Coding‑Decoding – Study Notes
(Reasoning Ability – Duolingo English Test / IIT‑JEE style)
1. What is Coding‑Decoding?
A coding‑decoding problem gives you one or more code–decoded pairs.
You must uncover the rule (or mapping) that transforms the coded word/phrase into the decoded one, and then use that rule to encode or decode a new statement.
Example
Code → Decode ABCD → WXYZHere the rule is “shift each letter 4 places back.”
2. Common Types of Coding‑Decoding Problems
| Type | Typical Pattern | Example |
|---|---|---|
| Alphabetic Shift | Each letter moved k positions forward/backward. | DOG → JAR (shift +3) |
| Substitution (Caesar/Mono‑alphabetic) | Fixed one‑to‑one mapping of letters. | HELLO → QEBBN (H→Q, E→B, etc.) |
| Reversal / Mirror | Letters reversed or mirrored across the alphabet (A↔Z, B↔Y). | ACME → ZNXV |
| Word/Letter Replacement | Whole words or letters replaced by synonyms/abbreviations. | FAST → QUICK |
| Pattern‑Based | Letters follow a numerical pattern (prime positions, even/odd). | ABCD → ACEG (keep only odd positions) |
| Mixed Rules | Combination of two or more of the above (shift + reversal). | ABC → XZC (shift + reverse) |
3. General Strategy for Solving
| Step | Action | Why It Helps |
|---|---|---|
| 1. Identify the alphabet | Confirm whether the code uses only A‑Z or includes a‑z / digits / punctuation. | Keeps mapping consistent. |
| 2. Map each letter | Write a table of the given code–decoded pairs. | Visualizing helps spot patterns. |
| 3. Look for simple operations | Check for constant shift, reversal, or mirroring. | Most exam problems use simple rules. |
| 4. Verify consistency | Ensure the rule works for all provided pairs. | Avoids false positives. |
| 5. Apply the rule | Encode/decode the target word. | Final answer. |
| 6. Check for edge cases | Spaces, punctuation, repeated letters. | Avoid mis‑interpretation. |
Quick Checks:
| Test | What to Do |
|---|---|
| Shift | Compute (decoded - coded) mod 26 for each letter. If all equal → constant shift. |
| Reversal | Reverse the coded word and compare to decoded. |
| Mirror | Check decoded = 27 - coded (A=1, Z=26). |
| Word‑by‑Word | If whole words differ, think of abbreviations, synonyms, or acronyms. |
4. Key Derivations & Formulae
Alphabetic Shift
For a letter represented by its position x (A=1 → Z=26):
decoded = (coded + k) mod 26
If the shift goes backwards:
decoded = (coded – k + 26) mod 26
Example:
D (4) → J (10) → k = 10 – 4 = 6.
Mirror (Reverse)
decoded = 27 – coded
Example:
A (1) → Z (26) → 27 – 1 = 26.
Combined Shift + Mirror
Apply one after the other:
decoded = 27 – ((coded + k) mod 26)
5. Tricky Points & Common Pitfalls
- Multiple Possible Rules – Always test if all pairs satisfy the same rule.
- Non‑Alphabetic Characters – Spaces, commas, and numbers usually stay unchanged.
- Repeated Letters – A single letter may map to a different letter in different positions if the rule is word‑based.
- Word‑Level Coding – The rule may apply to whole words (e.g.,
FAST → QUICK). Be alert for such patterns. - Mixed Rules – Some problems use two operations (e.g., shift + reversal). Test each separately before combining.
- Edge Cases – When the code ends with a letter that would wrap around (e.g.,
Y → Cwith shift +4). Always use modulo arithmetic.
6. Sample Problems & Solutions
6.1 Simple Shift
Given
Code → Decode
DOG → JAR