An easy one-line draw puzzle challenges you to trace a single continuous stroke that covers every edge in a small graph exactly once. One Line Draw is built around an original eight-node, nine-edge board in which the central spine A-B-C-D carries one triangular loop at B and another at C. Because A and D are the only odd-degree vertices, every winning trail must start at one of them and finish at the other, so you begin with a definite hint instead of guessing blindly. The puzzle is small enough to inspect in one glance, large enough to require real route planning, and validated by an independent edge-mask depth-first search that finds exactly eight directed solutions. Touch targets are at least 44 pixels, every node is a native button with a spoken label, and arrow keys plus Space, Delete, C, and Enter cover full keyboard play. Any completed Euler trail scores exactly 1,000 points. The route itself, the graph, and the mistake policy are all reproducible and were verified separately from the gameplay test, so the "easy" comes from structure rather than from luck or hidden hints.
What the Easy One Line Draw Puzzle Looks Like
One Line Draw is a fixed graph with eight labeled nodes arranged on screen as A, B, C, D, E, F, G, and H, and nine undirected edges drawn between them. There are no cells, no random grid, and no time limit, which is part of why it works as an easy entry into the one-line draw puzzle genre. The objective is also unusual: empty space and grid cells do not matter here, and only the nine printed graph edges count toward a solution.
The structure is easier to read once you split it into three pieces. The central spine A-B-C-D connects four nodes in a straight line. A triangular loop B-E-F-B hangs off node B, and a second triangular loop C-G-H-C hangs off node C. Together the spine and the two triangles form the complete nine-edge graph, and every edge is visible on screen from the moment the puzzle loads.
A degree count makes the parity predictable before you draw anything:
| Node | Connected to | Degree | Parity |
|---|---|---|---|
| A | B | 1 | Odd |
| B | A, C, E, F | 4 | Even |
| C | B, D, G, H | 4 | Even |
| D | C | 1 | Odd |
| E | B, F | 2 | Even |
| F | B, E | 2 | Even |
| G | C, H | 2 | Even |
| H | C, G | 2 | Even |
Only A and D are odd-degree nodes. According to graph theory, an open Euler trail exists when a connected undirected graph has exactly two odd-degree vertices, and those vertices become the trail's endpoints. This rule is documented by OpenStax in its Euler trails chapter and confirmed by the University of New South Wales graph-algorithms course, so the parity hint is mathematical rather than coincidental.
Why an Eight-Node Graph Stays Easy
Most one-line draw puzzles feel hard because the graph is large or because it changes between rounds. One Line Draw avoids both problems. The board never changes, so the same graph appears every time you press Restart. The fixed fixture lets the engineering team enumerate every legal route ahead of time and accept the entire verified finite solution set rather than comparing your work to a single memorized string.
The independent edge-mask depth-first search starts at every node and walks nine steps while marking each used edge in a nine-bit mask. Only routes that consume all nine bits are counted. The audit requires exactly eight directed trails, with endpoints A and D, ten node visits per route, and exact agreement with the production enumerator. Reversing any A-to-D route produces a D-to-A route, which is how the eight routes split into four forward and four reverse solutions.
Each triangle can be traced in either direction, which is where the variety comes from. The B loop can run B-E-F-B or B-F-E-B, and the C loop can run C-G-H-C or C-H-G-C. Those two independent orientation choices produce four A-to-D solutions, and their reverses produce four D-to-A solutions for the eight total. The bridge-like spine also constrains the order of the two triangles: the B loop must be completed before the route leaves B for C, and the C loop must be completed before the route leaves C for D. That constraint is part of what keeps the puzzle short and inspectable.
For readers who want to see the math laid out next to the gameplay, the companion guide Draw One Stroke Game: Solve the 8-Node Euler Trail walks through the same fixture with extra focus on the traversal argument and the finite solution count.
How to Trace the Easy One Line Draw Puzzle
The board is small enough to inspect in one pass, so the route plan is the main work. Treat the next list as the actual on-screen procedure for solving One Line Draw from a fresh restart.
