Coding‑Decoding – Study Notes for Assam TET (Reasoning Ability)
Target Exam: Assam TET – Reasoning Ability
Section: Coding‑Decoding
Level: Competitive (IIT‑JEE style)
Format: Multiple‑choice (5 options)
1. What is Coding‑Decoding?
Coding‑Decoding is a type of reasoning problem where a code (often a set of symbols, numbers, or letters) represents a message (a set of letters, words, or patterns).
The task is to decode a given code into the intended message using the rules of the particular code.
Key Idea:
Identify the rule (mapping) that connects the coded symbols to the uncoded ones, then use that rule to find unknowns.
2. Common Types of Coding‑Decoding Problems
| Category | Typical Pattern | Example | How to Identify |
|---|---|---|---|
| Alphabet ↔ Number | A=1, B=2… | 3 = C |
Look for arithmetic or positional relation. |
| Number ↔ Alphabet | 1 = Z, 2 = Y… | 7 = R |
Often reverse order or cyclic shift. |
| Letter ↔ Letter (Shift) | A→C, B→D… | X→Z |
Check for constant offset (+2). |
| Order‑Based | 1st word → A, 2nd word → B… | Third word? |
Count sequence or use position. |
| Group‑Based | Words in a group → same letter | Group 1 = A |
Identify grouping logic (e.g., words with same first letter). |
| Pattern‑Based | Shape, colour, size → letter | Red circle → B |
Visual or qualitative attributes. |
| Multi‑Layer | Two‑step mapping (e.g., number → letter → word) | 5 → E → EAR |
Break into sub‑problems. |
Tip: If the problem gives a table of codes and outputs, always start by finding a simple linear mapping (e.g.,
value = a * position + b). If that fails, look for non‑linear or categorical patterns.
3. General Strategy (Step‑by‑Step)
-
Collect all given pairs.
Write them in a table: Code | Decoded. -
Check for linearity.
- ( \text{value} = a \times \text{position} + b )
acould be 1, 2, -1, etc.- If all pairs satisfy a unique line, you’re done.
-
Look for cyclic patterns.
shiftof +k (mod 26).- Reverse order (A↔Z, B↔Y).
- Alternating shift (+1, –1, +2,…).
-
Identify categories.
- Group by first letter, word length, vowels/consonants, etc.
-
Test the rule.
- Apply to the unknown code(s).
- Check consistency with any hint or consistency constraint.
-
Handle ambiguous cases.
- If multiple rules fit, look for additional clues (e.g., “the coded message forms a meaningful word”).
- Use process of elimination among answer choices.
4. Key Formulae & Derivations
| Rule | Formula | Example |
|---|---|---|
| Alphabet Position | ( \text{value} = \text{pos}(L) ) | C → 3 |
| Reverse Alphabet | ( \text{value} = 27 - \text{pos}(L) ) | A → 26 |
| Modular Shift | ( \text{new_pos} = ((\text{pos}(L) + k - 1) \bmod 26) + 1 ) | A with +3 → D |
| Cyclic Map | ( \text{new_L} = \text{Alphabet}[ ((\text{pos}(L)+k-1) \bmod 26) + 1 ] ) | Y shift +3 → B |
| Two‑Step Mapping | Code → Number → Letter |
9 → 9 → I |
| Group Mapping | If Word[i] shares property P, assign Letter = f(P) |
All words ending in -ed → E |
| Pattern Matching | Shape → Letter via lookup table |
Triangle → T |
Derivation Note:
For a linear mapping, solve foraandbusing two pairs: [ \begin{cases} y_1 = a x_1 + b \