Coding-decoding: Reasoning Ability Notes for Manipur Police Sub-Inspector (SI)

Coding‑Decoding – Reasoning Ability

For Manipur Police Sub‑Inspector (SI) Examination

1. What is Coding‑Decoding?

Coding is the process of replacing an element (letter, number, word, symbol, etc.) with another according to a rule or pattern.
Decoding is the reverse process: restoring the original element from its coded form.

In reasoning tests, you are given a small sequence that is already coded (or a coded word) and then asked to find the next element, the missing element, or the original word.

2. Common Coding Patterns

Pattern	Example	How to Spot It
Alphabetical Shift	A‑B‑C → D‑E‑F	Each letter moves k places forward/backward
Reverse Alphabet	A ↔ Z, B ↔ Y	Mirror of alphabet
Alternating Pattern	A, C, E, … (odd positions) vs B, D, F, … (even positions)	Two interleaved sequences
Arithmetic Progression	1, 4, 7, … → add 3 each step	Numbers differ by constant
Geometric Progression	2, 6, 18, … → multiply by 3 each step	Ratios are constant
Positional Value	1 → A, 2 → B, …	Mapping numeric position to alphabet
Word Length/Letter Count	“ONE” (3) → “TWO” (3) → “THREE” (5)	Length changes may hint at rule
Substitution (scrabble value, Morse, etc.)	A=1, B=2, …	Use any external coding system
Pattern + Wordplay	“CAT” → “B” (first letter minus 1)	Combine multiple simple rules

Tip: The first few items in the series are usually enough to deduce the rule. If the series is short, try all common patterns.

3. Key Points to Remember

Identify the type of coding
- Is it letters, numbers, or both?
- Does the series involve a single rule or a combination?
Check for symmetry
- Reverse alphabet, mirror points (A↔Z, B↔Y).
Look for arithmetic relationships
- Differences or ratios between successive elements.
Consider positional indices
- The position (1st, 2nd, …) may influence the coding.
Test multiple hypotheses
- Write out the first few terms using a guessed rule; if a contradiction appears, try a different rule.
Use the “back‑track” method
- If a rule works for the first 3–4 items but fails later, discard it and try another.
Remember special cases
- Sometimes the rule is not linear – e.g., prime numbers, Fibonacci, etc.
Always cross‑check
- Verify that the decoded sequence satisfies the same rule as the coded one.
Practice speed
- The exam is time‑constrained; practice mental calculations.

4. Worked Example

Question

Coded Series:
Y, U, Q, O, M, ...
Find the next two coded letters.

Step‑by‑Step Solution

Position	Coded	Alphabet Position	Difference
1	Y	25	–
2	U	21	–4
3	Q	17	–4
4	O	15	–2
5	M	13	–2

Observation:

From 1→2: −4
From 2→3: −4
From 3→4: −2
From 4→5: −2

So the pattern of differences is −4, −4, −2, −2 – two steps of −4, then two steps of −2, repeating.

Predict next differences:

After two −2’s, the pattern restarts → next difference = −4
Then again −4

Apply to the last coded letter (M = 13):

13 − 4 = 9 → 9th letter = I
9 − 4 = 5 → 5th letter = E

Answer: I, E

Quick Check

Encoded series: Y(25) → U(21) → Q(17) → O(15) → M(13) → I(9) → E(5)
All differences follow the pattern –4, −4, −2, −2, −4, −4.

5. Quick Revision Summary

Step	Action	Why It Matters
1	Identify the element type (letters, numbers, words).	Determines the possible rules.
2	List positions & values.	Helps spot arithmetic or positional patterns.
3	Check for symmetry (reverse alphabet, mirror).	Common in coding puzzles.
4	Calculate differences/ratios between successive items.	Reveals linear or exponential patterns.
5	Look for alternation (odd/even positions).	Two interleaved sequences are frequent.
6	Test a hypothesis with the first few terms.	Quick validation or rejection.
7	Cross‑check the decoded series against the rule.	Ensures consistency.
8	Practice mentally with time limits.	Builds speed for exam conditions.

Remember: The key to success in coding‑decoding is pattern recognition. The more common patterns you know, the faster you’ll crack the code.

Good luck on your preparation!