Determine the count of letter pairs in the specified word based on their alphabetical spacing.
How many pairs of letters are there in the word ‘PROBLEM’, each of which has the same number of letters between them in the word as in the English alphabetical series (in both forward and backward directions)?

The correct option is Two.

To find the pairs of letters in the word PROBLEM that have the same number of letters between them as in the English alphabetical series (in both forward and backward directions), let us examine the alphabetical positions of each letter in the word:

P = 16
R = 18
O = 15
B = 2
L = 12
E = 5
M = 13

Now, let us check for valid letter pairs in both directions:

1. Forward Direction:

• Counting from P (16): 17, 18, 19, 20, 21, 22 (No match)
• Counting from R (18): 19, 20, 21, 22, 23 (No match)
• Counting from O (15): 16, 17, 18, 19 (No match)
• Counting from B (2): 3, 4, 5 (No match)
• Counting from L (12): 13, 14 (No match)
• Counting from E (5): 6 (No match)

2. Backward Direction:

• Counting from M (13):
- 13 to L: 14 (No match)
- 13 to E: 15 (No match)
- 13 to B: 16 (No match)
- 13 to O: 17 (No match)
- 13 to R: 18 (Match! M and R: 13 → 14(E) → 15(L) → 16(B) → 17(O) → 18(R). In the alphabet, there are 4 letters between M and R, and here also there are 4 letters between them.)
- 13 to P: 19 (No match)

• Counting from E (5):
- 5 to L: 6 (No match)
- 5 to B: 7 (No match)
- 5 to O: 8 (No match)
- 5 to R: 9 (No match)
- 5 to P: 10 (No match)

• Counting from L (12):
- 12 to B: 13 (No match)
- 12 to O: 14 (No match)
- 12 to R: 15 (No match)
- 12 to P: 16 (Match! L and P: 12 → 13(B) → 14(O) → 15(R) → 16(P). In the alphabet, there are 3 letters between L and P, and here also there are 3 letters between them.)

• Counting from B (2), O (15), and R (18) yield no further matches.

Thus, there are exactly 2 such pairs: (M, R) and (L, P).