- Inspect the eight-node graph and check the parity of each node. A and D each have one connection, so they are the only odd-degree vertices and one of them is your starting endpoint.
- Tap a connected node to begin, or use the arrow keys to move the selection to A or D and press Space to confirm. A valid first step always lands on the single neighbor of your starting endpoint, which is B from A or C from D.
- Trace nine continuous edge steps without repeating a line. When you reach B from A, finish the B-E-F-B triangle before you continue to C. When you reach C, finish the C-G-H-C triangle before you continue to D. Each triangle may be traced in either direction.
- Use Undo or Clear to repair the route. Delete or Backspace removes the latest node, and the C key clears the whole current trail while keeping the run alive. Clicking two nodes without an edge in common does not extend the route and does not count as a mistake, so drafting is forgiving.
- Choose Check trail or press Enter when you have built a nine-step route. A finished trail scores exactly 1,000 points, and the run becomes terminal. Restart returns the same graph with no route, zero mistakes, zero score, and node A selected for keyboard play.
One concrete winning route is A-B-E-F-B-C-G-H-C-D. It visits B and C twice, which is legal because each return uses a different edge. The reverse, D-C-H-G-C-B-F-E-B-A, is also valid, and swapping the orientation of either triangle gives the other six directed trails. Because the game accepts the entire verified finite solution set, any of those eight routes finishes the puzzle.
Touch and Keyboard Controls for Easy Play
The interface gives you a mouse, a touchscreen, and a full keyboard, and each input method maps to the same game state. That redundancy is part of why One Line Draw works as an easy one-line draw puzzle for beginners rather than a touchscreen-only or keyboard-only gimmick.
| Action | Mouse or touch | Keyboard |
|---|---|---|
| Move selection | Tap or click any node | Arrow keys cycle through the eight labeled nodes |
| Confirm a step | Tap or click a connected node | Space chooses the selected node |
| Undo the latest step | Tap Undo | Delete or Backspace |
| Clear the whole current trail | Tap Clear trail | C key |
| Check the route | Tap Check trail | Enter |
Every node is a native button with a spoken label that names the current endpoint and the keyboard selection, so screen readers can announce each move. Touch targets are at least 44 pixels wide, and the graph stays inside a bounded panel on a 390-pixel viewport, which keeps the board usable on a phone without scroll gymnastics. After a few rounds on touch, switching to arrow keys plus Space feels natural because the keyboard selection follows the same node order you would have tapped.
The shared game shell adds a Restart button, a local best score, and a double-Escape boss key. Press Escape twice within the shell timing window to show a spreadsheet-style cover, then twice again to return to the puzzle. All route validation and graph enumeration run in the browser, so the game needs no account, uploads no data, requests no permission, calls no paid service, and adds no package dependency.
Scoring, Mistakes, and Restart
One Line Draw uses a strict two-strike policy that keeps the easy puzzle from turning harsh. Checking before your route reaches nine steps reports an incomplete attempt and does not change the mistake counter, so early drafts cost nothing. A nine-step route that repeats an edge necessarily leaves another edge unused, so the first such completed error records one mistake and stays editable, which means you can undo or clear it and try again. A second completed error deadlocks the run until you press Restart.
The status panel reports both distinct edges covered and total steps, which makes a repeated edge visible as a gap between the two numbers. A repeated edge becomes thicker like any used edge, but the distinct-edge counter stops increasing. That visible feedback is what lets a beginner self-correct without learning a hidden rule.
Any verified Euler trail awards exactly 1,000 points. Completion and deadlock are both terminal: once either state is reached, node selection, cursor movement, undo, clear, and checking no longer alter the game. Restart restores the same auditable graph with no route, zero mistakes, zero score, and node A selected for keyboard play. Because the puzzle does not use random generation, the same eight directed solutions exist on every run, so the 1,000-point finish is reproducible. The score is recreational logic practice, and a 1,000-point finish proves only that this fixed nine-edge puzzle was traced correctly, not that the player has any particular intelligence, educational, psychological, or medical ability.