Coding-decoding: Reasoning Ability Notes for Nagaland PSC

Coding‑Decoding – Reasoning Ability

For Nagaland PSC & Competitive Exams

1. Simple Explanation

Coding‑decoding is a type of reasoning question where a set of symbols, letters, or numbers (the code) is mapped to another set (the decode).

Code → the original pattern.
Decode → the pattern that we have to find.

The test‑maker gives you one or more pairs of Code‑Decode and asks you to determine the rule that transforms one into the other. Once you know the rule, you can apply it to new pairs or to find missing elements.

2. Key Points & Problem‑Solving Strategy

#	Item	Why it matters
1	Identify the nature of elements	Are they letters, numbers, shapes, colours, or combinations?
2	Look for arithmetic/algebraic patterns	+, –, ×, ÷, exponent, alternating sequences, cumulative sums, etc.
3	Check for positional or alternating rules	Odd‑even, 1st‑3rd‑5th positions, reverse, skip‑n.
4	Consider letter‑number mapping	A=1, B=2 … or reverse, or using mod‑26 arithmetic.
5	Look for pattern of differences	Between consecutive codes or decodes.
6	Look for pattern of transformations	Rotations, mirroring, reflection, cycling through a list.
7	Verify with all given pairs	A rule that works for all pairs is the likely answer.
8	Apply the rule to new pair	Solve the target question.
9	Double‑check	Ensure no alternative rule fits better.

Common Encoding Types

Encoding	Example	Typical rule
Shift (Caesar)	A → D, B → E	Add +3 to alphabet index.
Reverse	123 → 321	Reverse the digits.
Alternating	1,2,3,4 → 1,3,2,4	Swap odd‑even positions.
Arithmetic Sequence	2,4,6,8 → 4,8,12,16	Multiply by 2.
Letter‑Number	A → 1, B → 2	Map letters to numbers.
Cyclic Shift (Rotations)	ABC → BCA	Move first element to the end.
Mirror	A → Z, B → Y	Reflect about the centre of alphabet.

3. Worked Example

Problem Statement

Code :  1  2  3  4  5  6
Decode : 1  4  9 16 25 36

Question: What will be the decode of the code 7?

Step‑by‑Step Solution

Step	Observation	Reasoning
1	Code numbers are consecutive integers starting from 1.	Simple linear sequence.
2	Decodes are 1, 4, 9, 16, 25, 36.	These are perfect squares: (1^2, 2^2, 3^2, 4^2, 5^2, 6^2).
3	Rule: Decode = (Code)²	Apply to any given code.
4	For Code = 7: (7^2 = 49).
5	Answer: 49

Quick Check

If Code = 4 → Decode = 16 ✔️
If Code = 6 → Decode = 36 ✔️

Everything fits the rule.

4. Quick Revision Summary

Understand the Input/Output – Identify whether the code is letters, numbers, shapes, etc.
Seek Arithmetic Patterns – Add, subtract, multiply, divide, square, cube, factorial, etc.
Check Positional Rules – Odd/even positions, alternations, reversals.
Consider Alphabetic Mapping – A=1, Z=26, or reverse, cyclic shifts.
Validate Across All Given Pairs – A rule that satisfies all is likely correct.
Apply the Rule to Solve – Use the discovered logic to decode new codes.
Re‑verify – Double‑check for any overlooked pattern or alternative mapping.

Quick Practice Set

#	Code	Decode	Rule
1	A B C	1 2 3	Alphabet → number
2	1 2 3	3 5 7	+2 each step (odd numbers)
3	4 5 6	16 25 36	Square each
4	X Y Z	24 25 26	Mirror in alphabet (Z→A)
5	1 3 5	1 9 25	Square of each (odd numbers)

Try decoding the following before checking the answer:

Code : 2 4 6 8
Decode : ?

Answer: 4 16 36 64 (square each even number).

Tip: Always write down all the given pairs and try at least two different transformation ideas before settling on one. Good luck preparing for the Nagaland PSC!