Chapter 28
Coding, Decoding & Analogies
Letter–number substitution, mirror/water coding, analogical reasoning.
Full Chapter Notes
Source · FPSC Trap Decoder · CSS MPT Smart Notes (2026 Edition)
28.1 High-Yield Snapshot
| Topic | MPT Weightage | Difficulty | Confirmed Questions (2022–2025) |
|---|---|---|---|
| Coding, Decoding & Analogies | 3–5 Marks | Low to Medium | 6 direct questions across 4 past papers |
Coding and decoding questions appear across every MPT paper and reward candidates who approach them methodically rather than randomly.
Four Question Types FPSC Uses
| Type | Description |
|---|---|
| Number-Value Coding | A word is given a numerical value using a hidden rule |
| Letter-Shift Coding | Each letter is replaced by another letter a fixed number of steps away in the alphabet |
| Word Analogy | If search means learn, then explore means…? |
| "None of These" Pattern | FPSC intentionally provides an unsolvable or ambiguous code — making option D correct |
Recognising when to attempt a code and when to identify it as None of These is itself a testable skill.
28.2 Concept Anchor
Every coding question has a rule. Your job is to find that rule from the examples given, then apply it to the target word.
Universal method — apply this to every coding question:
- Write the alphabet positions of every letter in every example.
- Look for a mathematical relationship between those positions and the given code.
- Confirm the rule with the second example.
- If no consistent rule can be found — the answer is None of these.
FPSC uses the None of these trap deliberately. Candidates who calculate properly will confidently choose D rather than guessing from A, B, C.
28.3 The Alphabet Reference — Memorise This
This is the single most important tool in the entire chapter. Every coding question requires it.
Forward Alphabet (A = 1 ... Z = 26)
| A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Reverse Alphabet (Z = 1 ... A = 26)
| A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 |
| N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
Reverse shortcut. The reverse position of any letter with position p = (27 − p). Example: A has position 1 → 27 − 1 = 26 = Z. Y has position 25 → 27 − 25 = 2 = B.
28.4 The Four Coding Types FPSC Uses
Type 1 — Number-Value Coding
Each word is assigned a number. The candidate must find the mathematical relationship between the letter positions and the assigned number, then apply it to the target word.
Three-step method for number-value coding.
- Write the position of each letter in the alphabet (A=1, B=2…).
- Test operations systematically: sum, product, first-letter × count, first-letter × unique letter count.
- Confirm the rule with the second example before applying to the target word.
- ME: M=13, E=5. First letter × unique letters: 13 × 2 = 26 ✓
- MEET: M=13, E=5, E=5, T=20. Unique = {M, E, T} = 3. 13 × 3 = 39 ✓
Applying the confirmed rule to NUT: N=14. Unique letters = {N, U, T} = 3. 14 × 3 = 42. Options given: 50, 53, 56. None equals 42 → answer = None of these.
Confirmed: CSS MPT 2023 Special Q83 and Q144.
Another common number-coding pattern — sum of positions: ACE = 1+3+5 = 9; BDF = 2+4+6 = 12; GIK = 7+9+11 = 27.
Type 2 — Letter-Shift Coding
Each letter in the word is replaced by a letter a fixed number of steps forward or backward in the alphabet. The shift is constant throughout the word.
Method for letter-shift coding.
- Take the first letter of the coded and decoded versions.
- Count how many steps forward or backward to get from one to the other.
- Verify the same shift with the second letter.
- Apply the same shift to every letter of the target word.
-
C(3) → F(6): +3 steps
-
A(1) → D(4): +3 steps
-
T(20) → W(23): +3 steps → Shift = +3 confirmed
-
DOG: D(4)+3 = G(7), O(15)+3 = R(18), G(7)+3 = J(10) → GRJ
Wraparound rule. If the shift takes you past Z, start again from A. Example: X(24) + 3 = A (X → Y → Z → A). Z + 1 = A.
Type 3 — Word Analogy Coding
A word is given a new meaning (e.g., search means learn). The candidate must find the pair in the answer options that has the same relationship.
Method for word analogy coding.
- Understand what the given word means in context.
- State the relationship as a full sentence, then verify your answer follows the same sentence structure.
