Coding‑Decoding – Study Notes (Reasoning Ability)
Exam Context – J&K Patwari / Lekhpal, IIT‑JEE & other competitive exams
Section – Coding‑Decoding (also called “Code‑Word” or “Cipher” problems)
The objective of coding‑decoding questions is to discover the hidden rule that links a set of symbols (letters, numbers, shapes, etc.) and then apply that rule to solve for the unknown symbol.
These problems test pattern recognition, logical deduction, and sometimes arithmetic/algebraic manipulation.
Below is a comprehensive, exam‑oriented guide that covers
- Basic concepts & terminology
- Common coding patterns & strategies
- Key “shortcuts” for quick elimination
- Derivations & formulae where useful
- Common pitfalls & tricky points
- A hard practice problem with full solution
1. Basics
| Term | Meaning |
|---|---|
| Code | A set of symbols (letters, numbers, shapes) that represent something else. |
| Decode | Reverse the code, i.e., find the original meaning of the symbols. |
| Coding‑Decoding | A question that presents a series of coded symbols and asks you to determine the next symbol (coding) or the meaning of a given symbol (decoding). |
| Cipher | A hidden or encoded message. |
| Pattern | The deterministic rule that maps an input to an output. |
| Key | The hidden rule or mapping. |
Note: In most exam questions, the key is not given; you must infer it from the given data.
2. General Strategy
-
List given pairs
Write the code and the decoded part side‑by‑side. -
Look for simple arithmetic or geometric progressions
- Check differences, ratios, sums, products.
-
Check alphabetic positions
A=1, B=2, …, Z=26- Modulo operations (e.g.,
A=1, B=2, …, Z=0).
-
Check for alternating patterns
- Two or more interleaved sequences.
-
Check for combinatorial patterns
- Concatenation, digit reversal, digit sum, etc.
-
Test a hypothesis on the first few terms
- If it works for all given pairs, it’s likely the key.
-
Validate – Apply the rule to the unknown symbol(s).
3. Common Coding Patterns
| Pattern | Example | Explanation |
|---|---|---|
| Alphabetic Position + Constant | A → 1, B → 3, C → 5 |
value = 2*position - 1 |
| Alphabetic Position + Arithmetic Sequence | A → 5, B → 7, C → 9 |
value = 2*position + 3 |
| Digit Sum of Alphabetic Position | A → 1, B → 2, C → 3 (trivial) J → 10 → 1+0=1 |
value = (position) mod 9 (or digit sum) |
| Reverse Alphabetic Position | A → 26, B → 25 |
value = 27 - position |
| Multiplication of Position & Constant | A → 2, B → 6, C → 12 |
value = position * 2 |
| Alternate Addition/Subtraction | A → 1, B → 3, C → 6, D → 10 |
value = n(n+1)/2 (triangular numbers) |
| Pattern Involving Shapes | ○ → 1, △ → 3, ◇ → 6 |
Count of sides or angles |
| Concatenation | AB → 12, BC → 23 |
concatenate numbers of letters |
| Digit Reversal | AB → 21, BC → 32 |
reverse digits |
| Sum of Digits | AB → 3, BC → 5 |
sum of individual letter values |
| Modulo Operation | A → 1, B → 2, …, Z → 0 |
value = position mod 9 or mod 26 |
Tip: Often the key is a combination of the above (e.g.,
value = 2*(position) + 3then apply digit sum).
4. Derivation & Formulae
-
Arithmetic Sequence
[ a_n = a_1 + (n-1)d ] -
Geometric Sequence
[ a_n = a_1 \cdot r^{(n-1)} ] -
Triangular Numbers
[ T_n = \frac{n(n+1)}{2} ] -
Digital Root (repeated digit sum until single digit)
[ \text{dr}(x) = 1 + ((x-1)\mod 9) ] Useful for codes where values are reduced to a single digit. -
Modular Arithmetic
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