To solve the problem step by step, we will follow these instructions:
### Step 1: Interchange the terms of the sequence
The original sequence is:
6, 7, 4, 8, 5, 8, 8, 4, 8, 3, 2, 5, 8, 6, 7, 8, 3, 8
We need to interchange the 1st term with the 2nd, the 3rd with the 4th, and so on.
- Interchanging:
1st with 2nd: 7, 6
3rd with 4th: 8, 4
5th with 6th: 8, 8
7th with 8th: 4, 8
9th with 10th: 3, 2
11th with 12th: 5, 8
13th with 14th: 6, 7
15th with 16th: 8, 3
17th with 18th: 8,
The new sequence after interchanging will be:
7, 6, 8, 4, 8, 8, 4, 8, 3, 2, 5, 8, 6, 7, 8, 3, 8
### Step 2: Identify the 8s in the new sequence
From the new sequence, we can see the positions of 8s:
- 3rd position: 8
- 5th position: 8
- 6th position: 8
- 8th position: 8
- 12th position: 8
- 14th position: 8
- 16th position: 8
So, there are a total of **7** occurrences of 8 in the new sequence.
### Step 3: Check divisibility of each 8 by its left and right neighbors
Now, we need to check each 8 to see if it is divisible by the numbers on its left and right:
1. **3rd position (8)**: Left = 6, Right = 4
- 8 is not divisible by 6 (8 % 6 ≠ 0)
2. **5th position (8)**: Left = 8, Right = 8
- 8 is divisible by both (8 % 8 = 0)
3. **6th position (8)**: Left = 8, Right = 4
- 8 is not divisible by 8 (8 % 8 = 0) but is divisible by 4 (8 % 4 = 0)
4. **8th position (8)**: Left = 4, Right = 3
- 8 is divisible by 4 (8 % 4 = 0) but not by 3 (8 % 3 ≠ 0)
5. **12th position (8)**: Left = 5, Right = 6
- 8 is not divisible by 5 (8 % 5 ≠ 0)
6. **14th position (8)**: Left = 6, Right = 3
- 8 is not divisible by 6 (8 % 6 ≠ 0)
7. **16th position (8)**: Left = 7, Right = None (no right neighbor)
- Cannot be checked as there is no right neighbor.
### Step 4: Count the 8s that are divisible by both neighbors
From the checks:
- Only the 5th position 8 is divisible by both its left (8) and right (8).
Thus, there is **only 1** occurrence of 8 that is divisible by both its left and right neighbors.
### Final Answer
The total number of 8s that are divisible by the number on their left as well as their right is **1**.
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