Solving deduction puzzles with a grid
When clues describe who has what, a small grid turns a confusing paragraph into a handful of ticks and crosses.
Turn the sentences into a grid
A paragraph of clues is hard to hold in your head. A grid is not.
List the people down the side and the possibilities across the top. Now every clue has somewhere to live, and you never have to remember anything twice.
Use the negative clues
Clues that say what is not true feel useless. They are usually the most powerful thing you have.
Every "Ana does not have the dog" is a cross, and crosses add up. Three crosses in a row of four leave only one place the tick can go.
And a tick does double work: once Ana has the bird, nobody else can, so the rest of that column fills with crosses too.
Work in passes
Go through the clues once, marking everything you can. Then go through them again.
The second pass is where puzzles crack. A clue that told you nothing the first time often tells you everything once two crosses have appeared next to it.
Do not guess
If you cannot place anything, you have missed a clue, not run out of them. Read them all again.
A guess that happens to be right teaches you nothing, and a guess that is wrong takes the rest of the grid down with it.
One tick does four jobs
The moment you are certain of a pairing, put a tick in that box — and then cross out the whole of that row and the whole of that column.
If Ana has the cat, then Ana has neither the dog nor the bird, and neither Ben nor Cara has the cat. One certainty settles four other boxes for free.
Students who lose time on these puzzles usually write the tick and stop. The crossing out is where the next clue becomes readable.
When the clues seem to run out
If no clue tells you anything new, the grid usually does. Look for a row or a column with crosses in every box but one — that last box has to be a tick, even though no clue said so directly.
That is the move most people miss. The puzzle is not only the sentences; it is the sentences plus what the grid has already ruled out.
Work in passes: read every clue in order, mark what you can, then go round again. A clue that told you nothing the first time often tells you everything on the second pass.
Worked examples
Ana, Ben and Cara have a dog, a cat and a bird. Ana does not have the dog or the cat. Ben does not have the dog. Who has what?
Ana has crosses against dog and cat, so her row leaves only the bird: tick. That tick crosses out bird for Ben and Cara.
Ben now has crosses against dog and bird, so Ben has the cat. That leaves the dog for Cara.
Answer: Ana the bird, Ben the cat, Cara the dog
In a grid of four people and four sports, you place a tick for Dev and tennis. What else can you fill in immediately?
Two whole lines. Dev plays tennis, so Dev plays nothing else: cross out the rest of Dev’s row. And tennis is taken, so nobody else plays it: cross out the rest of the tennis column. That is six crosses from one tick.
Answer: The rest of Dev’s row and the rest of the tennis column
A clue says "Cara does not sit next to Ben". Is that any use in a who-has-what grid?
Not on its own — it is about seating, not about who has what, so there is nowhere to put it in this grid. Keep it aside; clues like this usually matter once the grid is partly filled, or belong to a second grid about positions.
Answer: Not yet — it belongs to a different question
Three friends own a dog, a cat and a bird. Ana does not own the dog. Ben owns the bird. Who owns what?
Ben owns the bird, so cross out the bird for Ana and Cara, and the dog and cat for Ben. Ana does not own the dog, so Ana's only remaining box is the cat. That leaves the dog for Cara.
Answer: Ana the cat, Ben the bird, Cara the dog
In a four by four grid, a column has crosses in three of its four boxes and no clue mentions the fourth. What do you do?
The item in that column belongs to somebody, and three people have been ruled out. The remaining box must be a tick, then cross out the rest of its row.
Answer: Tick the only box left, then cross its row
A clue says "Dan finished before Mei". What can you mark?
Not a tick. But Dan cannot be last and Mei cannot be first, so cross those two boxes. Clues about order rule things out even when they name nobody's position exactly.
Answer: Cross Dan-last and Mei-first
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