About This Game
PathNum takes a classic puzzle mechanic that recently found new popularity through LinkedIn's daily puzzle lineup: drawing one continuous line that visits every square on the board exactly once, while passing through numbered squares in order. Mathematicians call this kind of puzzle a search for a Hamiltonian path — a route that touches every node of a graph exactly one time.
What's borrowed here is purely the mechanic as a puzzle format, not any content or visual identity — every board in PathNum is produced by its own generator (see How to Play below), not copied from anywhere else.
How to Play
Draw a line starting at square 1, through every empty square, ending at the last numbered square — and every square on the board must be crossed exactly once, with none skipped and none crossed twice. The line can only move horizontally or vertically to an adjacent square, never diagonally.
From level 3 onward, some boards have thick walls between certain squares — the line can't cross them, so walls naturally narrow down the available routes. Numbered squares other than the first must be entered in their correct order; the final numbered square specifically may only ever be entered as the very last square, never earlier.
A session has 5 levels with gradually larger boards and more walls. There's no way to lose — if you get stuck, drag back to an earlier square to undo part of the line, or use the Hint button to reveal one correct next step. Every board that appears is guaranteed to be solvable (and on most levels, the solution is unique), so Hint always reveals a genuinely correct move, never a guess.
Strategy & Tips
Since the line has to cover the entire board with nothing left over, the most effective approach isn't guessing a route from start to finish — it's spotting the forced moves first.
- Look for squares with only one or two possible exits (usually corners of the board or squares boxed in by walls) — these almost always have a forced route, so solve them before guessing your way through open areas.
- Treat the gap between two consecutive numbered squares as its own mini-puzzle: count how many empty squares sit between them, then make sure your route actually passes through all of them before moving on to the next number — if you leave an empty square stranded, your route went the wrong way.
- Before committing to a direction, check whether the remaining unvisited squares are still all connected to each other. If your line cuts the board so that a pocket of empty squares gets isolated, that pocket can never be reached again — back up and try a different path.
- Don't enter the final numbered square early just because your route happens to pass near it — save it for the true last step, as the rules require.