What is asked
"How many pairs of letters are there in the word ____ which have as many letters between them in the word as in the English alphabet?" The site generates these with computed answers. Variants ask for pairs in the forward direction only, or for pairs of digits in a number.
Rule
Take two letters of the word at positions i and j (i < j). The number of letters between them in the word is j - i - 1. The number of letters between them in the alphabet is |alphabet position difference| - 1. A pair counts when the two are equal, i.e. j - i = |difference of alphabet positions|.
- Forward direction: the letters are in alphabetical order from left to right (for example D ... G).
- Backward direction: the letters are in reverse alphabetical order from left to right (for example G ... D).
- "Both directions" means count forward and backward pairs together.
Systematic method
- Write the alphabet position under each letter of the word.
- Take the first letter and compare it with the 2nd, 3rd, 4th ... letter: check whether the gap in positions equals the gap in the word.
- Repeat with the second letter, and so on. Tick each valid pair.
- Shortcut: you only need to compare a letter with letters up to (difference) places away, so stop when the word gap exceeds 25.
Worked example
BANKING: B2 A1 N14 K11 I9 N14 G7.
| Pair | Gap in word | Gap in alphabet | Valid? |
|---|---|---|---|
| B-A | 1 | 1 | Yes (backward) |
| N-K | 1 | 3 | No |
| K-I | 1 | 2 | No |
| I-G | 2 | 2 | Yes (backward) |
| K-N (positions 4 and 6) | 2 | 3 | No |
Checking all remaining pairs finds no more, so the answer is 2.
Variants
In the digit version ("How many pairs of digits in 5 3 8 4 6 9 have as many digits between them as in the number series?"), apply the same rule to the digit values. For "forward only" questions count only pairs whose letters are in alphabetical order from left to right; in BANKING neither B-A nor I-G is forward, so the forward-only answer would be zero.
Time target
About 45 seconds for a 7-8 letter word with the systematic method.