A draw one stroke game is a logic puzzle in which the player must trace every edge of a fixed graph without lifting the pen and without repeating a line. One Line Draw applies that idea to a single, hand-crafted diagram of eight labeled nodes connected by nine undirected edges, and uses graph-theory parity to make the route entirely deterministic. A complete solution visits ten nodes, because nine edge steps must connect them, and a winning run is restricted to the eight directed Euler trails the graph actually admits. There is no random generation, no timed reveal, and no cell-filling gimmick — the only thing the player traces is the printed graph itself. Each verified trail awards exactly 1,000 points and freezes the board, while an incorrect nine-step attempt is editable once and deadlocks the run on the second. The result is a short, transparent practice loop for anyone studying Euler trails or simply looking for a clean, browser-based one-stroke puzzle, and the full interface lives at One Line Draw.
What the One Stroke Game Looks Like
One Line Draw presents a single static diagram: eight circular nodes labeled A through H and nine printed line segments. The central spine runs A-B-C-D. Two triangular loops are attached to that spine, with B-E-F-B sitting above and C-G-H-C sitting below. No other edges exist, no edges cross, and empty space plays no role. Every node sits inside a bounded panel sized for a 390-pixel viewport, and every node is its own clickable button with a spoken label so the cursor and keyboard always know which endpoint is currently highlighted.
The graph is not random. The fixed fixture reproduces itself exactly the same way on every visit and on every Restart, which is what allows an independent depth-first search to enumerate the full solution set in advance and to lock down a precise route count.
| Node | Degree | Role |
|---|---|---|
| A | 1 | Odd; spine endpoint |
| B | 4 | Even; spine junction and upper-loop anchor |
| C | 4 | Even; spine junction and lower-loop anchor |
| D | 1 | Odd; spine endpoint |
| E, F | 2 each | Even; upper triangle B-E-F-B |
| G, H | 2 each | Even; lower triangle C-G-H-C |
How to Play One Line Draw
- Inspect the eight-node graph and identify the two vertices that look like endpoints. The odd-degree nodes A and D sit at the two ends of the spine.
- Tap connected nodes in order, or use the arrow keys to cycle through nodes A through H and press Space to choose the highlighted one. Each step extends the route through one shared edge.
- Continue for nine edge steps so the route contains ten node visits and consumes every one of the nine printed edges without repeating a line.
- If the route goes wrong, press Undo (or Delete or Backspace) to remove the latest step, or Clear (or C) to erase the whole trail while preserving the run and the score.
- Press Check trail, or Enter, to validate the route. A verified Euler trail awards exactly 1,000 points and freezes the board.
The status panel reports both the number of distinct edges covered and the total steps taken, so any silent repeat shows up as a gap between those two numbers. A non-adjacent click does not extend the route and does not count as a mistake, which keeps the drafting phase forgiving.
Why A and D Are the Only Endpoints
The game applies the standard Euler-trail rule: a connected undirected graph admits an open trail that uses every edge exactly once if and only if it has exactly zero or exactly two vertices of odd degree. When two odd vertices exist, the trail must start at one and end at the other. One Line Draw's graph has exactly two odd-degree nodes, A and D, which means no winning route can begin or end at B, C, E, F, G, or H. That parity fact is more than trivia; it immediately narrows every valid route to two endpoint choices, which is why the interface always boots with node A selected for keyboard play.
OpenStax's contemporary-mathematics chapter on Euler trails supplies the trail definition, and the same parity rule underpins every published Euler-trail proof, so the hint rests on standard mathematics rather than on memorized moves. The graph's shape, by contrast, is original to the puzzle and is independently audited.
Parity combined with the spine-and-loop structure also fixes the order of the two triangles. When walking from A toward D, the upper loop must be traced before leaving B for C, and the lower loop must be traced before leaving C for D. Each triangle can be walked in either direction, so the B loop contributes two orderings and the C loop contributes two more, producing four A-to-D trails. Reversing each of those gives four D-to-A trails, for a total of eight directed Euler trails. One concrete A-to-D example is A-B-E-F-B-C-G-H-C-D, which is ten node visits and nine edge traversals; its reverse, D-C-H-G-C-B-F-E-B-A, is also valid.
Controls, Scoring, and Terminal States
Touch and keyboard inputs cover the same actions. Tapping a node selects it; the arrow keys cycle through A through H and Space confirms; Delete or Backspace performs an Undo step; C clears the whole trail; and Enter triggers Check trail. The shared game shell shows the live score, stores the best score locally in the browser, provides a Restart button, and includes a double-Escape boss key that briefly swaps the play area for a neutral spreadsheet-style cover before restoring it.
Checking a route with fewer than nine steps is reported as incomplete and does not increment the mistake counter. A nine-step route that repeats an edge necessarily leaves another edge unused, and the first such completed error records one mistake but stays editable, so the player can Undo or Clear and try again. A second completed error deadlocks the run until Restart. Either successful completion or deadlock is terminal: every node click, arrow press, Space, Undo, Clear, and Enter input is frozen until the next Restart.
| Game State | Visible Counter | Input Behavior |
|---|---|---|
| Drafting (fewer than 9 steps) | Mistakes 0; route editable | Taps and keyboard extend, undo, or clear freely |
| First completed wrong trail | Mistakes 1; route editable | Same drafting controls still active |
| Second completed wrong trail | Mistakes 2; locked | Only Restart responds |
| Verified Euler trail | Score 1,000; locked | Only Restart responds |
How One Line Draw Differs From Grid Drawing Puzzles
Several popular one-stroke games look similar from the outside but solve very different problems. Filling cells, connecting numbered pairs, or simply tracing a printed outline are all distinct puzzle families, and One Line Draw is none of them. The only object that matters here is the printed graph, and the only winning condition is covering every printed edge exactly once. That distinction shows up most clearly at the nodes, because B and C each have degree four, so a valid route is allowed to return to those nodes via different edges. Repeated vertices are not a bug; repeated edges would be, and the status panel's split between distinct edges covered and total steps makes that gap visible.
| Puzzle Type | Target Object | Winning Rule | Relevance to One Line Draw |
|---|---|---|---|
| One Line Draw (this game) | 9 graph edges | Trace each edge exactly once | The subject of this article |
| Fill One Line | Open cells in a grid | Cover every open cell with one path | Cell coverage, not edge coverage |
| Numberlink | Cells in a grid | Connect matching pairs without crossing | Endpoint pairs, not Euler trails |
| Draw-by-shape tracing | An outline silhouette | Follow a printed contour | No graph structure at all |
Because the fixed fixture has a verified route count, the puzzle is also reproducible: every regression test, every parity proof, and every score of exactly 1,000 comes back the same on every reload. The game runs entirely in the browser, needs no account, uploads no data, requests no permission, and adds no package dependency, which keeps the experience focused on the route itself rather than on setup, login, or level unlocks.