In the word ‘BONAFIDE’, how many pairs of letters have the same number of letters between them (both forward and backward direction) as in the alphabetical series?

The correct answer is More than Four.

We need to find all pairs of letters in the word BONAFIDE such that the number of letters between them in the word equals the number of letters between them in the English alphabet (considering both forward and backward directions in the alphabet).

Step 1 – Map the word to positions.

Write out each letter with its position in the word and its position in the alphabet:

B(pos 1, alpha 2)  –  O(pos 2, alpha 15)  –  N(pos 3, alpha 14)  –  A(pos 4, alpha 1)  –  F(pos 5, alpha 6)  –  I(pos 6, alpha 9)  –  D(pos 7, alpha 4)  –  E(pos 8, alpha 5)

Step 2 – Define the rule.

For any two letters at word-positions i and j (i < j) with alphabet values a and b:
  • Letters between them in word = (j - i - 1)
  • Letters between them in alphabet = |a - b| - 1
A pair qualifies when both counts are equal.

Step 3 – Check all pairs systematically.

Pair: B (pos 1) and F (pos 5)
Word gap = 5 - 1 - 1 = 3 (letters O, N, A lie between them)
Alphabet gap = |2 - 6| - 1 = 4 - 1 = 3 (letters C, D, E lie between B and F)
✅ Match!

Pair: O (pos 2) and N (pos 3)
Word gap = 3 - 2 - 1 = 0 (adjacent in word)
Alphabet gap = |15 - 14| - 1 = 1 - 1 = 0 (N and O are adjacent in alphabet)
✅ Match!

Pair: A (pos 4) and D (pos 7)
Word gap = 7 - 4 - 1 = 2 (letters F, I lie between them)
Alphabet gap = |1 - 4| - 1 = 3 - 1 = 2 (letters B, C lie between A and D)
✅ Match!

Pair: A (pos 4) and E (pos 8)
Word gap = 8 - 4 - 1 = 3 (letters F, I, D lie between them)
Alphabet gap = |1 - 5| - 1 = 4 - 1 = 3 (letters B, C, D lie between A and E)
✅ Match!

Pair: F (pos 5) and D (pos 7)
Word gap = 7 - 5 - 1 = 1 (letter I lies between them)
Alphabet gap = |6 - 4| - 1 = 2 - 1 = 1 (letter E lies between D and F)
✅ Match!

Pair: D (pos 7) and E (pos 8)
Word gap = 8 - 7 - 1 = 0 (adjacent in word)
Alphabet gap = |4 - 5| - 1 = 1 - 1 = 0 (D and E are adjacent in alphabet)
✅ Match!

Step 4 – Count the qualifying pairs.

1. B … F (3 letters between, both in word and alphabet)
2. O … N (0 letters between, both adjacent)
3. A … D (2 letters between, both in word and alphabet)
4. A … E (3 letters between, both in word and alphabet)
5. F … D (1 letter between, both in word and alphabet)
6. D … E (0 letters between, both adjacent)

There are 6 qualifying pairs, which is greater than four. Therefore, the answer is More than Four.