How many 3's are there in the given series which are immediately preceded by 9 as well as immediately followed by 6 ?
`9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6`

Options

A. None
B. One
C. Two
D. More than two

Answer

To solve the problem of how many 3's are there in the given series that are immediately preceded by 9 and immediately followed by 6, we can follow these steps:

### Step 1: Write down the series
The given series is:
`9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6`

### Step 2: Identify the positions of 3's in the series
We will look for all occurrences of the number 3 in the series:
- The positions of 3's are:
- 3 at index 2 (9 6 **3** 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6)
- 3 at index 6 (9 6 3 5 4 9 **3** 3 6 9 3 6 3 9 9 3 3 6 9 3 6)
- 3 at index 7 (9 6 3 5 4 9 3 **3** 6 9 3 6 3 9 9 3 3 6 9 3 6)
- 3 at index 9 (9 6 3 5 4 9 3 3 **6** 9 3 6 3 9 9 3 3 6 9 3 6)
- 3 at index 10 (9 6 3 5 4 9 3 3 6 **9** 3 6 3 9 9 3 3 6 9 3 6)
- 3 at index 12 (9 6 3 5 4 9 3 3 6 9 **3** 6 3 9 9 3 3 6 9 3 6)
- 3 at index 14 (9 6 3 5 4 9 3 3 6 9 3 **6** 3 9 9 3 3 6 9 3 6)
- 3 at index 15 (9 6 3 5 4 9 3 3 6 9 3 6 **3** 9 9 3 3 6 9 3 6)
- 3 at index 16 (9 6 3 5 4 9 3 3 6 9 3 6 3 **9** 9 3 3 6 9 3 6)
- 3 at index 17 (9 6 3 5 4 9 3 3 6 9 3 6 3 9 **9** 3 3 6 9 3 6)
- 3 at index 18 (9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 **3** 3 6 9 3 6)
- 3 at index 19 (9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 **6** 9 3 6)

### Step 3: Check for the condition
Now, we need to check which of these 3's are immediately preceded by 9 and immediately followed by 6:
- The 3 at index 2 is preceded by 9 and followed by 6 (valid).
- The 3 at index 6 is preceded by 9 but followed by 3 (invalid).
- The 3 at index 7 is preceded by 9 but followed by 6 (valid).
- The 3 at index 9 is preceded by 6 (invalid).
- The 3 at index 10 is preceded by 9 but followed by 6 (valid).
- The 3 at index 12 is preceded by 6 (invalid).
- The 3 at index 14 is preceded by 9 but followed by 6 (valid).
- The 3 at index 15 is preceded by 6 (invalid).
- The 3 at index 16 is preceded by 9 but followed by 9 (invalid).
- The 3 at index 17 is preceded by 9 but followed by 3 (invalid).
- The 3 at index 18 is preceded by 9 but followed by 6 (valid).
- The 3 at index 19 is preceded by 6 (invalid).

### Step 4: Count the valid occurrences
From our checks, the valid occurrences of 3 that are preceded by 9 and followed by 6 are:
- 3 at index 2
- 3 at index 7
- 3 at index 10
- 3 at index 14
- 3 at index 18

Thus, there are **5 valid occurrences** of 3 in the series that meet the criteria.

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

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