Coding‑Decoding – Reasoning Ability Study Notes
(For the Red Hat RHCE Reasoning Ability Section)
1. Simple Explanation
Coding‑decoding is a type of reasoning test where you are given a coding rule (a hidden pattern) that has been used to transform one set of items into another.
- Coding: converting a given item (letter, number, shape, etc.) into a new form.
- Decoding: reversing that process to find the original item.
The goal is to recognize the underlying rule and apply it to:
- Predict the next element in a sequence.
- Decode a coded message to its original form.
- Encode a new item using the discovered rule.
2. Key Points & Strategies
| # | Strategy | How to Use It | Example |
|---|---|---|---|
| 1 | Identify the Domain (letters, numbers, shapes, colours, etc.) | Notice if the input/output belong to the same set or a different set. | A→D, B→E (letters) |
| 2 | Look for One‑to‑One Mapping | Each input maps to exactly one output and vice‑versa. | A→1, B→2, C→3 |
| 3 | Check Positional Relationships | The position of the input in the alphabet/sequence matters. | 1st letter → 4th letter |
| 4 | Apply Arithmetic Operations | Addition, subtraction, multiplication, division, or modulo. | 3 → 3+2 = 5 |
| 5 | Use Increment/Decrement Patterns | Increment by 1, 2, 3, … or decrement. | A→C (+2 letters) |
| 6 | Look for Repeating Cycles | Pattern repeats after a fixed number of steps. | A→D, B→E, C→F, then back to A→D |
| 7 | Consider Mirror or Reverse Order | The sequence may be reversed or mirrored. | ABC → CBA |
| 8 | Check for Symmetry/Parity | Even/odd positions may follow different rules. | Even positions → +1, odd positions → -1 |
| 9 | Create a Small Table | List all given pairs side‑by‑side to spot regularities. | `Input |
| 10 | Test Hypotheses | Pick a rule, apply it to all given pairs; if all fit, rule likely correct. | If rule fails, backtrack and try another. |
General Flow to Solve a Coding‑Decoding Problem
- Gather All Pairs – Write them in two columns.
- Spot Patterns – Look for arithmetic, positional, or structural patterns.
- Formulate a Rule – Express the pattern as a clear mathematical or logical operation.
- Test the Rule – Apply to all given pairs.
- Decode/Encode – Use the rule to solve the problem (next item, decode a message, etc.).
- Double‑Check – Verify that the answer fits all constraints (e.g., stays within the same domain).
3. Worked Example
Problem
The following coding pairs are given:
| Input | Output |
|---|---|
| A | 3 |
| B | 5 |
| C | 7 |
| D | 9 |
| E | 11 |
Question
- What is the code for F?
- Decode the number 15.
Step‑by‑Step Solution
| Step | Action | Reasoning |
|---|---|---|
| 1 | List the pairs. | A→3, B→5, C→7, D→9, E→11 |
| 2 | Recognize the pattern. | Output increases by 2 each time. |
| 3 | Express as a rule. | Code = 2 × (position in alphabet) + 1. |
- A is 1st → 2×1+1 = 3.
- B is 2nd → 2×2+1 = 5, etc. |
| 4 | Encode F (6th letter). | 2×6 + 1 = 13. |
| 5 | Decode 15. | Solve
2 × x + 1 = 15→2x = 14→x = 7.
The 7th letter is G. |
Answers
- F → 13
- 15 → G
4. Quick Revision Summary
- Coding‑Decoding: Find the hidden rule that maps one set to another.
- Key Tools:
- Positional analysis (alphabet order, sequence index).