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 count of letter pairs in the word ‘PROBLEM’ that have the same number of letters between them as in the English alphabetical series, let us first write down the alphabetical position for each letter in the word:

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

Now, we check for letter pairs in both forward and backward directions:

1. Forward Direction:

• From P (16): Count forward → 17 (R), 18 (O), 19 (B), 20 (L), 21 (E), 22 (M). No match.
• From R (18): Count forward → 19 (O), 20 (B), 21 (L), 22 (E), 23 (M). No match.
• From O (15): Count forward → 16 (B), 17 (L), 18 (E), 19 (M). No match.
• From B (2): Count forward → 3 (L), 4 (E), 5 (M). No match.
• From L (12): Count forward → 13 (E), 14 (M). No match.
• From E (5): Count forward → 6 (M). No match.

2. Backward Direction:

• From M (13): Count backward → 14 (E), 15 (L), 16 (B), 17 (O), 18 (R), 19 (P). Match found for pair M and R (M = 13, R = 18; count: 14, 15, 16, 17, 18 landing on R).
• From E (5): Count backward → 6 (L), 7 (B), 8 (O), 9 (R), 10 (P). No match.
• From L (12): Count backward → 13 (B), 14 (O), 15 (R), 16 (P). Match found for pair L and P (L = 12, P = 16; count: 13, 14, 15, 16 landing on P).
• From B (2): Count backward → 3 (O), 4 (R), 5 (P). No match.
• From O (15): Count backward → 16 (R), 17 (P). No match.
• From R (18): Count backward → 19 (P). No match.

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