Maze puzzles: rules, strategy, and free play

THE RULES

1. Start at the marked start cell; end at the marked end cell. Both endpoints are pre-marked. Your path must begin at the start and finish at the end.
2. Walk between edge-sharing neighbours only. On a SQUARE maze, every interior cell has 4 neighbours (up/down/left/right). On a CIRCULAR maze, every cell has 4 neighbours too (inner/outer/clockwise/anticlockwise within the ring). On a HEX maze, every cell has 6 neighbours (covered separately on the Hex Mazes page).
3. Visit cells in strict numeric order. If you're on cell '4', your next step must land on a neighbouring cell showing '5'. No skipping numbers, no revisiting earlier numbers.
4. Visit every cell on the path exactly once. No revisits. The path forms a connected chain hitting each cell on the chain only once.

BEGINNER STRATEGY

• Trace from both ends. Working from both the start AND the end simultaneously usually meets in the middle faster than working forward only. Cells near the endpoints have fewer valid neighbours (grid edge) so they pin early steps.
• Spot forced single-neighbour moves. When you're on cell N and exactly one neighbour shows N+1, that step is forced. Place it; this often cascades 3-4 cells in a row.
• Eliminate dead-end branches. If a candidate next cell has only one onward neighbour with the right number, trace that branch forward. If it dead-ends (no valid neighbours mid-chain), the candidate is invalid — back up.
• Square vs Circular vs Hex. Square mazes feel like classic grid mazes (4 neighbours per cell). Circular mazes spiral around the centre with neighbours along ring + radial axes — different visual rhythm, same logic. Hex mazes have 6 neighbours per cell (more branching, deeper deductions) — see the dedicated Hex Mazes guide.
• Never guess. A legitimate maze has exactly one valid path. If you're guessing, look for an unevaluated single-neighbour-forced step or a dead-end branch you assumed was open.

COMMON MISTAKES

• Walking forward step-by-step without a dead-end check. Placing cell N+1 without first checking that N+2 is reachable from that cell is the most common trap. Always trace one step ahead: before committing to a cell, confirm that at least one of its neighbours shows the next number.
• Forgetting no-revisit after backtracking. When you undo a wrong step, it's easy to re-enter a previously visited cell on the second attempt. Re-entering a cell mid-path is illegal — make sure backtracked cells are fully cleared before re-tracing.
• Not tracing from both ends. Starting-end cells often have very few valid neighbours, making the first 2-3 steps trivially forced. Ending-end cells often have the same property. Solving both ends simultaneously finds the constrained segments first.
• Treating circular mazes like square mazes. In circular mazes, cells have four neighbours but arranged differently — an inner-ring cell's 'up' neighbour is the outer ring, not the next row. Misidentifying which cells are adjacent is the most common error when encountering circular topology for the first time.

HOW TO THINK ABOUT IT

Mazes are path-constraint puzzles, not number puzzles. The digits are order markers, not values — they define the sequence the path must follow. Think globally before locally: before committing to a step, ask 'can the remaining numbers form a valid connected path from here to the end?' Forced moves (single valid neighbour) cascade quickly once the endpoints are anchored. The solve rhythm is: identify forced moves → commit → reveal the next forced move → repeat.

WHY THIS PUZZLE REWARDS YOU

Mazes are GridJoy's accessible-but-deceptive puzzles. Anyone can understand 'go from start to end one step at a time'; few realise how quickly the deduction depth scales when you add the strict-numeric-order constraint. Square and circular mazes feel familiar to anyone who's solved a paper maze book; the topology shifts to circular (wraparound on the longest ring) or hex (six neighbours, three axes) change the spatial reasoning style without changing the rules. All three variants share the same number-order chain — the only difference is what 'neighbour' means.

VARIANTS

• Square Mazes. Four neighbours per interior cell, classic grid layout. Most familiar maze feel.
• Circular Mazes. Cells arranged in rings; four neighbours but along ring + radial axes. The topology wraps on the longest ring, creating a different spatial rhythm than the square grid.
• Hex Mazes. Six neighbours per hex cell. Higher branching factor makes dead-ends harder to spot, but more constraints mean individual forced moves are common. Full guide at the Hex Mazes page.

YOU MIGHT ALSO LIKE

• Square Maze →

  Dedicated guide to the square-grid variant — corner forcing, orthogonal only.

• Circular Maze →

  Dedicated guide to the ring-topology variant — radial axes, inner-ring forcing.

• Hex Mazes →

  Same rules on a hex grid — 6 neighbours, three axes.

• Shikaku →

  Spatial cousin — divide a grid into rectangles.

• Starlink →

  Path-routing cousin — trace consecutive numbers across an 8-direction grid.

• Hitori →

  Topology-heavy shading puzzle — connectivity matters.

• Beginner mistakes in logic puzzles →

  Quitting too early is the most common one — and the hardest to spot.

• Number Mazes strategy for beginners →

  Sort gaps, fill smallest first, use dead-ends — if the mindset guide feels abstract, start here.

• Number Mazes: how to think →

  Anchor-first strategy — gap counting, dead ends, connectivity checks.

• Hex Mazes vs Number Mazes →

  Same path puzzle, different cell shape — what six neighbours changes.

• Starlink vs Number Mazes →

  Diagonal moves added — what eight neighbours changes versus four.

READ MORE

• Number Mazes: the sequential path puzzle explained →

  Anchor from given numbers, count cells between clues, and dead-ends reveal themselves.

MORE NUMBER PUZZLES

• SUDOKU →
• KAKURO →
• NUMBER CROSSWORD →
• CALCUDOKU →
• KILLER SUDOKU →
• HITORI →
• TAKUZU →
• SKYSCRAPER →
• SHIKAKU →
• SUMPLETE →
• NUMBER BLOCKS →
• HEX MAZES →
• STARLINK →
• INEQUALITY →
• COUNTDOWN →