In the following series of numbers, find out how many times 1, 3 and 7 have appeared together, 7 being in the middle and 1 and 3 on either side of 7 .
2 9 7 3 1 7 3 7 7 1 3 3 1 7 3 8 5 7 1 3 7 7 1 7 3 9 0 6

Options

A. 3
B. 4
C. 5
D. more than 5

Explanation

To solve the problem of how many times the numbers 1, 3, and 7 appear together in the specified arrangement (with 7 in the middle, and 1 and 3 on either side), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Series**:
The given series of numbers is:
```
2, 9, 7, 3, 1, 7, 3, 1, 7, 3, 1, 7, 3, 1, 7, 3, 8, 5, 7, 1, 3, 7, 1, 7, 3, 9, 0, 6
```

2. **Look for the Pattern**:
We are looking for the pattern where 7 is in the middle, and 1 and 3 are on either side of 7. This means we are looking for the sequences of the form:
```
1, 7, 3
```
or
```
3, 7, 1
```

3. **Scan through the Series**:
We will scan through the series and check each triplet of numbers to see if they match the required pattern.

- Starting from the first number, we check each triplet:
- (2, 9, 7) → Not a match
- (9, 7, 3) → Not a match
- (7, 3, 1) → Not a match
- (3, 1, 7) → Not a match
- (1, 7, 3) → **Match found!**
- (7, 3, 1) → **Match found!**
- (3, 1, 7) → Not a match
- (1, 7, 3) → **Match found!**
- (7, 3, 1) → **Match found!**
- (3, 1, 7) → Not a match
- (1, 7, 3) → **Match found!**
- (7, 3, 8) → Not a match
- (3, 8, 5) → Not a match
- (8, 5, 7) → Not a match
- (5, 7, 1) → Not a match
- (7, 1, 3) → **Match found!**
- (1, 3, 7) → **Match found!**
- (3, 7, 1) → **Match found!**
- (7, 1, 7) → Not a match
- (1, 7, 3) → **Match found!**
- (7, 3, 9) → Not a match
- (3, 9, 0) → Not a match
- (9, 0, 6) → Not a match

4. **Count the Matches**:
After scanning through the series, we find that the patterns occur **5 times**:
- 1, 7, 3
- 3, 7, 1
- 1, 7, 3
- 3, 7, 1
- 1, 7, 3

### Final Answer:
The numbers 1, 3, and 7 appear together in the specified arrangement **5 times**.