How many pairs of letters are there in the word **STRUGGLING**, such that the number of letters between them in the word is equal to the number of letters between them in the English alphabet? Consider both forward and backward directions in the alphabet.

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Accepted Answer

**Solution:**

1. Write down the word with letter positions:

S(1) T(2) R(3) U(4) G(5) G(6) L(7) I(8) N(9) G(10)

2. We need to find pairs of letters where the number of letters between them in the word equals the number of letters between them in the English alphabet.

3. For each pair, calculate:
   - The gap between their positions in the word (number of letters between = difference in positions - 1)
   - The gap between their alphabetical positions (difference in alphabet indices)

4. Check both forward and backward directions in the alphabet.

5. Example checks:
   - Pair (S, U): Positions 1 and 4, letters between = 2
     Alphabet positions: S(19), U(21), difference = 2
     Matches!

- Pair (T, R): Positions 2 and 3, letters between = 0
     Alphabet positions: T(20), R(18), difference = 2
     No match.

- Pair (R, U): Positions 3 and 4, letters between = 0
     Alphabet positions: R(18), U(21), difference = 3
     No match.

- Pair (G, L): Positions 5 and 7, letters between = 1
     Alphabet positions: G(7), L(12), difference = 5
     No match.

- Pair (L, I): Positions 7 and 8, letters between = 0
     Alphabet positions: L(12), I(9), difference = 3
     No match.

- Pair (I, N): Positions 8 and 9, letters between = 0
     Alphabet positions: I(9), N(14), difference = 5
     No match.

- Pair (N, G): Positions 9 and 10, letters between = 0
     Alphabet positions: N(14), G(7), difference = 7
     No match.

6. By checking all possible pairs, we find more than three such pairs satisfying the condition.

**Answer:** More than three

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