Last reviewed 22 Sept 2026 · 6 min read
Every matching puzzle is a grid
Five people, five cities, five subjects — that is two grids, or one table with three columns. Draw the table before reading the clues a second time.
- Rows: the fixed set that never changes — usually the people, or the floors 1 to 7.
- Columns: each attribute to be matched.
- Fill a cell only when a clue forces it; write a small ✗ in a cell a clue forbids.
- Re-read the clue list from the top every time a new cell is filled: clues that were useless often become decisive.
Definite clues ("C lives on floor 3") → relative clues ("A lives two floors above B") → negative clues ("D does not teach physics"). A negative clue is worth little at the start and a great deal at the end.
Floor and stack puzzles
Seven floors, seven people: number the floors with 1 at the bottom and say so on your paper. Then:
- "A lives above B" means A's number is larger.
- "Exactly two people live between A and B" means their numbers differ by 3.
- "A lives immediately above B" means .
- The topmost and bottommost floors are the most constrained — clues about them are usually the ones to use first.
The same layout handles boxes stacked one on another and books piled on a shelf.
Scheduling puzzles
Days of the week, months, or dates in a month. Write the days in order along the top and mark what is fixed. Watch for two traps: a week that runs Monday to Sunday versus Sunday to Saturday, and clues that talk about "the day before" a day that is itself unknown.
Carrying two cases
When a clue allows two placements, start Case 1 and Case 2 side by side. Continue both until a later clue contradicts one. Deciding early which case "feels right" is the commonest reason a puzzle takes twenty minutes instead of four.
A worked puzzle
Five friends — Amit, Bina, Chetan, Deepa and Esha — live on five floors of a building (1 at the bottom to 5 at the top). Each likes a different colour: red, blue, green, white, yellow.
- Chetan lives on floor 4.
- The one who likes red lives immediately below Chetan.
- Amit lives on the topmost floor.
- Bina does not live on floor 1.
- The one who likes blue lives on floor 1.
- Deepa likes green.
- Esha does not like white.
From 1 and 3: Chetan is on 4, Amit on 5. Floors 1, 2 and 3 are left for Bina, Deepa and Esha; by 4, Bina is on 2 or 3.
From 2: the red-lover is on floor 3. From 5: the blue-lover is on floor 1. From 6: Deepa likes green, so Deepa is not on floor 1 or 3 → Deepa is on floor 2, so Bina is on 3 and Esha on 1.
So Bina (floor 3) likes red and Esha (floor 1) likes blue. By 7 Esha does not like white, which is consistent. White and yellow are left for Amit and Chetan, and no clue separates them — the puzzle fixes the floors and three colours, and leaves white and yellow undetermined.
| Floor | Person | Colour |
|---|---|---|
| 5 | Amit | white or yellow |
| 4 | Chetan | white or yellow |
| 3 | Bina | red |
| 2 | Deepa | green |
| 1 | Esha | blue |
A real exam set would add an eighth clue, such as "Chetan does not like yellow", which finishes the grid at once. Noticing what is not determined is itself a skill: several questions ask exactly that.
Worked examples
In a seven-floor building, P lives on floor 2 and exactly three people live between P and Q. Where does Q live?
Solution. Their floor numbers differ by 4 → Q is on floor 6 (floor does not exist).
R lives immediately above S, and S lives on floor 3 of six. Who lives on floor 4?
Solution. R.
Four people A, B, C, D take four subjects: maths, physics, chemistry, biology. A does not take maths or physics. B takes chemistry. C does not take biology. What does A take?
Solution. A takes chemistry or biology; chemistry is B's, so A takes biology. Then C takes maths or physics, and D takes the other.
A meeting is on a day between Tuesday and Friday, but not on Wednesday. Which day is it?
Solution. Between Tuesday and Friday means Wednesday or Thursday; not Wednesday → Thursday.
In a row of five boxes, box P is somewhere above box Q, and exactly one box lies between them. Box Q is not at the bottom. List the possible positions of P and Q.
Solution. Q at 2 → P at 4; Q at 3 → P at 5. Two cases survive, and neither can be ruled out without another clue.
Frequently tested points
- Draw the grid first; fill only what a clue forces, and mark ✗ for what it forbids.
- Use definite clues, then relative, then negative.
- In floor puzzles, state which end is floor 1 on your own paper.
- "Exactly between" means the numbers differ by .
- Carry two cases side by side rather than guessing.
- Re-read the clue list after every new entry.
- Filling a cell on a hunch and building the rest of the grid on it.
- Reading "above" as a bigger number in one puzzle and a smaller one in the next — fix the convention once.
- Treating "between A and B" as an order.
- Abandoning a case too early, or forgetting to finish the second one.
- Missing that the puzzle genuinely leaves something open.
- Matching puzzles are grids: rows for the fixed set, columns for each attribute.
- Clues are used in order — definite, relative, then negative.
- Floor and box puzzles need an explicit numbering convention before anything else.
- When a clue allows two placements, both are carried until one is contradicted.
- Recognising what the clues do not determine is part of the answer, not a failure.