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Matrix Puzzle

Introduction

Matrix Puzzles (जिसे grid puzzles भी कहा जाता है) ऐसे प्रश्न होते हैं जिनमें आपको rows और columns के बीच कई attributes को दिए गए logical clues के आधार पर match करना होता है। ये high-stakes exams में अक्सर आते हैं क्योंकि ये multi-attribute reasoning, elimination, और organised tabulation की क्षमता की परख करते हैं।

यह पैटर्न इसलिए ज़रूरी है कि यह आपको जानकारी को visual रूप में structure करने के लिए मजबूर करता है - verbal clues को एक साफ grid में बदलने से contradictions तुरंत दिखती हैं और समाधान तेज़ हो जाता है।

Pattern: Matrix Puzzle

Pattern

एक matrix puzzle N items और M attributes (अक्सर N = M) प्रस्तुत करता है। एक grid का उपयोग करके असंभव जोड़ों को eliminate करें और confirmed matches भरें।

  • Grid approach: Items को एक axis पर और attributes को दूसरी axis पर रखें; confirmed matches के लिए ✔ और impossibilities के लिए ✖ मार्क करें।
  • Use elimination: हर confirmed match उस attribute को बाकी items के लिए हटा देता है।
  • Chain clues: multi-step relations (उदा., A’s color → B’s food → C’s city) को ग्रिड में systematic तरीके से map करें।
  • Cross-check: भरने के बाद completed matrix के खिलाफ हर clue verify करें।

Step-by-Step Example

Question

चार students - Arjun, Binita, Chitra, Dev - अलग-अलग study resources उपयोग करते हैं (Book, Video, App, Notes) और अलग-अलग जगह पढ़ते हैं (Library, Home, Cafe, Park)। Clues:

  1. Arjun App का उपयोग नहीं करता और Cafe में नहीं पढ़ता।
  2. जो छात्र Video उपयोग करता है वह Park में पढ़ता है।
  3. Binita Notes का उपयोग करती है।
  4. Book-use करने वाला छात्र Home में पढ़ता है।
Question: कौन App का उपयोग करता है और वह कहाँ पढ़ता है?

Solution

  1. Step 1: Create the matrix

    Resource×Person और Place×Person के लिए 4×4 grid सेट करें। शुरू में सभी cells संभावित छोड़ें।

  2. Step 2: Fill direct facts

    Clue (3): Binita = Notes → Binita-Notes ✔ और बाकी लोगों के लिए Notes ✖।
    Clue (2): Video ↔ Park → Video-Park लिंक मार्क करें।
    Clue (4): Book → Home → Book-Home pair मार्क करें।

  3. Step 3: Apply exclusions

    Arjun ≠ App और Arjun ≠ Cafe (clue 1) → Arjun-App और Arjun-Cafe पर ✖ लगाएँ।

  4. Step 4: Use elimination to deduce linked pairs

    Binita = Notes रखने के बाद, बाकी लोगों के लिए resources {Book, Video, App} बचते हैं। Book→Home और Video→Park होने से, और Arjun के exclusions देखते हुए grid elimination से एक consistent mapping निकाला जा सकता है।

  5. Step 5: Build and show partial matrix

    Partial Resource × Person matrix (✔ = confirmed, ✖ = impossible)
    PersonBookVideoAppNotes
    Arjun✖✔✖✖
    Binita✖✖✖✔
    Chitra✔✖✖✖
    Dev✖✖✔✖
    और Places × Person:
    Place × Person mapping
    PersonLibraryHomeCafePark
    Arjun✖✖✖✔
    Binita✖✖✖✖
    Chitra✖✔✖✖
    Dev✔✖✖✖

  6. Step 6: Finalise mapping

    Partial matrices और linked clues (Video↔Park, Book↔Home, Notes↔Binita) से निष्कर्ष:
    • Chitra = Book और Home पर पढ़ती है।
    • Arjun = Video और Park में पढ़ता है।
    • Dev = App और Library में पढ़ता है।
    • Binita = Notes और बची हुई जगह Cafe में पढ़ती है (elimination से)।

  7. Final Answer:

    Dev App का उपयोग करता है और Library में पढ़ता है।

  8. Quick Check:

    सभी clues सत्यापित: Arjun ≠ App और ≠ Cafe (Arjun = Video, Park) ✔ Video→Park ✔ Binita→Notes ✔ Book→Home ✔

