How many pairs of letters are there in the word SEQUENTIAL which have as many letters between them in the word as they have between them in the English alphabet?

Introduction / Context:
Alphabet pair questions ask how many pairs of letters in a given word have the same spacing as in the standard alphabet. These problems are common in reasoning sections and test accuracy in counting and comparing positions. The word SEQUENTIAL must be examined for such pairs, which involves comparing both the positions of letters in the word and in the alphabet sequence from A to Z.

Given Data / Assumptions:
- Word given: SEQUENTIAL.
- We consider all possible ordered pairs of letters in the word, from left to right.
- For a valid pair, the number of letters between the two letters in the word must equal the number of letters between the same two letters in the alphabet.
- Alphabet positions are taken as A=1, B=2, ..., Z=26.

Concept / Approach:
We first assign each letter in SEQUENTIAL an alphabet position (S, E, Q, U, E, N, T, I, A, L). Then, for every pair of positions (i, j) where i is less than j, we compute the difference j − i for the word indices and compare it with the absolute difference in their alphabet positions. Whenever these two differences match, we count one valid pair. This systematic comparison prevents missing any suitable combination.

Step-by-Step Solution:
Step 1: Map letters to alphabet positions: S=19, E=5, Q=17, U=21, E=5, N=14, T=20, I=9, A=1, L=12. Step 2: Label the word positions from left to right as 1 to 10. Step 3: Check pairs and find where the number of letters between them in the word equals the alphabet spacing. The valid pairs are: (S, Q): positions (1, 3) with 1 letter between them in the word and alphabet positions 19 and 17, which also have one letter between. (S, N): positions (1, 6) with 4 letters between in the word and alphabet positions 19 and 14, which also have four letters between. (Q, N): positions (3, 6) with 2 letters between in the word and alphabet positions 17 and 14, which also have two letters between. (E, A): positions (5, 9) with 3 letters between in the word and alphabet positions 5 and 1, which also have three letters between. Step 4: Count these valid pairs. There are four such pairs in total.

Verification / Alternative check:
To verify, list all other pairs quickly and confirm they do not satisfy the condition. For example, (E at position 2, N at position 6) has three letters between them in the word but alphabet positions 5 and 14 have more than three letters between them, so this pair is invalid. A systematic scan confirms that only the four pairs identified earlier satisfy the matched spacing requirement.

Why Other Options Are Wrong:
- "One" underestimates the number of valid pairs and ignores several correct combinations.
- "Two" and "Three" similarly fail to recognise all valid pairs, indicating incomplete checking of the word.
Careful counting shows exactly four such pairs, not fewer.

Common Pitfalls:
Students sometimes count pairs only from a quick scan or stop after finding a couple of matches. Others confuse "number of letters between" with index difference, forgetting that being three positions apart means two letters between them. Writing out both word indices and alphabet positions clearly and computing differences carefully is the best way to avoid off by one errors and ensure full coverage of all possibilities.

Final Answer:
There are Four such pairs of letters in the word SEQUENTIAL that satisfy the given condition.