- Apply the same relationship to the answer options.
Search means learn → both are about acquiring information/knowledge. The answer pair must have the same relationship: explore : discover — both mean finding/acquiring knowledge. ✓
Confirmed: CSS MPT 2023 Special Q118.
Common relationship types FPSC uses:
| Relationship Type | Example | How to State It |
|---|---|---|
| Synonyms | fast : quick | "Fast means quick." |
| Antonyms | hot : cold | "Hot is the opposite of cold." |
| Part to whole | chapter : book | "A chapter is part of a book." |
| Tool to purpose | pen : write | "A pen is used to write." |
| Cause to effect | fire : smoke | "Fire causes smoke." |
| Professional to workplace | doctor : hospital | "A doctor works at a hospital." |
Type 4 — Letter-Substitution Coding (Custom Cipher)
Each letter is assigned a specific digit that does not follow standard alphabet positions or a simple shift. The cipher table must be derived from multiple examples.
- From CAT=283: C=2, A=8, T=3
- From HAT=383: H=3, A=8, T=3 (A=8, T=3 consistent ✓)
- From ARE=801: A=8, R=0, E=1 (A=8 consistent ✓)
Now attempt BETTER: B=?, E=1, T=3, T=3, E=1, R=0. B has never been defined in any of the given examples → without B's code, BETTER cannot be completed → answer = None of these.
Confirmed: CSS MPT 2023 Special Q141.
FPSC Trap — the 'Letter Not Defined' Rule. When FPSC gives a custom cipher and the target word contains a letter whose value has NOT been established in the examples — the answer is always None of these.
28.5 Section 1 — Position-Value Coding Worked Examples
Problem. If ME = 26 and MEET = 39, then NUT = ? (A) 50 (B) 53 (C) 56 (D) None of these
Step 1 — Positions. M = 13, E = 5, E = 5, T = 20. N = 14, U = 21, T = 20.
Step 2 — Test rules.
- Sum of positions: 13+5 = 18 ≠ 26 ✗
- Product: 13×5 = 65 ≠ 26 ✗
- 1st letter × total letters: 13×2 = 26 ✓; 13×4 = 52 ≠ 39 ✗
- 1st letter × unique letters: ME unique = {M, E} = 2 → 13×2 = 26 ✓; MEET unique = {M, E, T} = 3 → 13×3 = 39 ✓ Rule confirmed.
Step 3 — Apply. N=14, unique {N, U, T} = 3 → NUT = 14 × 3 = 42.
Step 4 — Verify. Options 50, 53, 56 — none equals 42 → answer = (D) None of these.
Rule: Value = (Position of 1st letter) × (Number of unique letters).
Golden Rule — Systematic Testing.
- Always test SUM first, then PRODUCT, then multiply variants.
- When a rule passes for one word but fails for another → discard and move on.
- When no standard rule works → the answer is almost always (D) None of these.
- Unique letters is the most common twist in FPSC elite coding questions.
Problem. If PEN = 36 and PIN = 38, then PUN = ? (A) 33 (B) 35 (C) 40 (D) None of these
Step 1 — Positions. P=16, E=5, N=14, Sum(PEN) = 35. P=16, I=9, N=14, Sum(PIN) = 39. P=16, U=21, N=14, Sum(PUN) = 51.
Step 2 — Test rules.
- Sum + 1: 35+1 = 36 ✓; 39+1 = 40 ≠ 38 ✗
- Sum + len: 35+3 = 38 ≠ 36 ✗
- P+N+1: 16+14+1 = 31 ≠ 36 ✗
- P×E+N: 16×5+14 = 94 ≠ 36 ✗
No rule satisfies both PEN=36 AND PIN=38 simultaneously.
Step 3 — Conclusion. Since no consistent rule holds for both clue-words, PUN cannot be determined → answer = (D) None of these.
FPSC Trap. Sum+1 passes for PEN but fails for PIN. A rule must work for ALL given examples. Do not select an option just because a rule works for one of the two examples.
28.6 Section 2 — Letter-Shift (Caesar Cipher) Coding
Problem. If COLD is coded as FROG, find the code for HEAT.
