To solve the problem of how many 6s in the given sequence are immediately preceded by 3 but not immediately followed by 0, we will follow these steps:
### Step 1: Write down the sequence
The sequence given is:
0, 3, 6, 9, 0, 6, 9, 3, 6, 9, 3, 6, 6, 3, 3, 6, 0, 6, 3, 3, 6, 0
### Step 2: Identify the occurrences of 6
Next, we will identify all the occurrences of the number 6 in the sequence:
- The positions of 6s are: 2, 5, 8, 11, 12, 15, 17, 19, 21
### Step 3: Check for 3 preceding each 6
Now, we will check which of these 6s are immediately preceded by 3:
- 6 at position 2: Preceded by 0 (not counted)
- 6 at position 5: Preceded by 9 (not counted)
- 6 at position 8: Preceded by 3 (counted)
- 6 at position 11: Preceded by 3 (counted)
- 6 at position 12: Preceded by 6 (not counted)
- 6 at position 15: Preceded by 3 (counted)
- 6 at position 17: Preceded by 0 (not counted)
- 6 at position 19: Preceded by 6 (not counted)
- 6 at position 21: Preceded by 3 (counted)
So, the 6s that are preceded by 3 are at positions 8, 11, 15, and 21.
### Step 4: Check if these 6s are followed by 0
Now, we will check if these 6s are immediately followed by 0:
- 6 at position 8: Followed by 9 (not counted)
- 6 at position 11: Followed by 6 (not counted)
- 6 at position 15: Followed by 0 (not counted)
- 6 at position 21: Followed by 0 (not counted)
### Step 5: Count the valid occurrences
From our findings:
- 6 at position 8 is valid (preceded by 3, not followed by 0)
- 6 at position 11 is valid (preceded by 3, not followed by 0)
Thus, the total count of 6s that are immediately preceded by 3 but not immediately followed by 0 is **2**.
### Conclusion
Since none of the 6s that are preceded by 3 are valid as they are all followed by 0, the answer is **0**.
