How to solve logic riddles: the grid method
The technique that turns «five people, five houses and ten clues» puzzles into something mechanical. With a worked example, step by step.
There is a kind of puzzle that turns up everywhere — civil service exams, puzzle books, job interviews — and it always looks the same:
Five friends live in five houses of different colours. Each drinks something different and keeps a different pet. The one in the red house drinks tea. The dog does not live next to the cat…
Plenty of people try them in their head, get lost by the fourth clue and conclude they are no good at them. It is not a question of talent: they cannot be done in your head, and the people who solve them fast are not doing them in their head. They use a grid.
The idea
The whole trick fits in one sentence: write down what is impossible, not only what is certain.
Instinct says you should note what you work out. But in these puzzles most clues do not tell you who is what, they tell you who is not what. «Martha does not drink coffee» looks like nothing, and crossing out that cell is what ends up solving the puzzle: when a row has a single cell left uncrossed, that is the answer, even though no clue ever told you.
How to set up the grid
Draw a grid with the two categories you want to cross. People in the rows, drinks in the columns:
tea coffee water wine juice
Martha · · · · ·
Louis · · · · ·
Anna · · · · ·And use two symbols: X for «impossible», O for «confirmed».
The rule that makes it all work: when you place an O, cross out its whole row and its whole column. If Martha drinks tea, Martha drinks nothing else and nobody else drinks tea. A single confirmation hands out eight crosses. That cascade is the engine of the method.
A small example, solved
Three friends — Martha, Louis and Anna — drink tea, coffee and water, one each.
- Martha does not drink coffee.
- Louis drinks neither tea nor coffee.
Off we go.
Clue 2 first. It is the most restrictive, and that is the other big trick: do not work in order, start with the clue that crosses out the most. Louis drinks neither tea nor coffee → two Xs in Louis's row. And since there are only three drinks, Louis has one left: water. An O confirmed without any clue ever saying «Louis drinks water».
Cascade. Louis drinks water → nobody else does. An X for Martha and Anna in the water column.
Clue 1. Martha does not drink coffee. Her row already had water crossed out (from the cascade) and now coffee too. She is left with tea.
Cascade again. Martha drinks tea → Anna does not. And Anna has only coffee left.
Solved — and notice that Anna's answer appeared in no clue at all. It came out of the crosses on its own. That is the part you cannot do in your head.
The types of clue and what to do with each
Direct. «Anna drinks coffee.» A straight O and a cascade. These are gifts, use them first.
Negative. «Martha does not drink coffee.» One X. They look useless and they are most of the puzzle.
Relational. «The tea drinker lives next to the dog.» These do not go in the grid: note them separately and revisit them every time you confirm something new. They are the ones that fire later on.
Mutual exclusion. «The one who drinks tea is neither Martha nor Louis.» Two Xs in one go, and sometimes an implicit O.
Positional. «It is immediately to the left of…». These work better on a separate strip, drawing the positions in a line and testing where the block fits.
Four tips that save a lot of time
Re-read the clues every time you confirm something. A clue that was useless three steps ago can solve the whole puzzle now. Most deadlocks are exactly that: a clue you already used which now says more.
Never guess. These puzzles are built to have a unique solution reachable by deduction. If you find yourself trying things out, there is a deduction you have not seen, usually a row with a single free cell.
Check whole rows and columns. The commonest error is not deducing badly, it is not looking. Get into the habit of sweeping: does any row have one free cell left? Any column?
Start with the smallest category. If there are five people but only three colours, start with the colours.
Where to practise
Classic logic riddles are in the Riddle puzzle, and the version with a grid and a criminal case is Criminoku: five suspects, a 5×5 grid, clues of several types and one culprit. There the grid comes ready drawn — it is the board itself — so it is a good place to practise the method without having to set it up on paper.
Every case has a verified unique solution, so if you catch yourself guessing, it is not the puzzle: it is a deduction that got away from you.
You can play here, and if deduction is your thing you might like what a murdoku is.