Multi Variable

• How multi-variable puzzles track three or more attributes per entity (name × city × profession × hobby).
• To build and maintain a logic matrix without contradiction as clues accumulate.
• To prioritise high-degree clues that link the most variables at once.
• To solve Class 12 and CLAT-level assignment puzzles under time limits.

Level 1 — Foundations

Verbal: Each person has multiple traits. Clues constrain combinations until one full matching grid remains.

Matrix setup: Rows = people (fixed count). Columns = attributes (City, Sport, Rank, etc.). Cell = value for that person-attribute pair.

Clue translation examples:

Consistency rule: After each placement, scan row and column for forced singles — if only one empty in row, fill it if column allows.

Level 2 — Exam depth

Anchor variable strategy: Pick attribute with most direct assignments (e.g. five cities each used once) — complete that column first.

Negative space: Heavy use of ✗ marks reduces cases faster than hunting ✓.

Combined ordering + matching: Solve rank order first if clues are mostly temporal; map names to ranks; then fill matrix columns.

3D puzzles: Age + floor + vehicle — treat floor as numeric ordering column.

Verification: Every clue type-checked: "only one between" re-read after grid full.

Match four people to cities and jobs

People: P,Q,R,S. Cities: Delhi, Mumbai, Chennai, Kolkata (one each). Jobs: Engineer, Doctor, Lawyer, Teacher.
(1) P ≠ Delhi. (2) Engineer is in Mumbai. (3) Q is Doctor. (4) R is in Chennai. (5) Lawyer not in Kolkata.
Step 1 — Q=Doctor. Engineer=Mumbai.
Step 2 — R=Chennai → R not Engineer unless Chennai=Mumbai ✗ → Engineer in Mumbai ≠ R.
Step 3 — P≠Delhi; assign R=Chennai. S gets remaining city slots by elimination.
Step 4 — Lawyer ≠ Kolkata → Lawyer in Delhi/Mumbai/Chennai; fill remaining jobs on empty cells.
Complete grid by ticking forced singles; **unique solution** when all cells filled consistently.

Cross-check one clue against finished grid

After assignment, re-read "Engineer is in Mumbai" — verify person with Engineer has Mumbai, not just that some engineer exists somewhere.
Multi-variable errors often swap two columns — column-level verification catches swaps.

• 5 people, 3 attributes each — minimum cells in full matrix?
• Why mark ✗ before guessing ✓?
• Clue ties two attributes directly — which cell to fill first?
• Stretch: Outline approach when one attribute can repeat (e.g. multiple red shirts).

Revision tip: Revisit adjacent topics in Advanced Puzzles before mixed practice on Multi Variable.

Open the Practice tab for graded questions on Multi Variable.

Use a pencil grid; pen only final answers. When n exceeds four people, column-complete one attribute (city, colour) before scattered fills. If stuck, list entities with the fewest remaining options — propagate from constrained rows. Multi-variable sets often share one anchor clue; find the entity appearing in three or more statements. Time-box at four minutes, then flag and return.