Matrix Puzzle

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Introduction

Matrix Puzzles (also called grid puzzles) require you to match multiple attributes across rows and columns using a set of logical clues. They appear frequently in high-stakes exams because they test multi-attribute reasoning, elimination, and organised tabulation.

This pattern is important because it forces you to structure information visually - turning verbal clues into a neat grid makes contradictions obvious and solutions faster.

Pattern: Matrix Puzzle

A matrix puzzle presents N items and M attributes (often N = M). Use a grid to eliminate impossible pairs and fill in confirmed matches.

Grid approach: Create a table with items on one axis and attributes on the other; mark ✔ for confirmed matches and ✖ for impossibilities.
Use elimination: Each confirmed match removes that attribute from other items.
Chain clues: Map multi-step relations (A’s color → B’s food → C’s city) across the grid systematically.
Cross-check: After filling, verify every clue against the completed matrix.

Step-by-Step Example

Question

Four students - Arjun, Binita, Chitra, Dev - each use a different study resource (Book, Video, App, Notes) and study in a different place (Library, Home, Cafe, Park). Clues:

Arjun does not use the App and does not study in the Cafe.
The student who uses Video studies in the Park.
Binita uses Notes.
The Book-user studies at Home.

Question: Who uses the App and where does that person study?

Solution

Step 1: Create the matrix
Set up a 4×4 grid for Resources vs Names and another for Places vs Names. Start with all cells blank (possible).
Step 2: Fill direct facts
From clue (3): Binita = Notes → mark Notes ✔ for Binita and ✖ for Notes with others.
From clue (2): Video ↔ Park → mark Video-Park pair as linked (we will map resource→place soon).
From clue (4): Book → Home → mark Book-Home pair.
Step 3: Apply exclusions
Arjun ≠ App and Arjun ≠ Cafe (clue 1) → mark ✖ for Arjun-App and Arjun-Cafe.
Step 4: Use elimination to deduce linked pairs
After placing Binita = Notes, remaining resources for {Arjun, Chitra, Dev} are {Book, Video, App}. But Book → Home and Video → Park; since Arjun ≠ App and Arjun ≠ Cafe, Arjun cannot be App and cannot be Cafe (place restrictions). Use grid elimination to see consistent mapping: one consistent solution is:
Step 5: Build and show partial matrix

Partial Resource × Person matrix (✔ = confirmed, ✖ = impossible)
Person Book Video App Notes
Arjun ✖ ✔ ✖ ✖
Binita ✖ ✖ ✖ ✔
Chitra ✔ ✖ ✖ ✖
Dev ✖ ✖ ✔ ✖

And Places × Person:

Place × Person mapping
Person Library Home Cafe Park
Arjun ✖ ✖ ✖ ✔
Binita ✖ ✖ ✖ ✖
Chitra ✖ ✔ ✖ ✖
Dev ✔ ✖ ✖ ✖
Step 6: Finalise mapping
From the partial matrices and the linked clues (Video↔Park, Book↔Home, Notes↔Binita) we conclude:
- Chitra = Book & studies at Home.
- Arjun = Video & studies at Park.
- Dev = App & studies at Library.
- Binita = Notes & studies at Cafe (by elimination).
Final Answer:
Dev uses the App and studies in the Library.
Quick Check:
All clues verified: Arjun ≠ App and ≠ Cafe (Arjun = Video, Park) ✅ Video→Park ✅ Binita→Notes ✅ Book→Home ✅

Quick Variations

1. Increase attributes: add time-of-day or tutor name (more columns).

2. Use a wrap-around schedule (circular ordering) to combine matrix + arrangement logic.

3. Introduce conditional clues: “If A uses Book, then B uses Video” - forces case-based grids.

Trick to Always Use

Step 1: Make two orthogonal grids - one for Resource×Person, one for Place×Person (or combine into a single multi-column matrix).
Step 2: Fill direct ✔ facts first, mark obvious ✖ exclusions, then propagate implications across the grid.
Step 3: Use elimination: when a row has all but one ✖, the remaining cell is a ✔; propagate that to other rows/columns immediately.

Summary

Create clear grids for every attribute pair and keep them updated as you deduce facts.
Place confirmed matches first (✔) and mark impossibilities (✖) to speed elimination.
Propagate each new confirmation across the whole matrix to reduce options quickly.
Always re-check every original clue against your final matrix before finalising the answer.

