Coding-Decoding — Study Notes

Overview

Coding-Decoding is a core pattern recognition topic in NSO's Logical Reasoning section. You'll see 2–4 questions in most papers, often scoring 1–2 marks each. The essence: a word or set of letters/numbers is converted using a hidden rule, and you must crack that rule to encode new words or decode given codes.

This topic tests your ability to spot systematic transformations — letter shifts, position swaps, numerical assignments, or symbolic substitutions. Unlike purely mathematical reasoning, Coding-Decoding rewards methodical comparison: line up the original with the coded form, track each character's change, and extrapolate the pattern. Mastery here is about speed and accuracy under pressure. Most students lose marks by misreading the pattern direction (forward vs backward alphabet) or miscounting positions. A disciplined approach — always write out the alphabet positions when stuck — will save you from silly errors.

Strong performance in Coding-Decoding also boosts confidence in related topics like Alphabet Test and Series Completion, since they share the skill of systematic tracking.

Key Concepts

• **Letter-Shift Coding**: Each letter moves a fixed number of steps forward or backward in the alphabet. Example: A → D (shift +3), B → E (shift +3). If BOOK codes to ERRN, every letter shifted +3.

• **Reverse Alphabet Coding**: Replace each letter with its counterpart from the opposite end. A ↔ Z, B ↔ Y, C ↔ X, and so on. Position formula: (26 – position + 1). If CAT codes to XZG, reverse coding is at work.

• **Letter-to-Number Coding**: Assign each letter its alphabet position (A=1, B=2, ... Z=26) and apply arithmetic. Example: If BAD codes to 214, then B=2, A=1, D=4 — direct positional coding.

• **Mixed Operations**: Combine shift + reverse, or alternate rules for odd/even positions. Example: First letter +2, second letter –1, third letter +2, repeat. These require careful pattern isolation for each position.

• **Word-to-Number Total Coding**: Sum the alphabet positions of all letters. Example: CAT = 3+1+20 = 24. Used less often but appears in Achievers-level questions.

• **Substitution Coding**: A consistent cipher where specific letters/symbols replace others throughout. Example: If "ROSE" is coded as "TQUG", check each letter pair: R→T (+2), O→Q (+2), S→U (+2), E→G (+2). Substitution often looks random but follows one hidden rule.

• **Conditional Coding**: Rule changes based on letter type (vowel vs consonant) or position (first letter vs others). Example: Vowels shift +1, consonants shift +2. Always test the pattern separately for vowels and consonants if a uniform shift doesn't fit.

Formulas / Key Facts

1. **Alphabet Position**: A=1, B=2, C=3, …, Z=26. Memorize at least A–J positions for quick reference.

2. **Reverse Position Formula**: Opposite letter position = 27 – (original position). Example: E (5th letter) ↔ V (22nd letter), because 5 + 22 = 27.

3. **Forward Shift**: New letter = (Old position + shift) mod 26. If result = 0, set it to 26 (Z).

4. **Backward Shift**: New letter = (Old position – shift). If result < 1, add 26.

5. **Pair Count Check**: If a word has n letters, the coded form must also have n characters (unless the question states otherwise, e.g., "middle letters dropped").

6. **Common Shift Values**: ±1, ±2, ±3 are most frequent. Always test small shifts first before assuming complex patterns.

7. **EJOTY Rule** (for reverse): E↔V, J↔Q, O↔L, T↔G, Y↔B. Remembering these pairs speeds up reverse-alphabet decoding.

8. **Zero-Sum Check**: In letter-to-number addition coding, if letters sum to a two-digit number, verify whether the code shows the full sum or digit-by-digit concatenation.

Worked Examples

**Example 1: Simple Forward Shift** *Question*: If MANGO is coded as PDQJR, how is APPLE coded? *Solution*: Compare M→P (M=13, P=16, shift +3), A→D (+3), N→Q (+3), G→J (+3), O→R (+3). Uniform +3 shift. Apply to APPLE: A→D, P→S, P→S, L→O, E→H. **Answer**: DSSOH

**Example 2: Reverse Alphabet Coding** *Question*: In a code, DOG is written as WLT. What is CAT in that code? *Solution*: D (4th) ↔ W (23rd): 4+23=27 ✓. O (15th) ↔ L (12th): 15+12=27 ✓. G (7th) ↔ T (20th): 7+20=27 ✓. Reverse coding confirmed. Apply to CAT: C (3rd) ↔ X (24th), A (1st) ↔ Z (26th), T (20th) ↔ G (7th). **Answer**: XZG

**Example 3: Letter-to-Number Coding** *Question*: If BAT is coded as 2120, find the code for RAT. *Solution*: B=2, A=1, T=20 → concatenated as 2120 (not summed). So code = position1|position2|position3. RAT: R=18, A=1, T=20 → 18120. **Answer**: 18120

**Example 4: Mixed Pattern (Odd-Even Positions)** *Question*: If FUN is coded as HVL, how is JOY coded? *Solution*: F (6, 1st position) → H (8): +2. U (21, 2nd position) → V (22): +1. N (14, 3rd position) → L (12): –2. Pattern: Position 1 (+2), Position 2 (+1), Position 3 (–2). Apply to JOY: J (10) → L (+2), O (15) → P (+1), Y (25) → W (–2). **Answer**: LPW

Common Mistakes

• **Miscounting Alphabet Positions**: Students often confuse D as 3rd or 5th letter. *Fix*: Write A=1, B=2, … up to the required letter whenever unsure. Don't rely on memory under exam stress.

• **Ignoring Direction (Forward vs Backward Alphabet)**: Seeing A→Z, a student might think "shift +25" instead of recognizing reverse coding. *Fix*: Always check if the sum of original position + coded position = 27. If yes, it's reverse alphabet, not a shift.

• **Applying Pattern Only to First Letter**: In mixed coding, the rule for the first letter may differ from the rest. Assuming a uniform shift leads to wrong codes for later letters. *Fix*: Check the transformation of *every* letter individually before concluding the pattern.

• **Confusing Concatenation with Addition**: If BAT → 2120, students might wrongly compute 2+1+20=23. *Fix*: Look at the length of the code. A 4-digit code from a 3-letter word suggests concatenation, not summation.

• **Modulo Errors in Cyclic Shifts**: Shifting Z forward by +1 should give A, but students write AA or skip the wraparound. *Fix*: Use (position + shift – 1) mod 26 + 1 formula, or manually: after Z(26), loop to A(1).

Quick Reference

• Letter shift ±n: Add/subtract n to each letter's position; wrap around after 26.
• Reverse alphabet: Position + opposite position = 27. E ↔ V, J ↔ Q, etc.
• Letter-to-number: Direct position (A=1…Z=26) or sum all positions.
• Mixed patterns: Check odd vs even positions, or vowel vs consonant separately.
• Always verify pattern on *all* letters before answering.
• Write out alphabet positions explicitly if the pattern isn't obvious in 10 seconds.