A logic puzzle gives you a story and a few clues. You work out the answer by proving what cannot be true until only one thing is left. This page solves one small puzzle with you, one step at a time, then shows the two extra ideas the harder puzzles need.
In each picture the newest marks are orange.
Three friends, Ava, Ben and Mia, each have one pet: a cat, a dog and a fish. The names go down the side and the pets go across the top. Every box asks one question. The top left box asks: does Ava have the cat?
Clue 1 says Ava does not have the dog, so put an ✕ where Ava meets dog. Clue 2 says the same about Ben, so put an ✕ where Ben meets dog.
Look down the dog column. Two boxes are crossed out and one is empty. Somebody has the dog, so it has to be Mia. Put a ● there.
Mia has the dog, so she cannot also have the cat or the fish. Cross out the rest of Mia's row. Do this every time you place a ●.
Clue 3 says Ben does not have the cat. Mark the ✕. Now Ben's row has one empty box, so Ben has the fish. Put the ● and cross out the rest of the fish column.
Ava's row has one box left, so Ava has the cat. Every row and every column now has exactly one ●. Read each clue once more against your answer to make sure none is broken.
The answer: Ava has the cat, Ben has the fish and Mia has the dog.
A ● crosses out its row and column. Each person has one pet and each pet has one owner, so one yes makes every other box in that row and column a no.
One empty box left is a ●. Every row and every column needs exactly one yes. If all the other boxes are crossed out, the last one is it.
Most of a puzzle is these two rules, used again and again after each new clue.
Puzzles in books and on tests often come with only the story and the clues. You can rule the grid yourself in a minute.
If you would rather not rule lines, print the blank grids or use a sheet of graph paper.
Bigger puzzles ask two things about each person, such as a pet and an age. That takes three grids joined in an L shape: names against pets, names against ages, and pets against ages. Some clues never mention a name at all: "The dog's owner is not 9."
The new idea is carrying. A ● says two things belong together, so whatever is true of one is true of the other. Suppose you know Mia has the dog, and a clue says the dog's owner is not 9. Then Mia is not 9, and you can mark that ✕ in the names-and-ages grid even though no clue said it.
Every time you place a ●, look along both of its lines into the other grids and copy the marks across.
In the hardest puzzles you reach a point where no clue gives you another mark. There is still a way forward, and it is not a lucky guess.
Scientists and programmers use the same move. When you cannot see the answer directly, test an idea, and let a failure tell you something true.
Start with a starter puzzle, which uses only the six steps above. The medium puzzles add carrying, and the hard puzzles each need one try-it-and-see step.