Find 5s Preceded by 7 and Followed by 6

The question asks us to find the number of times the digit '5' appears in the given sequence such that it has '7' immediately before it and '6' immediately after it. This means we are looking for the specific three-digit pattern '756' within the sequence.

Let's look at the given number sequence:

5 6 4 6 4 5 6 4 6 7 7 5 6 4 5 7 5 4 4 5 7 4 6 5 4

We need to examine the sequence from left to right and identify instances where a '5' is present, and then check if the number before it is '7' and the number after it is '6'.

Let's scan the sequence and highlight any occurrences of the pattern '756':

• Starting from the beginning, we look for '756'.
• Sequence: 5 6 4 6 4 5 6 4 6 7 7 5 6 4 5 7 5 4 4 5 7 4 6 5 4
• We can see the pattern '756' appears at one place in the sequence. The '5' is immediately preceded by '7' and immediately followed by '6'.

Let's list all the '5's and check their neighbors:

• The first '5' is at the beginning. It is followed by 6, but not preceded by 7.
• The second '5' is followed by 6, but not preceded by 7.
• The third '5' is in '7 7 5 6'. This '5' is preceded by a '7' and followed by a '6'. This matches the condition.
• The fourth '5' is preceded by 4 and followed by 7. Does not match the condition.
• The fifth '5' is preceded by 7 and followed by 4. Does not match the condition.
• The sixth '5' is preceded by 4 and followed by 7. Does not match the condition.
• The seventh '5' is preceded by 6 and followed by 4. Does not match the condition.

By carefully scanning the sequence and checking the numbers immediately before and after each '5', we find only one instance where '5' is immediately preceded by '7' and immediately followed by '6'. This instance is the sequence '756'.

Therefore, there is only one such '5' in the given number sequence.

The count is 1.