How many letters A are there in the following sequence which are immediately followed by B and also immediately preceded by Z: A M B Z A N A A B Z A B A Z B A P Z A B A Z A B?

Introduction / Context:
This question is a typical example of pattern counting in a sequence of letters. We must focus on occurrences of a specific letter, A, that satisfy two simultaneous conditions: each such A must be immediately preceded by Z and immediately followed by B. Such questions test not only counting skills but also attention to local patterns around each target letter.

Given Data / Assumptions:
- Sequence: A M B Z A N A A B Z A B A Z B A P Z A B A Z A B.
- We look only at the letter A in this sequence.
- For a qualifying A, the letter just before it must be Z, and the letter just after it must be B.
- Positions at the very beginning or end that cannot have both neighbours do not qualify.

Concept / Approach:
The strategy is to scan through the sequence from left to right, identify each position where the letter is A, and then check the letters immediately before and after that position. If both conditions (preceded by Z and followed by B) are satisfied, we count that A. Writing the sequence with indices helps avoid miscounting, especially when similar patterns appear several times.

Step-by-Step Solution:
Step 1: Write the sequence with positions: 1 A, 2 M, 3 B, 4 Z, 5 A, 6 N, 7 A, 8 A, 9 B, 10 Z, 11 A, 12 B, 13 A, 14 Z, 15 B, 16 A, 17 P, 18 Z, 19 A, 20 B, 21 A, 22 Z, 23 A, 24 B. Step 2: Inspect each A position and check its neighbours: - Position 1: A has no letter before it, so it cannot qualify. - Position 5: preceded by Z (position 4) and followed by N (position 6). The next letter is not B, so this A does not qualify. - Position 7: preceded by N and followed by A; the left neighbour is not Z, so this A does not qualify. - Position 8: preceded by A and followed by B; again, the left neighbour is not Z. - Position 11: preceded by Z (position 10) and followed by B (position 12). This A qualifies. - Position 13: preceded by B and followed by Z; the right neighbour is not B, so this A does not qualify. - Position 16: preceded by B and followed by P; neither neighbour pattern matches Z and B together. - Position 19: preceded by Z (position 18) and followed by B (position 20). This A qualifies. - Position 21: preceded by B and followed by Z; the right neighbour is not B. - Position 23: preceded by Z (position 22) and followed by B (position 24). This A qualifies. Step 3: Count all qualifying A positions: 11, 19, and 23. There are three in total.

Verification / Alternative check:
Another quick method is to scan for the pattern Z A B directly in the sequence and count how many times it appears. Observing the sequence, we find Z A B at positions (10, 11, 12), (18, 19, 20), and (22, 23, 24). Each occurrence corresponds to one A that is preceded by Z and followed by B. Since there are exactly three such triples, this confirms the earlier count of three qualifying A letters.

Why Other Options Are Wrong:
- "Two" and "One" underestimate the number of A letters that satisfy both conditions and result from incomplete scanning.
- "More than three" would require finding a fourth Z A B pattern, which does not exist in the given sequence.
Careful inspection shows that exactly three A letters meet the criteria.

Common Pitfalls:
Candidates sometimes forget that both conditions must be met simultaneously and count A letters that have either Z before or B after, but not both. Another common error is overlapping patterns: one can mistakenly double count or misalign Z A B triples. The safest approach is to write indices, carefully check neighbours around each A, or search for Z A B sequences directly in a systematic way.

Final Answer:
There are Three A letters in the sequence that are immediately preceded by Z and immediately followed by B.