In the word **CHAIRMAN**, how many pairs of letters have the same number of letters between them in the word as they do in the English alphabet? Consider both forward and backward directions.

Question

Accepted Answer

**Solution:**

1. Write down the word: **C H A I R M A N**

2. Identify all possible pairs of letters and count the number of letters between them in the word.

3. For each pair, check the number of letters between them in the English alphabet.

4. The pairs that have the same number of letters between them in both the word and the alphabet are counted.

Let's analyze the pairs:

- Pair (C, H): In the word, letters between C and H are H is 2nd letter, C is 1st, so 0 letters between. In alphabet, C(3), H(8), letters between = 8 - 3 - 1 = 4, not equal.

- Pair (H, A): Positions 2 and 3, 0 letters between in word; H(8), A(1), letters between = 6 (since backward), not equal.

- Pair (A, I): Positions 3 and 4, 0 letters between; A(1), I(9), letters between = 7, no.

- Pair (I, R): Positions 4 and 5, 0 letters between; I(9), R(18), letters between = 8, no.

- Pair (R, M): Positions 5 and 6, 0 letters between; R(18), M(13), letters between = 4 (backward), no.

- Pair (M, A): Positions 6 and 7, 0 letters between; M(13), A(1), letters between = 11 (backward), no.

- Pair (A, N): Positions 7 and 8, 0 letters between; A(1), N(14), letters between = 12, no.

Now check pairs with letters between:

- Pair (C, A): Positions 1 and 3, letters between = 1 (H)
  Alphabet: C(3), A(1), letters between = 1 (backward), matches.

- Pair (H, I): Positions 2 and 4, letters between = 1 (A)
  Alphabet: H(8), I(9), letters between = 0, no.

- Pair (A, R): Positions 3 and 5, letters between = 1 (I)
  Alphabet: A(1), R(18), letters between = 16, no.

- Pair (I, M): Positions 4 and 6, letters between = 1 (R)
  Alphabet: I(9), M(13), letters between = 3, no.

- Pair (R, A): Positions 5 and 7, letters between = 1 (M)
  Alphabet: R(18), A(1), letters between = 16 (backward), no.

- Pair (M, N): Positions 6 and 8, letters between = 1 (A)
  Alphabet: M(13), N(14), letters between = 0, no.

- Pair (C, I): Positions 1 and 4, letters between = 2 (H, A)
  Alphabet: C(3), I(9), letters between = 5, no.

- Pair (H, R): Positions 2 and 5, letters between = 2 (A, I)
  Alphabet: H(8), R(18), letters between = 9, no.

- Pair (A, M): Positions 3 and 6, letters between = 2 (I, R)
  Alphabet: A(1), M(13), letters between = 11, no.

- Pair (I, A): Positions 4 and 7, letters between = 2 (R, M)
  Alphabet: I(9), A(1), letters between = 7 (backward), no.

- Pair (R, N): Positions 5 and 8, letters between = 2 (M, A)
  Alphabet: R(18), N(14), letters between = 3 (backward), no.

- Pair (C, R): Positions 1 and 5, letters between = 3 (H, A, I)
  Alphabet: C(3), R(18), letters between = 14, no.

- Pair (H, M): Positions 2 and 6, letters between = 3 (A, I, R)
  Alphabet: H(8), M(13), letters between = 4, no.

- Pair (A, A): Positions 3 and 7, letters between = 3 (I, R, M)
  Alphabet: A(1), A(1), letters between = 0, no.

- Pair (I, N): Positions 4 and 8, letters between = 3 (R, M, A)
  Alphabet: I(9), N(14), letters between = 4, no.

From above, only the pair (C, A) satisfies the condition.

Check one more pair:

- Pair (H, N): Positions 2 and 8, letters between = 5 (A, I, R, M, A)
  Alphabet: H(8), N(14), letters between = 5, matches.

So, pairs are (C, A) and (H, N).

**Answer:** Two pairs satisfy the condition.

Answer

Answer

Answer