Example to remember:
When multiple attributes exist, maintain separate but linked matrices (Resource×Person, Place×Person). Fill direct clues first, then use elimination to lock remaining cells.

Practice

(1/5)

1. Four employees - A, B, C, and D - each use a different mode of transport (Car, Bike, Bus, Train) and live in different cities (Delhi, Mumbai, Chennai, Kolkata). Clues: 1) A does not travel by Bike or Bus. 2) The one who uses Train lives in Mumbai. 3) D uses Car. 4) C lives in Chennai. Who travels by Bus?

easy

A. A

B. B

C. C

D. D

Solution

Step 1: Write down fixed clues
A ≠ Bike/Bus → A uses Car or Train.
D = Car.
C = Chennai.
Train user → Mumbai.
Step 2: Partial matrix
Person Transport City
A ≠ Bike/Bus -
B - -
C - Chennai
D Car -
Step 3: Deduce Train-Mumbai link
D = Car → D ≠ Train. So Train user is not D. A uses Car or Train, but D already uses Car, so A must be Train → A = Train → Mumbai.
Step 4: Remaining assignments
C = Chennai → cannot be Mumbai → assign C = Bike (since Bus remains for B). Thus, B = Bus.
Step 5: Final matrix
Person Transport City
A Train Mumbai
B Bus Delhi
C Bike Chennai
D Car Kolkata
Final Answer:
B → Option B
Quick Check:
A=Train→Mumbai ✅ D=Car ✅ C=Chennai ✅ Bus left for B ✅

Hint: If one pair is linked (like Train-Mumbai), fix it first to reduce grid options.

Common Mistakes: Overlooking unique city-transport mapping.

2. Five students - P, Q, R, S, and T - each like a different color (Red, Blue, Green, Yellow, Pink) and subject (Math, English, Science, History, Geography). Clues: 1) Q likes Green. 2) The student who likes Yellow studies History. 3) T likes Pink but not Geography. 4) P likes Math. 5) R likes English. Who studies History?

easy

A. Q

B. P

C. S

D. T

Solution

Step 1: Identify fixed entries
Q = Green; P = Math; R = English; T = Pink ≠ Geography.
Step 2: Use History clue
Yellow → History.
Step 3: Partial matrix
Person Color Subject
P - Math
Q Green -
R - English
S Yellow History
T Pink ≠ Geography
Step 4: Remaining colors
Red left for P or R → fits with Math.
Step 5: Final matrix
Person Color Subject
P Red Math
Q Green Science
R Blue English
S Yellow History
T Pink Geography
Final Answer:
S → Option C
Quick Check:
Yellow-History ✅ Pink-T ✅ Green-Q ✅

Hint: Link color-subject clues first to lock one full row in matrix.

Common Mistakes: Forgetting that 'not Geography' doesn’t fix a subject immediately.

3. Three friends - L, M, and N - have different favorite drinks (Tea, Coffee, Juice) and favorite fruits (Apple, Banana, Orange). Clues: 1) M likes Coffee. 2) The one who likes Tea also likes Orange. 3) N does not like Banana. 4) L does not like Juice. Who likes Orange?

medium

A. L

B. M

C. N

D. Cannot be determined

Solution

Step 1: Assign given facts
M = Coffee; N ≠ Banana; L ≠ Juice.
Step 2: Orange ↔ Tea (linked pair)
The person who likes Tea must also like Orange.
Step 3: Partial matrix
Person Drink Fruit
L Tea Orange
M Coffee Banana
N Juice Apple
Final Answer:
L → Option A
Quick Check:
Tea→Orange ✅ N≠Banana ✅ L≠Juice ✅

Hint: When one clue binds two attributes directly (Tea ↔ Orange), assign them together early.

Common Mistakes: Treating each clue separately instead of pairing dependent attributes.

4. Four people - J, K, L, M - work in four companies (Infosys, Wipro, TCS, HCL) and drive four cars (Honda, Tata, Ford, Hyundai). Clues: 1) J works in Infosys. 2) The TCS employee drives a Tata. 3) M drives a Ford and works in HCL. 4) L works in Wipro. 5) The Infosys employee drives a Honda. Who drives Hyundai?

medium

A. J

B. K

C. L

D. M

Solution

Step 1: Record direct facts
J → Infosys; L → Wipro; M → HCL & Ford; TCS → Tata; Infosys → Honda.
Step 2: Build partial matrix
Person Company Car
J Infosys Honda
K TCS Tata
L Wipro -
M HCL Ford
Step 3: Deduce the remaining car
Cars used: Honda, Tata, Ford → only Hyundai left → goes to L.
Step 4: Final matrix
Person Company Car
J Infosys Honda
K TCS Tata
L Wipro Hyundai
M HCL Ford
Final Answer:
L → Option C
Quick Check:
Infosys→Honda ✅ TCS→Tata ✅ HCL→Ford ✅ Remaining→Hyundai ✅

Hint: Assign direct one-to-one pairs first; then eliminate for the remaining column.

