No — in standard Numberlink, paths cannot cross, share a cell, overlap, or branch. Each pair of matching numbers must be connected by one continuous line that visits each cell at most once, moves only orthogonally through cell centers, and may turn only at right angles. A line that touches or passes through another line's cell is treated as a collision; a line that bends into more than one new direction from a single step creates a branch and is also rejected. This is the same-number-pair definition published by Nikoli and reproduced independently by the National Museum of Mathematics.
The rule exists because the puzzle is fundamentally a routing problem with a single shared resource: empty cells. Once any cell is claimed by a path, every other path must detour around it. That constraint is what makes Numberlink solvable in a deliberate, step-by-step way rather than as a free drawing exercise. If you remember only one thing, remember this: one cell, one line, one path. A different game sometimes called Number Link asks players to connect 1, 2, 3, and later numbers in sequence with straight segments; that sequential variant uses a different rule and is not what this board implements.
What the no-crossing rule looks like on the board
On a 5x5 grid, the practical effect is clear. Each cell can belong to at most one continuous path. That means the four numbered endpoints sit on four distinct cells, and the route connecting one pair must stay inside a corridor that the other pair's route leaves alone. The two routes together fill ten cells — the four numbered endpoints plus six intermediate path cells from the eight accepted steps — leaving fifteen cells open for free cursor navigation.
Three specific situations are forbidden by the rule, and each one is reported the moment you try it:
- Crossing. A cell that already holds part of path A cannot be stepped through by path B, even for a single orthogonal move. The second line would visually cross the first.
- Sharing. Two paths cannot run through the same cell on different moves; the cell belongs to whoever arrived first and stays locked for the rest of the solve.
- Branching. A single path cannot split into two directions from one cell; every cell on a path has at most two orthogonal neighbours that are also on the same path, so a fork or a T-junction is rejected.
Wrong endpoints are a separate rule but worth noting alongside the others. A path for the pair labeled 1 must terminate at the other cell labeled 1; trying to step into a cell labeled 2 reports a wrong-endpoint error rather than a collision, because the cell is empty but the label is wrong. The puzzle is finished only when both 1s are connected and both 2s are connected, with no shared, crossed, or branched cells between them.
How to play Numberlink Puzzle by keyboard
The full keyboard workflow is short and reproducible. The board is a fixed 5x5 layout: the two 1s sit on the top row and the two 2s sit on the bottom row, which makes the optimal route a pair of straight horizontal lines plus a free move between them. Numberlink Puzzle ships with that layout, so the eight-step clean solution can be replayed identically on every load.
- Use the arrow keys to move the cursor onto an unused numbered endpoint (one of the 1s).
- Press Space or Enter to start that pair's path. The cursor now extends the line one orthogonal step at a time with each arrow press.
- Draw four steps across the top row to connect both 1s, then press Backspace if you want to undo any cell you just placed; Backspace at the starting cell cancels the route entirely.
- When no route is active, move freely with the arrows to either endpoint of pair 2.
- Press Space or Enter to start pair 2, then draw four steps across the bottom row to connect both 2s.
- Both pairs are now finished. Use Restart to replay the same board, or press Escape twice within 400 milliseconds to reveal the shared simulated operations spreadsheet, then repeat the double press to restore the unchanged puzzle.
The implementation enforces every rule above as you play. Trying to enter a cell already occupied by either path produces a collision warning; trying to enter the other pair's numbered endpoint produces a wrong-endpoint warning. In both cases the line is not silently altered, so Backspace or a different direction recovers the active route without resetting the rest of the board.
Controls and what each key does
| Key | Action | When it counts |
|---|---|---|
| Arrow keys (no active route) | Move the cursor freely across cells | Does not reduce score |
| Space or Enter on an endpoint | Start that pair's path | Does not reduce score |
| Arrow keys (route active) | Attempt to extend the path by one orthogonal cell | Only accepted extensions count as a move |
| Backspace (route active) | Remove the last path cell, or cancel the route at its start | Restores the cell and any score it had consumed |
| Restart | Clear both paths, selection, contradictions, move count, and score | Resets to the 1,000 starting points |
| Escape twice within 400 ms | Toggle the shared simulated operations spreadsheet, then return to the unchanged puzzle | Puzzle state is preserved |
Board edges stop the cursor rather than wrap, so an arrow press at the rim is simply ignored instead of teleporting to the opposite side. The selected cell always carries a visible outline, and every cell announces its position and whether it is an endpoint or part of a path, which keeps the puzzle readable under any active theme. There is no canvas, image asset, hard-coded palette, pointer-only gesture, or audio dependency — the whole game works with a keyboard.
Scoring, moves, and why path steps matter
Score begins at 1,000 and decreases only when the puzzle accepts a path extension. The formula is straightforward: score = max(0, 1000 − 10 × accepted path steps). Free cursor moves and route starts do not reduce the score, and a rejected extension (collision or wrong endpoint) does not either — the cell you tried to enter simply does not get added to the line, and the score stays where it was.
On the fixed 5x5 board, the cleanest solution uses exactly eight accepted path steps. Starting from 1,000 points: 1,000 − 10 × 8 = 920. The puzzle then freezes drawing and preserves the final score until you press Restart, which clears both paths, selection, active pair, contradictions, move count, and score. If you want to keep a best score, it is stored only in your browser's localStorage under a game-specific key; it is not uploaded, attached to an account, or compared on a public leaderboard.
Contradiction detection runs continuously, not just at the end. The automated tests for the implementation exercise orthogonal and diagonal movement, reused cells, overlapping paths, wrong endpoints, the four-endpoint invariant, and the full eight-step completion sequence. Practically, that means the moment you step into a forbidden cell you know exactly which rule you broke, which is the fastest way to internalise the no-crossing, no-sharing, no-branching rule by feel rather than by reading.
Other path-planning puzzles with strict cell rules
Numberlink's no-crossing cell rule is shared, in different forms, by several other logic puzzles. If you enjoy planning a single route that respects every cell, try one of these next.
- Hashi Bridges connects numbered islands with non-crossing single or double bridges; every bridge claims its own cells and two bridges between the same pair must run on parallel, non-overlapping cells.
- Hitori Puzzle shades repeated numbers from a 5x5 grid while keeping every black cell apart and every remaining white cell connected; the connectivity requirement echoes the way Numberlink paths must stay reachable.
- Pipes Puzzle rotates nine fixed pipe tiles until every opening matches a neighbour and all tiles form one connected network without a closed loop, which is the rotation-based cousin of Numberlink's orthogonal routing.
- Tents Puzzle pairs trees with tents while matching row and column clues and keeping every tent apart, including diagonally — a no-touch cell rule applied to placements instead of lines.
All four share the same Numberlink discipline: one resource per cell, no reuse, no overlap. You can rotate between them as short route-planning challenges, not as measures of cognition.
A short recap of the no-crossing rule
The standard Numberlink rule, as published by Nikoli and reproduced by the National Museum of Mathematics, is that each cell belongs to at most one path, paths cannot cross, paths cannot overlap, paths cannot branch, and a route cannot terminate at the other pair's number. Numberlink Puzzle applies that rule to a fixed 5x5 board with two 1s and two 2s, draws paths only orthogonally through cell centers, reports collisions and wrong endpoints the moment you make them, and lets Backspace recover the active route without resetting the whole board. Start at an unused endpoint, draw four steps across the top, free-move to a 2, draw four steps across the bottom, and the eight-step solution scores 920 points from a 1,000 starting value — proof that the no-crossing rule is not a limitation but the structure that makes the puzzle solve cleanly.