How many pairs of letters are there in the word **REVOLUTION** 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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**Solution:**

1. Write down the word: **REVOLUTION**

2. Assign positions to each letter in the word:
   - R(1), E(2), V(3), O(4), L(5), U(6), T(7), I(8), O(9), N(10)

3. For each pair of letters, calculate:
   - The number of letters between them in the word (i.e., difference in their positions minus 1)
   - The number of letters between them in the English alphabet (considering both forward and backward directions)

4. Check which pairs satisfy the condition that these two numbers are equal.

5. Example checks:
   - Pair (R, U): Positions 1 and 6
     - Letters between in word = 6 - 1 - 1 = 4
     - Alphabet positions: R(18), U(21)
     - Letters between in alphabet = 21 - 18 - 1 = 2 (forward), or 18 - 21 - 1 = negative (backward not valid)
     - Not equal.

- Pair (E, L): Positions 2 and 5
     - Letters between in word = 5 - 2 - 1 = 2
     - Alphabet positions: E(5), L(12)
     - Letters between in alphabet = 12 - 5 - 1 = 6
     - Not equal.

- Pair (V, T): Positions 3 and 7
     - Letters between in word = 7 - 3 - 1 = 3
     - Alphabet positions: V(22), T(20)
     - Letters between in alphabet = |22 - 20| - 1 = 1
     - Not equal.

- Pair (O, I): Positions 4 and 8
     - Letters between in word = 8 - 4 - 1 = 3
     - Alphabet positions: O(15), I(9)
     - Letters between in alphabet = |15 - 9| - 1 = 5
     - Not equal.

- Pair (L, O): Positions 5 and 9
     - Letters between in word = 9 - 5 - 1 = 3
     - Alphabet positions: L(12), O(15)
     - Letters between in alphabet = 15 - 12 - 1 = 2
     - Not equal.

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

**Answer:** More than three

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