Common Mistakes: Overlooking elimination logic for the final unassigned attribute.

5. Five houses are painted in different colors (Red, Blue, Green, Yellow, White). Their owners - A, B, C, D, and E - have different pets (Dog, Cat, Parrot, Fish, Rabbit). Clues: 1) The Red house owner has a Dog. 2) The Green house owner lives next to the Yellow house owner. 3) B owns a Rabbit. 4) C lives in the Blue house. 5) A does not have a Fish. Who has the Parrot?

medium

A. A

B. B

C. C

D. D

E. E

Solution

Step 1: Record fixed facts
From clues: B = Rabbit; C = Blue; Red → Dog; A ≠ Fish.
Step 2: Build partial matrix
Owner House Color Pet
A - ≠ Fish
B - Rabbit
C Blue -
D - -
E - -
Step 3: Deduce remaining pairs
Assign C = Fish (since A ≠ Fish). Red-Dog pair must belong to one of D or E. To satisfy all clues, consistent arrangement:
Owner House Color Pet
A Yellow Cat
B Green Rabbit
C Blue Fish
D Red Dog
E White Parrot
Final Answer:
E → Option E
Quick Check:
B = Rabbit ✅ C = Blue & Fish ✅ Red owner D has Dog ✅ Green (B) adjacent to Yellow (A) ✅ A does not have Fish ✅

Hint: Start from color-pet pairs (like Red-Dog), then use adjacency to place Green/Yellow and fill remaining cells by elimination.

Common Mistakes: Assuming 'next to' implies a fixed left/right order without checking both neighbour placements; failing to assign the Fish early when A is excluded.

Person	Book	Video	App	Notes
Arjun	✖	✔	✖	✖
Binita	✖	✖	✖	✔
Chitra	✔	✖	✖	✖
Dev	✖	✖	✔	✖

Person	Color	Subject
P	Red	Math
Q	Green	Science
R	Blue	English
S	Yellow	History
T	Pink	Geography

Person	Transport	City
A	≠ Bike/Bus	-
B	-	-
C	-	Chennai
D	Car	-

Person	Transport	City
A	Train	Mumbai
B	Bus	Delhi
C	Bike	Chennai
D	Car	Kolkata

Person	Drink	Fruit
L	Tea	Orange
M	Coffee	Banana
N	Juice	Apple

Person	Company	Car
J	Infosys	Honda
K	TCS	Tata
L	Wipro	-
M	HCL	Ford

Matrix Puzzle

Start learning this pattern below

Introduction

Pattern: Matrix Puzzle

Step-by-Step Example

Question

Solution

Step 1: Create the matrix

Step 2: Fill direct facts

Step 3: Apply exclusions

Step 4: Use elimination to deduce linked pairs

Step 5: Build and show partial matrix

Step 6: Finalise mapping

Final Answer:

Quick Check:

Quick Variations

Trick to Always Use

Summary

Practice

Solution

Step 1: Write down fixed clues

Step 2: Partial matrix

Step 3: Deduce Train-Mumbai link

Step 4: Remaining assignments

Step 5: Final matrix

Final Answer:

Quick Check:

Solution

Step 1: Identify fixed entries

Step 2: Use History clue

Step 3: Partial matrix

Step 4: Remaining colors

Step 5: Final matrix

Final Answer:

Quick Check:

Solution

Step 1: Assign given facts

Step 2: Orange ↔ Tea (linked pair)

Step 3: Partial matrix

Final Answer:

Quick Check:

Solution

Step 1: Record direct facts

Step 2: Build partial matrix

Step 3: Deduce the remaining car

Step 4: Final matrix

Final Answer:

Quick Check:

Solution

Step 1: Record fixed facts

Step 2: Build partial matrix

Step 3: Deduce remaining pairs

Final Answer:

Quick Check: