Letter Shifting Codes

🎯 Learning Objective

Detect forward/backward letter shifts from a solved pair and apply the same shift to a new word.

💡 Concept

• A code replaces each letter by another using one fixed rule — the most common rule is shifting
• CAT → DBU: every letter moves +1 (C→D, A→B, T→U)
• Find the shift from the first letter pair, then CONFIRM it on the remaining pairs
• Apply the same shift to the new word, letter by letter
• The alphabet is a circle — wrap at the ends: Z + 1 = A, and A − 1 = Z

🧮 Key Formulas

New letter = old position ± k

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Wrap: Z + 1 = A, A − 1 = Z

✏️ Easy Example

Q. If CAT is written as DBU, how is DOG written in the same code?

1. C→D, A→B, T→U — every letter +1
2. D→E, O→P, G→H

Answer: EPH

🇮🇳 Real-Life Example

School friends passing secret notes — write every letter one step ahead and the teacher reads only nonsense. Armies and signals use the same idea: a rule known to both sides.

📝 Exam-Level Example

Q. In a certain code, TRAIN is written as XVEMR. How is BUS written in that code?

1. T→X is +4; check R→V, A→E, I→M, N→R — all +4
2. B + 4 = F, U + 4 = Y, S + 4 = W

Answer: FYW

📝 Exam-Level Example

Q. In a certain code, DELHI is written as CDKGH. How is MEERUT written in that code?

1. D→C, E→D, L→K — every letter −1
2. M→L, E→D, E→D, R→Q, U→T, T→S

Answer: LDDQTS

🪄 Memory Trick

Compare the FIRST letters to guess the shift, verify on one more pair, then code the whole word in one sweep using EJOTY positions.

⚠️ Common Mistakes

• ❌ Reading the shift in the wrong direction (D→C is −1, not +1)
• ❌ Forgetting the wrap: Y + 3 = B
• ❌ Applying the shift to some letters and copying the rest unchanged

🏆 Exam Tips

• ✅ Write letter positions using EJOTY anchors before shifting
• ✅ Always verify the shift on at least two letter pairs

📌 Summary

• Shift codes move every letter by the same ±k
• Find the shift from one pair, confirm with another
• Alphabet wraps: Z + 1 = A
• Apply letter by letter — no shortcuts