How many pairs of letters are there in the word “DIPLOMAT” which have as many letters between them in the word as in the English alphabetical series (in both forward and backward directions)?

The correct answer is Two.

To find the pairs of letters in the word “DIPLOMAT” that have as many letters between them in the word as in the English alphabetical series (in both forward and backward directions), let us first analyze the position of each letter in the word along with its position in the English alphabet:

• D : Position in word = 1, Alphabet position = 4
• I : Position in word = 2, Alphabet position = 9
• P : Position in word = 3, Alphabet position = 16
• L : Position in word = 4, Alphabet position = 12
• O : Position in word = 5, Alphabet position = 15
• M : Position in word = 6, Alphabet position = 13
• A : Position in word = 7, Alphabet position = 1
• T : Position in word = 8, Alphabet position = 20

Now, let us evaluate the distance between pairs of letters:

1. Forward Pair (I - M):

• I is at position 2 and M is at position 6 in the word.

The difference in positions in the word is

$6-2=4$

The difference in their alphabetical positions is

$13-9=4$

Since both differences are equal (there are 3 letters between them in both cases), (I, M) forms a valid pair in the forward direction.

2. Backward Pair (P - M):

• P is at position 3 and M is at position 6 in the word.

The difference in positions in the word is

$6-3=3$

The difference in their alphabetical positions is

$16-13=3$

Counting backwards from M to P in the alphabet (M, N, O, P), there are 2 letters between them, which matches the 2 letters (L, O) between P and M in the word. Thus, (P, M) forms a valid pair in the backward direction.

Checking all other letter combinations reveals no additional matching pairs.

Therefore, there are a total of 2 such pairs of letters (I-M and P-M).