How many 6's are there in the following number series, each of which is immediately preceded by 1 or 5 and immediately followed by 3 or 9?
263756429613416391569231654321967

Options

A. One
B. Two
C. Three
D. Four

Answer

To solve the problem of how many 6's in the number series are immediately preceded by 1 or 5 and immediately followed by 3 or 9, we will go through the series step by step.

### Step 1: Identify the number series
The number series given is:
**263756429613416391569231654321967**

### Step 2: Locate all occurrences of the digit '6'
We will scan through the series to find all the positions of '6':
- The positions of '6' in the series are:
2637**56**42961341**6**391569231654321967
(The '6's are at positions 5 and 13)

### Step 3: Check the conditions for each '6'
We need to check if each '6' is preceded by either '1' or '5' and followed by either '3' or '9'.

1. **First '6' at position 5**:
- Preceded by '5' (which satisfies the condition of being '1' or '5')
- Followed by '4' (which does not satisfy the condition of being '3' or '9')
- **Conclusion**: This '6' does NOT meet the criteria.

2. **Second '6' at position 13**:
- Preceded by '1' (which satisfies the condition of being '1' or '5')
- Followed by '3' (which satisfies the condition of being '3' or '9')
- **Conclusion**: This '6' meets the criteria.

### Step 4: Count the valid occurrences
From our checks, we found:
- The first '6' does not satisfy the conditions.
- The second '6' does satisfy the conditions.

Thus, there is **1 valid occurrence of '6'** that meets the criteria.

### Final Answer
The total number of '6's that are immediately preceded by 1 or 5 and immediately followed by 3 or 9 is **1**.

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