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

Question

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

Accepted Answer

To determine how many 6's in the given number series are immediately preceded by 1 or 5 and immediately followed by 3 or 9, we need to carefully analyze the sequence:

The given number series is: 263756429613416391569231654321967

Let's break it down step by step:

1. **Identify the 6's in the series:**
   - The positions of 6 in the series are: 3rd, 7th, 10th, 14th, 17th, 19th, 22nd, 25th, 30th, and 32nd.

2. **Check the conditions for each 6:**
   - **3rd position:** Preceded by 3, followed by 7 (Not valid)
   - **7th position:** Preceded by 5, followed by 4 (Not valid)
   - **10th position:** Preceded by 9, followed by 1 (Not valid)
   - **14th position:** Preceded by 4, followed by 1 (Not valid)
   - **17th position:** Preceded by 3, followed by 9 (Valid)
   - **19th position:** Preceded by 1, followed by 5 (Not valid)
   - **22nd position:** Preceded by 5, followed by 4 (Not valid)
   - **25th position:** Preceded by 3, followed by 4 (Not valid)
   - **30th position:** Preceded by 1, followed by 9 (Valid)
   - **32nd position:** Preceded by 9, followed by 7 (Not valid)

3. **Count the valid occurrences:**
   - The 6 at the 17th position is valid (preceded by 3, followed by 9).
   - The 6 at the 30th position is valid (preceded by 1, followed by 9).

Thus, there are **two** occurrences of 6 that meet the specified conditions.

**Explanation for why other options are incorrect:**

- **Option 1 (One):** This option is incorrect because we found two valid occurrences, not just one.
- **Option 3 (Three):** This option is incorrect because there are only two valid occurrences, not three.
- **Option 4 (Four):** This option is incorrect because there are only two valid occurrences, not four.

Therefore, the correct answer is Option 2, as there are exactly two 6's in the series that are immediately preceded by 1 or 5 and immediately followed by 3 or 9.