Digit pattern counting — exact adjacency rule How many 3's appear in the list below that are immediately followed by 9 and immediately preceded by 2, 3, or 4? 1 1 2 3 9 4 4 5 5 5 5 3 3 9 8 7 7 7 8 8 8 5 5 4 3 9 6 6 6 6

Introduction / Context:This is a local-pattern counting problem: we must scan each occurrence of the digit 3 and check two immediate neighbors — the one just before and the one just after — against the stated condition.

Given Data / Assumptions:

• Sequence: 1 1 2 3 9 4 4 5 5 5 5 3 3 9 8 7 7 7 8 8 8 5 5 4 3 9 6 6 6 6
• Count only those 3's with: left neighbor in {2,3,4} and right neighbor = 9.

Concept / Approach:Index the sequence, find indices where value = 3, then check immediate neighbors.

Step-by-Step Solution:3's are at positions 4, 12, 13, 25 (0-based reasoning avoided; we use the visible order).Pos 4: left=2 (valid), right=9 (valid) ⇒ count.Pos 12: left=5 (invalid), right=3 ⇒ reject.Pos 13: left=3 (valid), right=9 (valid) ⇒ count.Pos 25: left=4 (valid), right=9 (valid) ⇒ count.

Verification / Alternative check:Re-scan with a ruler/underline to ensure only those three positions satisfy both neighbor conditions.

Why Other Options Are Wrong:1 or 2 undercounts (misses qualifying 3's); 4 overcounts (includes a 3 without valid neighbors).

Common Pitfalls:Accidentally counting a 3 where the follower is not 9 or where the predecessor is 5 (disallowed).

Final Answer:3