Matrix
Logic grids, elimination, one-to-one matching.
Matrix
Matrix (Logic Grid) Puzzles
What you'll learn
- To solve logic grids matching two or three categories (person–colour–pet) using elimination.
- One-to-one rule: each item matches exactly one in each column unless stated otherwise.
- To mark ✓ and ✗ on a table — systematic, not guess-and-check randomly.
- Foundation for Class 5 reasoning and later competitive exam grid puzzles.
NCERT / CBSE link
Math-Magic 5, Chapter 12 (Smart Charts) uses tables and grids — the same systematic marking skills as matrix puzzles. CBSE olympiad reasoning papers use similar grids for Class 5–6.
Key concepts
Level 1 — Grid setup
Verbal: Rows = one category (names); columns = another (favourite fruit); cells = match yes/no.
Symbolic: If Ali → mango, then Ali ≠ apple and no one else → mango (one-to-one).
| Clue | Grid action |
|---|---|
| Riya has cat | Riya–cat ✓; others–cat ✗ |
| Cat not with Sam | Sam–cat ✗ |
| Only two boys | Use gender row |
Method: 1) Draw empty grid. 2) Fill definite ✓. 3) Cross ✗ in same row/column. 4) Repeat.
Level 2 — Elimination chains
Verbal: When a row has only one blank left, that must be the match — forced move.
Real-life: Sudoku-like thinking without numbers — attribute matching.
| Step | Action |
|---|---|
| Definite match | Mark ✓, cross rest of row/column |
| Forced cell | Only one option left in row |
| Check consistency | Re-read clues if contradiction |
Worked example
3 children: Ana, Ben, Cy. Pets: dog, fish, parrot. Clues: Ana has dog. Ben does not have parrot. Who has fish?
Step 1 — Grid 3×3 pets.
Step 2 — Ana–dog ✓ → Ben,Cy not dog; Ana not fish/parrot.
Step 3 — Ben not parrot → Ben fish or dog; dog taken → Ben fish ✓
Step 4 — Cy parrot ✓
Answer: Ben has fish.
Colours: Red, Blue. Owners: P, Q. P not Red. Who has Blue?
Step 1 — P not Red → P Blue ✓, Q Red ✓
Answer: P has Blue.
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Two ✓ in same row | Broke one-to-one | Only one match per row |
| Guess without crosses | Random filling | Every ✓ forces ✗ |
| Skip re-reading clues | Miss "not" | Highlight NOT in question |
| Grid too small | Missing category | List all categories first |
Quick check
- What does one-to-one mean in a grid?
- Ana–dog ✓ — what crosses follow in Ana's row?
- Two people, two cities: clue "X not Delhi" — what follows?
- Stretch: 3×3 grid — after two ✓ marks, how many cells resolved by elimination?
Revision tip: Print a blank 4×4 grid — practise with names and sports until ✓/✗ feels automatic.
Open the Practice tab for graded questions on Matrix Puzzles.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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