Analysing Letter Pairs in COMFORTS
The task is to find pairs of letters within the word 'COMFORTS' where the number of letters separating them in the word is equal to the number of letters separating them in the English alphabet. This analysis must cover both forward (left-to-right) and backward (right-to-left) directions.
Word Representation
We represent the word 'COMFORTS' with letter positions (0-indexed) and their corresponding alphabetical values (A=1, B=2, etc.).
| Letter | C | O | M | F | O | R | T | S |
| Position (0-indexed) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Alphabetical Value (A=1) | 3 | 15 | 13 | 6 | 15 | 18 | 20 | 19 |
Forward Direction Analysis
We look for letter pairs (letter at index $i$, letter at index $j$) where $i < j$ such that the absolute difference in their alphabetical values equals the number of letters between them in the word ($j - i - 1$).
- Pair (O, R): O (index 1, value 15), R (index 5, value 18).
- Alphabetical difference: $abs(18 - 15) = 3$.
- Word gap: $5 - 1 - 1 = 3$.
- These match. (1 pair found)
- Pair (R, S): R (index 5, value 18), S (index 7, value 19).
- Alphabetical difference: $abs(19 - 18) = 1$.
- Word gap: $7 - 5 - 1 = 1$.
- These match. (1 pair found)
Total pairs in the forward direction: 2.
Backward Direction Analysis
We look for letter pairs (letter at index $i$, letter at index $j$) where $i > j$ such that the absolute difference in their alphabetical values equals the number of letters between them in the word ($i - j - 1$).
- Pair (R, O): R (index 5, value 18), O (index 1, value 15).
- Alphabetical difference: $abs(18 - 15) = 3$.
- Word gap: $5 - 1 - 1 = 3$.
- These match. (1 pair found)
- Pair (S, R): S (index 7, value 19), R (index 5, value 18).
- Alphabetical difference: $abs(19 - 18) = 1$.
- Word gap: $7 - 5 - 1 = 1$.
- These match. (1 pair found)
Total pairs in the backward direction: 2.
Conclusion
The total count is the sum of pairs found in both directions.
Total Pairs = (Forward Pairs) + (Backward Pairs) = 2 + 2 = 4.
There are 4 such pairs of letters in the word COMFORTS.
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