance counts. (Count = 2)
• $...778...$: The first $\text{7}$ is preceded by $\text{2}$ (not $\text{8}$). The second $\text{7}$ is preceded by $\text{7}$ (not $\text{8}$). Neither meets the first condition.
• $...874...$: Here, $\text{7}$ is preceded by $\text{8}$ and followed by $\text{4}$. Since $\text{4}$ is not $\text{3}$, this instance counts. (Count = 3)
• $...779...$: The first $\text{7}$ is preceded by $\text{4}$ (not $\text{8}$). The second $\text{7}$ is preceded by $\text{7}$ (not $\text{8}$). Neither meets the first condition.

After scanning the entire series, there are exactly 3 occurrences of the digit $\text{7}$ that meet both specified conditions.