Step 1 — Find shift.
| Letter | Original Position | Coded Letter | Coded Position | Shift |
|---|---|---|---|---|
| C | 3 | F | 6 | +3 |
| O | 15 | R | 18 | +3 |
| L | 12 | O | 15 | +3 |
| D | 4 | G | 7 | +3 |
Shift = +3 confirmed.
Step 2 — Apply +3 to HEAT.
| Letter | Original | +3 | New Position | Code |
|---|---|---|---|---|
| H | 8 | +3 | 11 | K |
| E | 5 | +3 | 8 | H |
| A | 1 | +3 | 4 | D |
| T | 20 | +3 | 23 | W |
Answer: HEAT → KHDW.
Caesar Cipher — Key Rules.
- Forward shift: add the shift value to each letter's position.
- Backward shift: subtract the shift value.
- Wrap-around: if position > 26, subtract 26 (Z+1 wraps back to A). If position < 1, add 26 (A−1 wraps to Z).
- Example wrap: Y(25) + 3 = 28 → 28 − 26 = 2 = B.
Problem. In a code: A=Z, B=Y, C=X (reverse alphabet). What does YES mean in code?
Formula. Mirror position = 27 − Original position (because A=1 ↔ Z=26, and 1+26 = 27; B=2 ↔ Y=25, and 2+25 = 27, etc.).
| Letter | Position | 27 − Position | Mirror Letter |
|---|---|---|---|
| Y | 25 | 27 − 25 = 2 | B |
| E | 5 | 27 − 5 = 22 | V |
| S | 19 | 27 − 19 = 8 | H |
Answer: YES → BVH.
Exam Strategy — Mirror Pairs always sum to 27. A(1) + Z(26) = 27; M(13) + N(14) = 27; T(20) + G(7) = 27. If you know A=Z and M=N, you can derive any mirror letter instantly.
28.7 Section 3 — Word Analogy
Problem. Doctor is to Hospital as Teacher is to: (A) School (B) Student (C) Book (D) Lesson
Step 1 — Relationship. "A Doctor works in a Hospital." Relationship type = Professional → Workplace.
Step 2 — Apply. "A Teacher works in a ____." → A Teacher works in a School.
Eliminate distractors.
- (B) Student → Teacher's client, not workplace.
- (C) Book → Teacher's tool, not workplace.
- (D) Lesson → Teacher's output, not workplace.
Answer: (A) School. Relationship = Professional → primary workplace.
FPSC Trap. Options (B) Student and (D) Lesson are planted to catch candidates who think of related words instead of the correct relationship. Always state the relationship as a sentence first, then apply it.
Common FPSC Analogy Relationship Types
| Relationship Type | Example Pair | Test Sentence |
|---|---|---|
| Professional → Workplace | Doctor : Hospital | "A ___ works in a ___." |
| Tool → User | Pen : Writer | "A ___ is used by a ___." |
| Part → Whole | Petal : Flower | "A ___ is a part of a ___." |
| Cause → Effect | Heat : Fire | "___ is caused by ___." |
| Antonym | Hot : Cold | "___ is the opposite of ___." |
| Synonym | Big : Large | "___ means the same as ___." |
| Product → Source | Wool : Sheep | "___ comes from a ___." |
| Degree of intensity | Warm : Hot | "___ is a weaker form of ___." |
28.8 Quick Reference — Coding Methods & Strategies
| Coding Type | Formula / Rule | FPSC Tip |
|---|---|---|
| Position-Value | Value = f(letter positions) | Test sum, product, multiply variants |
| 1st × Unique | Value = pos(1st) × unique letters | Most common FPSC elite twist |
| Caesar Cipher | Code pos = orig pos ± shift | Find shift from one letter pair |
| Wrap-around | > 26 → subtract 26; < 1 → add 26 | Z+1 = A; A−1 = Z |
| Mirror (Atbash) | Code pos = 27 − orig pos | A↔Z, B↔Y, M↔N (pairs sum to 27) |
| Word Analogy | State relationship as sentence | Never pick a related word — pick same relationship |
| None of These (D) | Rule fails for ≥ 1 example | Test ALL given examples before choosing D |
28.9 Common Mistakes
| Mistake | Wrong Approach | Correct Approach |
|---|---|---|
| Testing only one operation | ME=26: sum gives 18, doesn't work → give up | Test multiple operations systematically: sum, product, first×count, first×unique count. Confirm rule with BOTH examples before applying |
| Guessing "None of These" without calculating | Question looks hard → mark D immediately | Calculate your specific answer (e.g., 42 for NUT). Then check: does it appear in A, B, or C? If not → D |
| Applying the wrong shift direction | Shift is +3, so apply −3 to target | Confirm direction: if coded letter is later in alphabet → shift is positive (+) |
| Forgetting wraparound in letter shifts | "Past Z" → error or skip | X(24)+3 = A: wrap around after Z (Y=25, Z=26, A=1) |
28.10 FPSC Trap Alerts
The MEET Pattern Trap. FPSC presents ME=26, MEET=39 and expects candidates to find the rule. Students who test sum of positions get 18 for ME — and stop. The actual rule (first letter × count of unique letters) requires testing multiple operations. Always test at least four operations before concluding a code is undecipherable.
