Matching

Core Idea

Match items across two or more categories (e.g., person → city → profession) using a set of clues, most of which rule OUT combinations rather than confirming them directly.

Strategy

1. Build a grid — rows = one category, columns = another (add a third grid if there are 3+ categories)
2. Mark ✓ for confirmed matches and ✗ for ruled-out combinations as you read each clue
3. Apply direct/positive clues first ("Sara likes apple") — these give you free ✓ marks and let you cross off that row/column elsewhere
4. Apply negative clues next ("Ali does not like mango") — mark ✗ and use elimination: if a row has only one unmarked cell left, it must be ✓
5. Repeat elimination until the grid is fully solved — every row and column should end with exactly one ✓

Worked Example

Ali, Bilal, and Sara each like a different fruit: mango, apple, banana.

• Ali does not like mango.

• Sara likes apple.

• Bilal does not like banana.

• Sara = apple (given directly)
• Ali ≠ mango, and apple is taken by Sara, so Ali = banana (only option left)
• Bilal ≠ banana (given), banana is taken by Ali anyway, mango is the only option left → Bilal = mango
• Final: Sara=apple, Ali=banana, Bilal=mango

Worked Example (3 categories)

Three people (Amna, Bilal, Ceena) live in different cities (Lahore, Karachi, Multan) and have different jobs (Doctor, Engineer, Teacher).

• The person in Lahore is not a Teacher.

• Bilal lives in Karachi.

• Amna is a Doctor.

• Ceena is not in Multan.

• Bilal = Karachi (given)
• Ceena ≠ Multan, and Karachi is taken → Ceena = Lahore → Amna = Multan (only city left)
• Amna = Doctor (given)
• Lahore person (Ceena) ≠ Teacher → Ceena = Engineer (only non-teacher job left) → Bilal = Teacher (last one)
• Final: Amna=Multan/Doctor, Bilal=Karachi/Teacher, Ceena=Lahore/Engineer

Drill

1. Three friends (X, Y, Z) each own a different pet (Cat, Dog, Fish). X does not own a Dog. Y owns a Cat. Who owns the Fish? — X (Y=Cat, X≠Dog so X=Fish, Z=Dog)
2. Four people (A,B,C,D) sit in seats 1-4. A is not in seat 1 or 4. B is in seat 2. C is in seat 4. Where is D? — Seat 1 (A must be seat 3 since not 1/4 and 2/4 taken, D gets remaining seat 1)
3. Three students study different languages (French, German, Spanish). Sara doesn't study French. Ravi studies Spanish. Who studies French? — The remaining third student (since Sara≠French and Ravi=Spanish, French goes to whoever is left)

Practice tracker

YYYY-MM-DD

• Attempted/Correct:
• Mistake pattern: