In the following series, how many times is $5$ immediately preceded by $6$ but NOT followed by $9$? $8976597365432887776596546598765$
Analyzing the Series for the Specific Pattern
The question asks us to find the number of times the digit $5$ appears immediately after the digit $6$ (forming the sequence $65$) but is NOT immediately followed by the digit $9$.
Identifying the Target Pattern
The pattern to find is:
- The sequence $65$ must be present.
- The digit immediately following $5$ must NOT be $9$.
We will examine the given series: $8976597365432887776596546598765$
Step-by-Step Pattern Search
Let's scan the series and identify occurrences of $65$ and check the condition:
- $897$$65$$9$: This $65$ is followed by $9$. This does not meet the condition "NOT followed by $9$".
- $73$$65$$4$: This $65$ is followed by $4$. This meets both conditions ($65$ present and not followed by $9$). Count = 1.
- $777$$65$$9$: This $65$ is followed by $9$. This does not meet the condition.
- $4$$65$$4$: This $65$ is followed by $4$. This meets both conditions. Count = 2.
- $4$$65$$9$: This $65$ is followed by $9$. This does not meet the condition.
- $87$$65$$: This $65$ is at the end of the series. It is not followed by any digit, therefore it is not followed by $9$. This meets both conditions. Count = 3.
Final Count
By scanning the series and applying the conditions, we found the pattern $65$ not followed by $9$ occurs $3$ times.
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