How many pairs of letters are there in the word **MASCULINE** such that the number of letters between them in the word is the same as the number of letters between them in the English alphabetical order? Consider both forward and backward directions in the alphabet.

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Accepted Answer

**Solution:**

1. Write down the word: **M A S C U L I N E** (Positions 1 to 9).

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.

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 alphabetical order - 1).

4. Check pairs in both forward and backward alphabetical order.

5. Let's analyze pairs:

- M (13) and A (1): Positions 1 and 2, gap in word = 0, gap in alphabet = 11 (13-1-1=11) → No

- M (13) and S (19): Positions 1 and 3, gap in word = 1, gap in alphabet = 5 (19-13-1=5) → No

- M (13) and C (3): Positions 1 and 4, gap in word = 2, gap in alphabet = 9 (13-3-1=9) → No

- M (13) and U (21): Positions 1 and 5, gap in word = 3, gap in alphabet = 7 (21-13-1=7) → No

- M (13) and L (12): Positions 1 and 6, gap in word = 4, gap in alphabet = 0 (13-12-1=0) → No

- M (13) and I (9): Positions 1 and 7, gap in word = 5, gap in alphabet = 3 (13-9-1=3) → No

- M (13) and N (14): Positions 1 and 8, gap in word = 6, gap in alphabet = 0 (14-13-1=0) → No

- M (13) and E (5): Positions 1 and 9, gap in word = 7, gap in alphabet = 7 (13-5-1=7) → Yes (Pair 1)

- A (1) and S (19): Positions 2 and 3, gap in word = 0, gap in alphabet = 17 (19-1-1=17) → No

- A (1) and C (3): Positions 2 and 4, gap in word = 1, gap in alphabet = 1 (3-1-1=1) → Yes (Pair 2)

- A (1) and U (21): Positions 2 and 5, gap in word = 2, gap in alphabet = 19 (21-1-1=19) → No

- A (1) and L (12): Positions 2 and 6, gap in word = 3, gap in alphabet = 10 (12-1-1=10) → No

- A (1) and I (9): Positions 2 and 7, gap in word = 4, gap in alphabet = 7 (9-1-1=7) → No

- A (1) and N (14): Positions 2 and 8, gap in word = 5, gap in alphabet = 12 (14-1-1=12) → No

- A (1) and E (5): Positions 2 and 9, gap in word = 6, gap in alphabet = 3 (5-1-1=3) → No

- S (19) and C (3): Positions 3 and 4, gap in word = 0, gap in alphabet = 15 (19-3-1=15) → No

- S (19) and U (21): Positions 3 and 5, gap in word = 1, gap in alphabet = 1 (21-19-1=1) → Yes (Pair 3)

- S (19) and L (12): Positions 3 and 6, gap in word = 2, gap in alphabet = 6 (19-12-1=6) → No

- S (19) and I (9): Positions 3 and 7, gap in word = 3, gap in alphabet = 9 (19-9-1=9) → No

- S (19) and N (14): Positions 3 and 8, gap in word = 4, gap in alphabet = 4 (19-14-1=4) → Yes (Pair 4)

- S (19) and E (5): Positions 3 and 9, gap in word = 5, gap in alphabet = 13 (19-5-1=13) → No

- C (3) and U (21): Positions 4 and 5, gap in word = 0, gap in alphabet = 17 (21-3-1=17) → No

- C (3) and L (12): Positions 4 and 6, gap in word = 1, gap in alphabet = 8 (12-3-1=8) → No

- C (3) and I (9): Positions 4 and 7, gap in word = 2, gap in alphabet = 5 (9-3-1=5) → No

- C (3) and N (14): Positions 4 and 8, gap in word = 3, gap in alphabet = 10 (14-3-1=10) → No

- C (3) and E (5): Positions 4 and 9, gap in word = 4, gap in alphabet = 1 (5-3-1=1) → No

- U (21) and L (12): Positions 5 and 6, gap in word = 0, gap in alphabet = 8 (21-12-1=8) → No

- U (21) and I (9): Positions 5 and 7, gap in word = 1, gap in alphabet = 11 (21-9-1=11) → No

- U (21) and N (14): Positions 5 and 8, gap in word = 2, gap in alphabet = 6 (21-14-1=6) → No

- U (21) and E (5): Positions 5 and 9, gap in word = 3, gap in alphabet = 15 (21-5-1=15) → No

- L (12) and I (9): Positions 6 and 7, gap in word = 0, gap in alphabet = 2 (12-9-1=2) → No

- L (12) and N (14): Positions 6 and 8, gap in word = 1, gap in alphabet = 1 (14-12-1=1) → Yes (Pair 5)

- L (12) and E (5): Positions 6 and 9, gap in word = 2, gap in alphabet = 6 (12-5-1=6) → No

- I (9) and N (14): Positions 7 and 8, gap in word = 0, gap in alphabet = 4 (14-9-1=4) → No

- I (9) and E (5): Positions 7 and 9, gap in word = 1, gap in alphabet = 3 (9-5-1=3) → No

- N (14) and E (5): Positions 8 and 9, gap in word = 0, gap in alphabet = 8 (14-5-1=8) → No

6. The pairs that satisfy the condition are:
   - (M, E)
   - (A, C)
   - (S, U)
   - (S, N)
   - (L, N)

7. Total such pairs = **5**.

**Answer:** Five

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