How to solve murder mystery logic puzzles without guessing

Most murder mystery logic puzzles share one idea: you are not hunting for a motive or reading a story for hints, you are working out where everyone was. Once every person has a place, the killer falls out of the arrangement on its own. That shift matters. You stop asking who seems guilty and start asking who could possibly have stood where.

In Motive the arrangement follows a sudoku rule. Suspects stand on a floor plan divided into rooms, no two people share a row or a column, and the body takes up its own row and column too. Every statement under the board is true. Whoever ends up alone with the body is the killer. Those few rules are enough to turn a crime scene into a grid you can reason about square by square.

The methods below work for this family of puzzles in general, but the examples use Motive's rules because they are precise, and precision is what lets you solve without guessing.

Reading the statements in the order they are listed is the most common way to stall. Instead, sort them by how many squares they leave open. A statement that names a row or a column is strong, because it leaves at most one line of the board. A statement that names a small room is strong for the same reason. A statement like "east of someone" is weak on its own, because it rules out very little until one of the two people is placed.

1. Strongest: a named row or column, a small room, standing on a particular piece of furniture.
2. Middle: a larger room, alone in a room, back to an outer wall.
3. Weakest at the start: beside someone, north, south, east or west of someone, statements that pair two suspects.

In Motive you can tap a statement to pick the person it is about, and rings show every square that person could still be standing on. Counting rings is a quick way to confirm your ranking: the person with the fewest rings is usually where to begin.

The single most useful habit is to see each placement as a cross drawn through the board. When you place someone, their whole row and their whole column are now closed to everyone else. The body does the same from the very start, so begin every case by mentally striking out the body's row and column.

Here is a small worked example, described in words. Picture a 5×5 floor plan with the body in row 2, column 4. Before reading a single statement, you already know that nobody stands anywhere in row 2 or column 4. That removes nine of the twenty-five squares for the whole cast. The rules and the statements always fit together, so if a statement ever seems to point into a struck-out line, you have misread it, not found a trick.

Now change the example. The cook was in column 1, and column 1 has only two squares that are not blocked by furniture or struck out by the body's row. You have just reduced the cook to two options without placing anyone. Add a second statement that the cook stood with their back to an outer wall, and if only one of those two squares is on the edge of the floor plan, the cook is placed. Two modest statements, read together, did what neither could do alone.

Room statements are easy to underrate because each one seems to allow many squares. Their real power comes when you combine them. "Alone in a room" means nobody else was in that room, not even the body. "An empty room" means nobody stood anywhere inside it. Both remove a whole room from every other suspect at once, which is often more than a row statement removes.

Try this habit: after every placement, look at each room and ask how many open squares it still has and how many people could still reach them. If a room that someone must stand in is down to one open square, place them. If a room is empty by statement, cross off every square in it for the whole cast. You can use Rule out to pencil those crosses onto the board so you do not have to hold them in your head.

Statements that link two people, such as one suspect being beside another or north of another, are weak until one of the two is fixed. Once you have an anchor, they become very strong. "Beside" in Motive means directly above, below, left or right, and inside the same room, so a wall between two squares breaks it. With one person placed, "beside" leaves at most four squares, and walls and the row and column rule often cut that to one.

Direction statements work the same way. North is up the board and west is to the left. If the gardener is north of the butler and the butler is placed in row 2, the gardener must be in row 1. On a small board that alone can be decisive. Keep a short list of these linked statements and revisit it every time you place someone new.

It is tempting to go straight for the culprit. Resist it. In these puzzles the killer is defined by the final arrangement: the one person who ends up alone in the body's room. If you place everyone else first, the answer usually reveals itself without any extra work. Some statements describe the killer without naming them; treat those as one more constraint on the final position rather than as a shortcut.

Leaving the killer for last also protects you from a classic error, which is placing someone in the body's room early because they look guilty, then building the rest of the solution around a guess.

• Forgetting the body's row and column. Strike them out first, every time.
• Treating beside as diagonal. Diagonal squares are never beside, and a wall breaks the link even when the squares touch.
• Reading alone in a room as alone with the body. Alone means nobody else at all, the body included.
• Placing on a hunch. If two squares are still possible, find the statement that separates them instead of trying one.
• Re-reading only the statements you have not used. A placement can make an old, weak statement decisive.

Motive is a free murder mystery logic puzzle for iPhone, iPad and Android, supported by ads. Every case has exactly one solution and can be solved without guessing, so the steps above always lead somewhere. The first cases use 5×5 floor plans with four suspects, which is a comfortable size for building the habits of ranking statements and drawing crosses. Floor plans later grow to 8×8 with seven suspects, where pairing room statements and anchoring relative clues start to pay off.

Each case gives you three hearts: a placement that breaks a statement costs one, and losing all three starts the case again. When you are stuck, a hint shows where someone can still be, and undo takes back a move. Cases work offline and Motive is translated into 40 languages, statements included.