The 'B is Not Defined' Trap. In CAT=283, HAT=383, ARE=801, the cipher defines A=8, C=2, T=3, H=3, R=0, E=1. The target word BETTER needs B — which was never defined. Answer = None of these. This is an intentional FPSC design, not a flawed question.
The Analogy Direction Trap. Doctor : Hospital — the relationship is "professional works at location." In harder analogies, direction matters. Always identify which element comes first and what it means about the second element.
The Synonym vs Category Trap. Cat : Animal means "specific to general category." Dog : Cat means both are animals — same category. These look similar but represent different relationships. Always state the relationship in a full sentence before selecting.
28.11 The 5-Minute Battle Card
- Alphabet forward: A=1, B=2, C=3… M=13, N=14… Z=26.
- Alphabet reverse: A=26, B=25… M=14, N=13… Z=1.
- ME=26 rule: first letter position (M=13) × number of UNIQUE letters (2) = 26.
- MEET=39: M=13 × unique letters {M, E, T} = 3. 13 × 3 = 39.
- NUT: N=14 × 3 unique letters = 42 → None of these (42 not in options).
- CAT=283: C=2, A=8, T=3. HAT=383: H=3, A=8, T=3. ARE=801: A=8, R=0, E=1.
- BETTER needs B — B was never defined in examples → None of these.
- Letter-shift rule: find the shift from the first letter, verify with the second, apply to all.
- X+3 = A (wraparound after Z). Z+1 = A.
- Reverse alphabet shortcut: reverse position of letter p = (27 − p). Y → 27 − 25 = 2 = B.
- Word analogy method: state the relationship as a full sentence, then verify the answer matches.
- Doctor works at Hospital → Teacher works at School. Search means learn → Explore means discover.
- None of these is correct ONLY when your calculated answer genuinely does not appear in options.
- Always calculate first. Never guess None of these.
- Four operations to test in number-coding: sum, product, first×count, first×unique count.
28.12 Practice MCQs — FPSC Level
Basic Recall (Green Level)
Direct rule application (Q1–Q5).
If A=1, B=2, C=3… Z=26, what is the value of the word ACE?
Show explanation
A=1, C=3, E=5. Sum = 1+3+5 = 9. This is the simplest coding question — direct sum of letter positions.
MPT 2022, 2024 — sum of positions
In a code where each letter is shifted 3 places forward (A→D, B→E…), what is the code for CAT?
Show explanation
Shift = +3. C(3)+3=F(6). A(1)+3=D(4). T(20)+3=W(23). Code = FDW. Verify: C→F ✓, A→D ✓, T→W ✓.
MPT 2023
Doctor is to Hospital as Teacher is to:
Show explanation
Doctor works at Hospital. Professional → workplace. Teacher works at School. Trap: Student (teacher's client, not workplace). Lesson (teacher's product, not workplace).
MPT 2022, 2023
If A=Z, B=Y, C=X (reverse alphabet coding), what is the code for BAD?
Show explanation
Reverse alphabet: A=Z, B=Y, C=X, D=W. BAD: B → Y. A → Z. D → W (27−4=23=W). Code = YZW.
