How many pairs of letters are there in the word **PRESENCE**, each of which have as many letters between them as they have in the English alphabetical series (considering both forward and backward directions)?

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**Solution:**

1. The word is **P R E S E N C E**.

2. We need to find pairs of letters such that the number of letters between them in the word equals the number of letters between them in the English alphabet,![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755455794/aptidude_questions/bbhr0xataofcn6qbmy4n.png)either forward or backward.

3. Assign positions to each letter in the word:
   - P (1)
   - R (2)
   - E (3)
   - S (4)
   - E (5)
   - N (6)
   - C (7)
   - E (8)

4. Check pairs:
   - (P, S): Positions 1 and 4, letters between = 2 (positions 2 and 3)
     Alphabet positions: P(16), S(19), difference = 2 (19 - 16 - 1 = 2)
     Matches condition.

- (R, N): Positions 2 and 6, letters between = 3 (positions 3,4,5)
     Alphabet positions: R(18), N(14), difference = 3 (18 - 14 - 1 = 3)
     Matches condition (backward).

- (E, C): Positions 3 and 7, letters between = 3 (positions 4,5,6)
     Alphabet positions: E(5), C(3), difference = 1 (5 - 3 - 1 = 1)
     Does not match.

- (S, E): Positions 4 and 5, letters between = 0
     Alphabet positions: S(19), E(5), difference = 13
     Does not match.

- (E, E): Positions 3 and 5, letters between = 1 (position 4)
     Alphabet positions: E(5), E(5), difference = -1 (same letter)
     Does not match.

- (N, E): Positions 6 and 8, letters between = 1 (position 7)
     Alphabet positions: N(14), E(5), difference = 8
     Does not match.

5. The pairs that satisfy the condition are (P, S), (R, N), and (E, N) if checked carefully.

6. Re-check (E, N): Positions 3 and 6, letters between = 2 (positions 4,5)
   Alphabet positions: E(5), N(14), difference = 8
   No match.

7. So the valid pairs are:
   - (P, S)
   - (R, N)
   - (E, C) reconsidered:
     Positions 3 and 7, letters between = 3
     Alphabet positions: E(5), C(3), difference = 1
     No match.

8. Check (E, E) at positions 5 and 8:
   Letters between = 2 (positions 6,7)
   Alphabet positions: E(5), E(5), difference = -1
   No match.

9. Check (S, E) at positions 4 and 8:
   Letters between = 3 (positions 5,6,7)
   Alphabet positions: S(19), E(5), difference = 13
   No match.

10. Check (E, N) at positions 5 and 6:
    Letters between = 0
    Alphabet positions: E(5), N(14), difference = 8
    No match.

11. So only two pairs found so far: (P, S) and (R, N).

12. Check (E, C) again:
    Positions 5 and 7, letters between = 1 (position 6)
    Alphabet positions: E(5), C(3), difference = 1 (5 - 3 - 1 = 1)
    Matches condition.

13. Therefore, the three pairs are:
    - (P, S)
    - (R, N)
    - (E, C)

**Answer:** Three

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