Quick Variations

1. Attributes बढ़ाएँ: time-of-day या tutor name जोड़ें (अधिक columns)।

2. Wrap-around schedule (circular ordering) - matrix + arrangement logic मिलाएँ।

3. Conditional clues जोड़ें: “If A uses Book, then B uses Video” - case-based grids बनाना होगा।

Trick to Always Use

  • Step 1: दो orthogonal grids बनाएं - एक Resource×Person के लिए और दूसरा Place×Person के लिए (या single multi-column matrix)।
  • Step 2: पहले direct ✔ facts भरें, फिर obvious ✖ exclusions mark करें, और उन प्रभावों को पूरे grid में फैलाएँ।
  • Step 3: जब किसी row में सभी but one ✖ हों तो शेष cell ✔ होगा - इसे तुरंत propagate करें।

Summary

Summary

  • हर attribute pair के लिए clear grids बनाएँ और जैसे-जैसे निष्कर्ष निकले उन्हें अपडेट रखें।
  • Confirmed matches पहले रखें (✔) और impossibilities (✖) मार्क करें ताकि elimination तेज़ हो।
  • हर नया confirmation पूरे matrix में propagate करें ताकि options जल्दी कम हों।
  • Final matrix के खिलाफ मूल clues को हमेशा दोबारा चेक करें।

याद रखने योग्य बात:
जब multiple attributes हों तो अलग-अलग परस्पर जुड़े matrices बनाएँ (Resource×Person, Place×Person)। पहले direct clues भरें, फिर elimination से बाकी cells lock करें।

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

  1. Step 1: Write down fixed clues

    A ≠ Bike/Bus → A uses Car or Train.
    D = Car.
    C = Chennai.
    Train user → Mumbai.

  2. Step 2: Partial matrix

    PersonTransportCity
    A≠ Bike/Bus-
    B--
    C-Chennai
    DCar-

  3. 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.

  4. Step 4: Remaining assignments

    C = Chennai → cannot be Mumbai → assign C = Bike (since Bus remains for B). Thus, B = Bus.

  5. Step 5: Final matrix

    PersonTransportCity
    ATrainMumbai
    BBusDelhi
    CBikeChennai
    DCarKolkata

  6. Final Answer:

    B → Option B

  7. 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

  1. Step 1: Identify fixed entries

    Q = Green; P = Math; R = English; T = Pink ≠ Geography.

  2. Step 2: Use History clue

    Yellow → History.

  3. Step 3: Partial matrix

    PersonColorSubject
    P-Math
    QGreen-
    R-English
    SYellowHistory
    TPink≠ Geography

  4. Step 4: Remaining colors

    Red left for P or R → fits with Math.

  5. Step 5: Final matrix

    PersonColorSubject
    PRedMath
    QGreenScience
    RBlueEnglish
    SYellowHistory
    TPinkGeography

  6. Final Answer:

    S → Option C

  7. 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

  1. Step 1: Assign given facts

    M = Coffee; N ≠ Banana; L ≠ Juice.

  2. Step 2: Orange ↔ Tea (linked pair)

    The person who likes Tea must also like Orange.

  3. Step 3: Partial matrix

    PersonDrinkFruit
    LTeaOrange
    MCoffeeBanana
    NJuiceApple

  4. Final Answer:

    L → Option A

  5. 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

  1. Step 1: Record direct facts

    J → Infosys; L → Wipro; M → HCL & Ford; TCS → Tata; Infosys → Honda.

  2. Step 2: Build partial matrix

    PersonCompanyCar
    JInfosysHonda
    KTCSTata
    LWipro-
    MHCLFord

  3. Step 3: Deduce the remaining car

    Cars used: Honda, Tata, Ford → only Hyundai left → goes to L.

  4. Step 4: Final matrix

    PersonCompanyCar
    JInfosysHonda
    KTCSTata
    LWiproHyundai
    MHCLFord

  5. Final Answer:

    L → Option C

  6. 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

  1. Step 1: Record fixed facts

    From clues: B = Rabbit; C = Blue; Red → Dog; A ≠ Fish.

  2. Step 2: Build partial matrix

    OwnerHouse ColorPet
    A-≠ Fish
    B-Rabbit
    CBlue-
    D--
    E--

  3. 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:
    OwnerHouse ColorPet
    AYellowCat
    BGreenRabbit
    CBlueFish
    DRedDog
    EWhiteParrot

  4. Final Answer:

    E → Option E

  5. 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.

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