Letter Pairs — Same Gap as in the Alphabet

🎯 Learning Objective

Count the pairs of letters in a word that have exactly as many letters between them as in the alphabet.

💡 Concept

• The question: how many letter PAIRS in the word have the same number of letters between them as between those letters in the alphabet
• Exact method: write each letter's alphabet position below it (A=1 ... Z=26)
• For letters at word positions i and j: letters between them in the word = j − i − 1; in the alphabet = (difference of their position values) − 1
• The pair counts when these are equal, i.e. |position value difference| = |word place difference|
• Count BOTH directions — the pair also counts if the letters run in reverse alphabetical order (like O before N)
• Scan systematically: all pairs with word-gap 0 (adjacent), then gap 1, then gap 2 — no pair gets missed

🧮 Key Formulas

Pair counts when |alphabet numbers' difference| = |word positions' difference|

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EJOTY: E=5, J=10, O=15, T=20, Y=25

✏️ Easy Example

Q. How many pairs of letters in FIGHT have as many letters between them as in the alphabet?

1. Number the letters: F=6, I=9, G=7, H=8, T=20
2. Check pairs: G(3rd) and H(4th) → word gap 1, number gap |7−8| = 1 → match
3. No other pair matches

Answer: 1 pair (GH)

🇮🇳 Real-Life Example

Stations between stops: Kanpur to Lucknow may have 2 halts on the line and 2 entries between them in the timetable — same gap in both lists. That is exactly what you check for letters.

📝 Exam-Level Example

Q. How many pairs of letters in CREATION have as many letters between them as in the English alphabet?

1. Positions: C=3, R=18, E=5, A=1, T=20, I=9, O=15, N=14
2. C(1st) & E(3rd): word gap 2, number gap |3−5| = 2 → match
3. O(7th) & N(8th): word gap 1, number gap |15−14| = 1 → match (reverse order still counts)
4. All other pairs fail the equality

Answer: 2 pairs (CE and ON)

🪄 Memory Trick

Use EJOTY to number letters in seconds: E=5, J=10, O=15, T=20, Y=25 — every other letter is within 2 steps of one of these anchors.

⚠️ Common Mistakes

• ❌ Counting only forward-order pairs and missing reverse-order ones like ON
• ❌ Comparing letter gaps with number DIFFERENCE instead of letters BETWEEN (both must be gaps, or both differences — stay consistent)
• ❌ Checking only adjacent letters — distant pairs like C...E with a gap of 2 also qualify

🏆 Exam Tips

• ✅ Write alphabet numbers under the word FIRST — never test pairs from memory
• ✅ Scan in order of word gap (0, then 1, then 2 ...) so every pair is examined exactly once

📌 Summary

• Count pairs where word gap = alphabet gap
• Both directions count — reverse-order pairs included
• Number the letters using EJOTY anchors
• Systematic gap-wise scanning misses nothing