Types of Logic Puzzles: Nine Kinds and How to Start Each

The nine main types of logic puzzles are grid and deduction puzzles, truth-teller and liar puzzles, weighing puzzles, sliding tile puzzles, peg-jumping puzzles, knight's tours and other chessboard puzzles, packing and dissection puzzles, path and maze puzzles, and sequence puzzles. Each one asks you to reach a single answer from fixed rules, but each rewards a different first move.

This guide describes every type in turn: what it is, how to start, and a live riddle to try where one fits. A comparison table near the end puts them side by side.

What do all logic puzzles have in common?

Every logic puzzle has three parts: a starting position, a set of rules and a goal. You never need outside knowledge, only careful reasoning about what the rules allow.

What changes from type to type is the thing you reason about. In some it is facts about people, in others it is weights, positions on a board or the shapes of pieces. Knowing which type you face tells you which tool to pick up first.

What are grid and deduction puzzles?

A grid puzzle gives you groups of things, such as people, colours and places, and clues that link them. Each item in one group matches exactly one item in each other group, and the clues are enough to pin down every match.

How to start: draw a small table for every pair of groups. Put an X where a clue rules a pairing out and a tick where it confirms one. When only one empty cell is left in a row or column, it must be a tick. After every tick, look across to the other tables and copy what it tells you there.

Deduction puzzles without a grid, such as working out a lock code from hints, use the same idea: list the possibilities, then let each clue rule some out.

What are truth-teller and liar puzzles?

Each person in these puzzles either always tells the truth or always lies, and you must work out who is who from what they say.

How to start: pick one speaker and assume they tell the truth. Follow what that means for everyone else. If you reach a contradiction, the assumption was wrong and that speaker is a liar. Then check every statement against your final answer.

What are weighing puzzles?

You have several coins that look identical. One is fake and lighter than the rest, and you must find it with a balance scale in as few weighings as possible ^[1]. This puzzle first appeared in 1945, and many variations have been studied since ^[1].

A balance can show only three results: the pans level, the left pan lighter or the right pan lighter ^[1]. Each fake coin must lead to its own string of results, so two weighings can separate at most nine coins and three weighings at most twenty-seven ^[1].

How to start: split the coins into three equal groups, not two. Weigh two groups against each other. If one pan rises, the fake is in that group; if the pans stay level, it is in the group you kept off. Each weighing leaves a third as many suspects.

Newer versions are much harder. A paper published on 26 June 2025 studied a fake coin that changes its weight each time it goes on the scale, switching between lighter, heavier and normal in a fixed pattern ^[1].

Here is a balance riddle with shapes instead of coins:

What are sliding tile puzzles?

A sliding tile puzzle is a square tray of numbered tiles with one empty space. You slide a tile next to the space into it, one move at a time, until the tiles are back in order ^[2]. Accounts place the fifteen-tile version as far back as the 1870s ^[2].

For square trays of any size, working out the fewest possible moves has been proved NP-hard ^[2]. In plain words, it belongs to a class of problems that get very slow to solve exactly as they grow.

For small trays the answers are known. No position of the eight-tile puzzle needs more than 31 moves, and no position of the fifteen-tile puzzle needs more than 80 ^[2].

One surprise: some tile arrangements can never be reached by sliding. A tray where someone has swapped two tiles by hand cannot be put right by sliding alone.

How to start: finish the top row, then the left column, and treat what remains as a smaller puzzle ^[2]. A paper published on 10 July 2015 showed that this row-by-row approach needs about eight thirds of n cubed moves on average for a tray with n tiles on each side ^[2].

What are peg-jumping puzzles?

Peg solitaire uses a board of holes filled with pegs, with at least one hole left empty. A move is a peg jumping over a neighbour into an empty hole, and the jumped peg comes off the board. The usual goal is to finish with a single peg.

The game was invented in the late 17th century and set off an early craze for puzzles ^[3]. On the 33-hole plus-shaped board alone, 150,077 solvable symmetric positions were counted in a 2017 paper ^[3]. Puzzles where only one opening jump leads to a solution turn out much harder than symmetric ones, and a few of them have just one complete solution, which is rare for this game ^[3].

How to start: count the pegs so you know how many jumps you need. Keep the pegs in a compact group, avoid stranding single pegs in corners and arms, and when a position looks hopeless, try thinking backwards from the final peg.

What are knight's tours and other chessboard puzzles?

A knight's tour moves a chess knight so that it lands on every square of the board exactly once. If the last square is a knight's move away from the first, the tour is called closed ^[4].

Not every board allows one. A 1991 result showed that a rectangular board has a closed tour unless both sides are odd, the shorter side is 1, 2 or 4, or the shorter side is 3 and the longer side is 4, 6 or 8 ^[4]. The standard board of 8 by 8 passes this test, but the small 4 by 4 board has no tour of any kind ^[4].

The idea even works in three dimensions: a paper published on 9 May 2007 showed that, for side lengths of 4 or more, a cube of cells has a closed knight's tour exactly when its side length is even ^[4].

How to start: from each square, move to the square that has the fewest onward moves still open. Corners and edges get used up early that way, so you usually meet fewer dead ends near the finish.

Other chessboard puzzles ask you to place pieces rather than move them, such as fitting as many queens as possible so that none attacks another. Start those by filling one row at a time and backing up as soon as a row has no safe square.

What are packing and dissection puzzles?

A packing puzzle asks you to fit a set of pieces into a space without overlaps or gaps. A dissection puzzle runs the other way: cut one shape into pieces that rearrange into another shape of the same area.

The best-known packing challenge starts from a neat coincidence: squares of side 1 to 24 have areas that add up exactly to the area of a square of side 70 ^[5]. Even so, they cannot fill it. The best arrangement has to leave out the square of side 7, and a computer search proved that no packing wastes less space ^[5].

How to start: place the largest pieces first, against the corners and edges, because they have the fewest places they can go. Save the small pieces for the gaps at the end.

What are path, maze and sequence puzzles?

A maze or path puzzle asks for a route from a start to a goal, sometimes the shortest one. A sequence puzzle shows a run of numbers or shapes and asks what comes next.

How to start a maze: work backwards from the goal as well as forwards from the start, and fill in dead ends as you find them so you never walk them twice. For shortest-route puzzles, write the shortest distance to each point as you go.

How to start a sequence: look at the gaps between neighbouring terms. If the gaps themselves follow a pattern, such as growing by the same amount each time, you have the rule.

How do the types compare?

Which type should you try first?

If you are new to logic puzzles, start with grid and sequence puzzles. They need only a pencil, and the methods carry over to almost every other type. Weighing and truth-teller puzzles come next, because they train the habit of testing an assumption. Board and tray puzzles reward patience and planning, so save them for when you want a longer challenge.

Whatever the type, the same three habits help: write down what the rules allow, never mark a guess as a fact, and check your final answer against every rule.

For one more deduction puzzle, try cracking this lock from its clues: