Logic grid puzzles (Zebra and Einstein puzzles): how to solve them

Updated 2026-10-30

Logic grid puzzles give you a short story, a list of clues and a few categories, and ask you to work out which items belong together. You solve them by marking a grid with X for “no” and ✓ for “yes” until only one answer is left in every row.

What is a logic grid puzzle?

A typical puzzle has three to five categories, each with the same number of items. For example: four friends, four pets and four favourite colours. Each friend has exactly one pet and one colour, and no two friends share either. The clues say things like “The person with the cat doesn’t like green” or “Ana owns either the dog or the parrot.” From these, you deduce the full set of matches.

These puzzles go by many names: logic grid puzzles, logic problems, Zebra puzzles, and Einstein puzzles or Einstein’s riddle. The core skill is the same in all of them.

Setting up the grid

The classic logic grid is a staircase of smaller squares. Each square compares two categories: friends against pets, friends against colours, and pets against colours. Each cell in a square answers one question, such as “Does Ana own the cat?”

• Put an X in a cell when the pairing is impossible.
• Put a ✓ in a cell when the pairing is certain.

Many puzzle books print the grid for you. If yours doesn’t, drawing it takes a minute and saves a lot of confusion later.

The main solving techniques

Direct clues

Start with the easy ones. “Ben doesn’t own the cat” is one X. “The dog owner likes red” is one ✓ in the pets-against-colours square. Go through every clue once and record what it says directly.

Eliminating after a ✓

Because each item matches exactly one item in every other category, a ✓ lets you X out the rest of its row and its column within that square. If Ana owns the dog, nobody else owns the dog and Ana owns nothing else. This is the most frequent move in the whole puzzle.

The last empty cell

The reverse also holds: if a row in a square has X in every cell but one, that last cell is a ✓. Scan for nearly full rows and columns often.

Transitive reasoning

This is where logic grids get interesting. If Ana owns the dog, and the dog owner likes red, then Ana likes red. Likewise for negatives: if Ana owns the dog, and the dog owner does not like blue, then Ana does not like blue. Whenever you place a ✓, copy everything you know about one item over to its partner in the other squares.

“Either–or” and ordering clues

Clues like “the parrot belongs to Ana or to the person who likes green” tell you two different things: Ana can’t like green (otherwise the clue names one person twice, which such clues usually rule out), and the parrot can only go to one of two people. Ordering clues work similarly: “Ben finished somewhere before the cat owner” means Ben did not finish last, the cat owner did not finish first, and Ben is not the cat owner. Read each clue slowly and list every fact it implies.

The famous Zebra puzzle

The best-known logic grid puzzle is the Zebra puzzle. Five houses stand in a row, each painted a different colour. In each lives a person of a different nationality, who keeps a different pet, prefers a different drink and smokes a different brand of cigarette. Around fifteen clues follow, such as “The Englishman lives in the red house” and “The green house is immediately to the right of the ivory house.” The questions at the end: who drinks water, and who owns the zebra?

Neither water nor the zebra appears in any clue, which is what makes the puzzle famous: you must fill in everything else and find the answer by elimination. In the usual version, the answer is that the Norwegian drinks water and the Japanese man owns the zebra.

The puzzle is often called “Einstein’s riddle,” sometimes with the claim that he wrote it or that only a small percentage of people can solve it. There is no evidence for either claim. It is better to enjoy it simply as a classic. Position clues (“next to,” “immediately to the right of”) make it harder than a basic grid, and many solvers use a table with one column per house instead of the staircase grid.

Tips for solving faster

• Re-read clues. A clue that was useless at the start often becomes decisive after a few marks.
• Tick off used clues. Once a clue is fully recorded, mark it so you don’t keep re-reading it.
• Write down chains. For position puzzles, jot a short list of possible arrangements for a pair of houses.
• Avoid guessing. A good puzzle has one solution reachable by logic. If you are stuck, a clue has probably been under-used.
• Check at the end. Go through every clue against your final answer to catch mistakes.

If you like logic grids

Murder-mystery formats add a story and a floor plan to the same deduction; see our guide to Murdoku and murder-mystery puzzles. If you enjoy the “exactly one per row and column” feel of a logic grid, Star Battle uses the same idea on a picture-free grid with regions. You can play Star Battle for free here, or browse more puzzles like Sudoku.