Number Series Analysis

The given number series is: $6 2 1 5 7 3 7 8 5 3 4 5 2 4 8 4 3 6 9 7 4 2 1 5 7 9 1$

The question asks us to find the count of specific odd digits within this series. The criteria for counting an odd digit are:

• The digit itself must be odd.
• The digit immediately preceding it must be an even digit.
• The digit immediately following it must be an odd digit.

Essentially, we are looking for the pattern: $Even Digit - Odd Digit - Odd Digit$. We need to count how many times the middle 'Odd Digit' in this specific sequence appears.

Identifying and Counting Occurrences

Let's analyze the series from left to right, looking for the $Even - Odd - Odd$ pattern:

• $6 2 1 5$: The sequence is $2 1 5$. The digit 1 is odd. It is preceded by 2 (even) and followed by 5 (odd). This fits the criteria. (Count: 1)
• $7 3 7$: The digit 3 is odd, but it's preceded by 7 (odd). This does not fit the criteria.
• $7 8 5 3$: The sequence is $8 5 3$. The digit 5 is odd. It is preceded by 8 (even) and followed by 3 (odd). This fits the criteria. (Count: 2)
• $3 4 5 2$: The digit 5 is odd, but it's followed by 2 (even). This does not fit the criteria.
• $4 8 4 3$: The digit 3 is odd, but it's followed by 6 (even). This does not fit the criteria.
• $6 9 7$: The sequence is $6 9 7$. The digit 9 is odd. It is preceded by 6 (even) and followed by 7 (odd). This fits the criteria. (Count: 3)
• $4 2 1 5$: The sequence is $2 1 5$. The digit 1 is odd. It is preceded by 2 (even) and followed by 5 (odd). This fits the criteria. (Count: 4)
• $5 7 9 1$: All digits in this segment ($5 7 9$ and $7 9 1$) are odd. Therefore, none of them are preceded by an even digit. No matches here.

Final Count Calculation

By systematically checking the series against the required pattern (Even - Odd - Odd), we found exactly 4 instances that satisfy all the conditions.

The odd digits fulfilling the criteria are:

• The digit 1 (in the sequence 2 1 5)
• The digit 5 (in the sequence 8 5 3)
• The digit 9 (in the sequence 6 9 7)
• The digit 1 (in the sequence 2 1 5)

Therefore, the total count is 4.