How to solve logic puzzles (grid method)

The rules

A logic grid puzzle gives you a few categories, such as people, pets and ages, with the same number of items in each. Every person is matched with exactly one item from every other category, and no item is shared. Your job is to use the clues to work out every match. A well-made puzzle, like every puzzle on this site, has exactly one solution, so you never need to guess.

How the grid works

The grid is a set of small boxes, one for every pair of categories. Each square asks one question: do these two items belong together? You answer with one of two marks:

• ✕ means "definitely not". Most of your marks will be crosses.
• ● means "these two match".

Inside any box, each row and each column has exactly one ●. So the moment you place a ●, you can cross out the rest of its row and column in that box. And when a row has every square but one crossed out, the last square must be the ●. Those two facts do most of the work in every puzzle.

A step-by-step method

1. Mark the direct clues first. Clues like "Grace has the parrot" give you a ● straight away. Clues like "the person who plays the violin isn't Hugo" give you a ✕.
2. Fill in the consequences. After every ●, cross out the rest of its row and column in that box. Then look for rows or columns with only one square left.
3. Carry matches between boxes. If Grace has the parrot, and the parrot's owner is 27, then Grace is 27. Anything you know about one, you know about the other. This step is the one beginners most often miss.
4. Work the harder clues. Go back through the either-or and comparison clues, which usually only make sense once some matches are in place.
5. Repeat until done. Go through the clues again whenever you add a mark. A clue that told you nothing on the first pass often unlocks something on the third.

The five deductions that solve hard puzzles

1. Transfer through a match

If two items are matched, they share every other match and every other cross. If Ben has the dog and the dog's owner doesn't live in Carlow, Ben doesn't live in Carlow either.

2. Transfer crosses through a match

A cross also travels. If Ben has the dog, and you've ruled out "the dog's owner is 30", then Ben isn't 30.

3. Comparison clues remove the ends

"The person with the cat is older than Maya" tells you more than it seems. The cat's owner can't be the youngest age, Maya can't be the oldest, and Maya doesn't have the cat. "Exactly 3 years older" is even stronger: if the ages are 24, 27, 30 and 33, the pair must be 27/24, 30/27 or 33/30.

4. Either-or clues

"Dev either plays the piano or plays the drums" means Dev plays one of those two and nothing else, so you can cross out all of Dev's other instruments at once. If you later rule one option out, the other becomes a ●.

5. Two possibilities, two people

If two people can each only be 27 or 30, those two ages belong to them between them, so nobody else can be 27 or 30. This "pair" logic is often the final key in hard puzzles.

A short worked example

Three friends, Amara, Ben and Chloe, each have one pet: a cat, a dog or a rabbit. The clues:

1. Amara doesn't have the dog.
2. The person with the rabbit is Ben or Chloe.
3. Chloe doesn't have the rabbit.

Clue 2 rules out Amara for the rabbit, and clue 1 rules out Amara for the dog, so Amara has the cat. Clue 3 means Ben has the rabbit, leaving the dog for Chloe. Real puzzles have more categories, but every step is the same idea: cross out, look for the last square standing, and pass facts across matches.

Common mistakes

• Reading too much into a clue. "The cat's owner is older than Ben" doesn't mean they're next to each other in age unless it says "exactly".
• Forgetting the clue itself is a cross. "The person who chose red is younger than Zoe" also tells you Zoe didn't choose red.
• Not transferring. If you find yourself stuck with half the grid empty, go back to deductions 1 and 2. That's almost always the missing step.

Practise

Start with an easy logic grid puzzle, then work up to medium and hard. Or try today's daily puzzle.