Drawing a web flat
In maths, a web of dots and lines is called a graph. A graph that can be drawn with no crossing lines is called planar. Every Untangle board is planar by design. It was built from a flat layout first, then its dots were moved onto a circle to tangle it. Your job is to find a flat layout again. It doesn't have to be the original one. Any arrangement with no crossings wins.
This shapes how you should think. You aren't fixing crossings one by one. You are rebuilding a picture, and the crossings disappear as the picture comes together.
Build a frame, then fill it
The board starts with every dot on a ring, so almost every line cuts across the middle. Nudging dots on that ring rarely helps. A steadier approach is to build outward from a small, clean core.
- Find a triangle. Look for three dots that are all joined to each other. Drag them apart to form a large triangle that fills most of the board. A triangle can never cross itself, and it splits the board into an inside and an outside.
- Add dots that join two placed dots. A dot linked to two corners of your triangle can sit near the line between them, just inside or just outside. A dot linked to all three corners usually belongs inside the triangle.
- Keep growing. Each dot you place makes new small faces, the spaces enclosed by lines. A new dot goes inside the face whose corners it is joined to.
Here is a short example on Easy, which has eight dots and about a dozen lines. Say dots A, B and C are joined in a triangle, and dot D is linked to all three. Drag A, B and C out to three corners of the board. Then drop D in the middle of them. Its three lines run to the corners without crossing anything. Any dot joined to D and to two of the corners now has an obvious smaller triangle to sit in.
Using the crossing count
The Crossings number above the board tells you how much tangle is left. Red lines show exactly which pairs still cross. A ring marks each crossing, and the dots at the ends of crossing lines turn amber. When one area is red, find the dot that most of the red lines share and move that first. One well-placed dot often clears several crossings.
Dots with only two lines are the easiest to tidy. Put such a dot on or near the straight path between its two partners. Its lines then follow a route that is already clear. If that route is blocked, the problem is elsewhere.
Spread things out. Dots packed close together make it hard to see which lines cross. A line can also slip past a dot by a hair. Use the whole board, and leave gaps you can drop dots into later.
Mistakes that add moves
- Many small nudges. One move is one drag, however far it goes. Five small adjustments cost five moves, while one decisive drag costs one. Decide where a dot belongs, then put it there.
- Leaving dots on the starting ring. The ring is the most tangled layout possible. Any dot still sitting there is probably part of the problem.
- Fixing one crossing and causing two. Before you let go, watch the crossing count. If it went up, keep dragging until it drops.
- Ignoring the outside. The area outside your frame is space too. A dot joined to only one corner of your triangle often fits best outside it.
From eight dots to sixteen
Easy has eight dots, Medium twelve and Hard sixteen, and the webs get denser as the dots increase. On Easy, practise the triangle-and-fill approach until it feels natural. On Medium and Hard, finding a good first triangle matters more. Pick one whose dots have many lines, since that leaves fewer dots outside the frame. Your fewest-moves best is kept for each difficulty on this device, so try to lower it once you can solve reliably.