MPT 2024
If 'search' means 'learn', which pair has the same relationship?
Show explanation
Search means learn — both involve finding/acquiring knowledge. Explore means discover — the same relationship: the act of searching leads to finding.
MPT 2023 Special Q118
Trap-Based (Red Level)
Custom ciphers and 'None of these' detection (Q6–Q10).
If ME=26 and MEET=39, what is the value of NUT?
Show explanation
Rule: first letter position × number of UNIQUE letters. ME: unique=2, M=13, 13×2=26 ✓. MEET: unique=3, M=13, 13×3=39 ✓. NUT: unique {N,U,T}=3, N=14, 14×3=42. 42 is not among options → None of these.
MPT 2023 Special Q83 and Q144
If CAT is coded as FDW using a letter-shift, what is the code for DOG?
Show explanation
Shift = +3 (from CAT→FDW: C+3=F, A+3=D, T+3=W). DOG: D(4)+3=G(7). O(15)+3=R(18). G(7)+3=J(10). Code = GRJ.
Trap: FPSC Elite Trap — applying shift to multi-letter word
If PEN=36 and PIN=38, what is PAN?
Show explanation
PEN sum = 35, PIN sum = 39. Sum+1 passes PEN (36) but fails PIN (40 ≠ 38). No consistent single-operation rule works for both examples. Answer = None of these.
Trap: FPSC Elite Trap — find the hidden rule
Pen is to Write as Knife is to:
Show explanation
Pen is used to write. Tool → its primary purpose. Knife is used to cut. Trap: Sharp (property), Metal (material), Kitchen (location).
MPT 2023 — tool to purpose
If CAT=283, HAT=383, and ARE=801, what is the code for BETTER?
Show explanation
From examples: C=2, A=8, T=3, H=3, R=0, E=1. BETTER: B=?, E=1, T=3, T=3, E=1, R=0. B has never been defined in any example → cannot be determined → None of these.
MPT 2023 Special Q141
Elite Simulation (Highest Difficulty)
Multi-step verification (Q11–Q15).
If SUN=19+21+14=54 (sum of positions), what is MOON?
Show explanation
Rule: sum of letter positions. MOON: M=13, O=15, O=15, N=14. Sum = 13+15+15+14 = 57.
Trap: Sum of letter positions
In a code, BOOK is written as CPPL. What is the code for READ?
Show explanation
BOOK→CPPL: B(2)→C(3)+1, O(15)→P(16)+1, O(15)→P(16)+1, K(11)→L(12)+1. Shift = +1. READ: R(18)+1=S, E(5)+1=F, A(1)+1=B, D(4)+1=E. Code = SFBE.
Trap: Letter shift +1
Statements: (1) Fish:Water :: Bird:Air. (2) Pen:Ink :: Car:Petrol. (3) Doctor:Patient :: Teacher:Lesson. Which analogies are correctly stated?
Show explanation
(1) Fish lives in Water, Bird lives in Air — creature : natural medium ✓. (2) Pen uses Ink, Car uses Petrol — tool : consumable ✓. (3) Doctor serves Patient (person); Teacher serves Students (not Lesson) ✗.
Trap: Statement 3 has a wrong object
If MANGO is written as OCPIQ, by what rule is the coding done?
Show explanation
MANGO → OCPIQ: M(13)+2=O(15) ✓, A(1)+2=C(3) ✓, N(14)+2=P(16) ✓, G(7)+2=I(9) ✓, O(15)+2=Q(17) ✓. Shift = +2 for every letter.
Trap: Identify the shift
If SIT=57 and HIT=49, then BIT = ?
Show explanation
SIT positions sum = 48, HIT sum = 37. Sum+9: SIT=57 ✓ but HIT=46 ≠ 49 ✗. First letter ×3: SIT=57 ✓ but HIT=24 ≠ 49 ✗. No consistent rule emerges → None of these.
Trap: Decode the rule first
Answer Key with Trap Analysis
Coding, Decoding & Analogies (Q1–Q15)
| Q | Correct | Type | Primary Trap | Why Others Fail |
|---|