How to solve logic puzzles, step by step

Zebra puzzles, logic grids and picture puzzles like Hence all come down to the same handful of moves. Here are six of them, each shown on a real board, plus a tiny puzzle to try them on.

The idea underneath every logic puzzle

A logic puzzle, or zebra puzzle, gives you a few categories (people, houses, pets, or in Hence, monsters, hats and sweets) and a set of clues about how they line up. Each item belongs in exactly one place. You don't find the answer by guessing. You find it by keeping track of what is still possible, and crossing things off until only one option is left everywhere.

The boards below are drawn the way Hence draws them. Each row is one category. Each square shows the pictures it could still hold, and a square settles into one big picture when only one is left. A green ring marks the squares a step changed.

1. Direct placement

The simplest move: a clue ties two things together, and one of them is already placed. Then the other goes in the same spot. In a written zebra puzzle that's "the Norwegian lives in the first house". In Hence it's two tiles stacked together: they share a column.

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Notice the bonus: once the ghost is placed, it disappears from every other square in its row. Each item is used exactly once, so a placement is always an elimination too.

2. Direct elimination

Most clues don't place anything on their own, but they almost always rule something out. Read every clue asking "where can this not be?" A picture between two others can't be on an edge. A picture somewhere left of another can't be in the last column, and the one on the right can't be in the first.

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These edge rules are the best way into a fresh puzzle. They work before anything else is known.

3. Either-or pairs

Sometimes you can't place anything yet, but two squares have narrowed down to the same two options. You don't know which is which, but you know those two pictures are spoken for.

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The same goes for three squares sharing the same three options. Hence also has a clue built on either-or: a tile with a fork is in the same column as one of two others, never both.

4. Cross-category chaining

Clues connect across rows, and connections stack. If the ghost shares a column with the crown, and the crown shares one with the donut, then all three move as a group. Anything that rules out one of them rules out all three.

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This is where the hard puzzles are won. When you're stuck, look for two clues that mention the same picture and combine them into one bigger fact.

5. Negative clues

"Not" clues feel weaker, but they're often the ones that finish a puzzle. In Hence a red ✕ turns a clue into its opposite: not in the same column, or not next to each other. Read them precisely. Not next to means not in the neighboring columns, and nothing more.

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6. The only remaining position

The flip side of direct placement. Instead of asking "what can this square hold?", ask "where can this picture go?" If a picture is still possible in only one square of its row, it goes there, whatever else that square still shows.

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It's easy to miss because the square doesn't look solved. Make a habit of scanning each row picture by picture, not just square by square.

Putting it together

1. Open with the edge rules from between and left-of clues.
2. Place anything a clue ties to a picture that's already placed.
3. After every placement, clear that picture from the rest of its row.
4. Scan each row for a picture with only one square left.
5. Look for pairs, then chain clues that share a picture.
6. Read the negative clues again. They're usually what's left at the end.

The techniques are the same whether the clues are written or drawn. To see them on a classic written puzzle, work through the solution to Einstein's riddle. To try them on a picture puzzle, Hence has a new one every day, from an easy Monday to a tricky Sunday.