Untangle
A free untangle puzzle that runs in the browser. Dots sit around a ring, straight lines join them, and those lines cut across each other. Move the dots until no two lines cross. That is the whole game.
- Free
- No ads
- No account
- No download
- Works offline
- Single player
How do you play?
- Pick up a dot - Tap a dot and it lights up. Dragging it straight away works too, with no tap first.
- Put it down - A second tap on empty space moves the lit dot there. Tapping the dot again puts it down where it was.
- Read the lines - A line caught in a crossing changes colour and gets thicker. A thin quiet line is one that is already fine.
- Watch the count - The number in the top row is how many crossings are left. It is the only number that has to come down.
- Finish - Zero crossings ends the board. The restart button deals a different board of the same size.
About this game
Drag a dot. Or tap it, then tap the spot it should go to. The arrow keys do the same job, one step at a time.
Nothing here is scattered and checked afterwards. The board is drawn backwards: dots first, one to a cell of a coarse grid, then lines added a pair at a time from the shortest to the longest, and a line is kept only when it cuts across nothing already drawn and runs through no third dot. What comes out of that is a picture with zero crossings in it, tested by the very same function that later judges you. Only then do the dots get thrown onto a ring in a random order. So the answer existed before the puzzle did. That matters more than it sounds: a puzzle generator that scatters and hopes has to run a solver to check its own work, and a solver that gives up under a budget says the same thing about a board with no answer as it does about a board that is merely deep.
Measured over 3,000 dealt boards per size. The small board is 6 dots and 9 lines, the middle one 9 and 15, the big one 12 dots and 21 lines. Density runs the other way from what you would guess: 60% of all possible dot pairs carry a line on the small board and only 31.8% on the big one, which is why the big board looks like a mess and the small one looks like a knot.
The big board opens with 49.6 crossings on average. The worst deal had 88. That count only ever falls.
The admission, and it belongs to the small board rather than the big one. On six dots, a single dot is caught up in 90.7% of the crossings on average, so finding it and moving it once is most of the answer. Four moves clear that board on average, out of six dots. For a five-year-old that is exactly right and it is the reason the size exists. For anybody older it can be finished before it starts, and the honest advice is to skip it.
What does it teach?
Same thing, different shape
The lines never change. Only where the dots sit changes, and that turns a tangle into a clean drawing. Children meet that idea here years before anyone gives it a name.
Local effects
A dot only touches the lines that touch it. Working that out is the moment the game stops being about luck.
Going backwards on purpose
Sometimes the board has to look worse before it comes right, and here that costs nothing at all. Practising it is the point.
Reading a number
The crossing count answers a question the eye gets wrong. Learning to trust it over the picture is a real skill.
Tips
Pull toward the middle
Every dot starts on the ring, so all the empty room is in the centre. A dot dragged inward usually shortens two lines at once, and short lines cross less.
Follow the thick lines
Ignore the picture and follow the heavy ones. They are the only lines in trouble, and every crossing you can see has two of them.
One dot, then look again
Moving a dot changes only the lines that touch it, and nothing else on the board. That makes this a puzzle you can check rather than one you have to guess at.
Let it get worse
A move that helps right now is not always a move that helps. Our own bot, which only ever accepts an immediate improvement, clears the big board 4.8% of the time and stalls on the rest.
Expect to move nearly everything
The big board needs 11 of its 12 dots put somewhere new before the last crossing goes. Hunting for the one dot that fixes everything is hunting for something that is not there.
What age is it for?
5 to 6
The six-dot board. It opens with 5.7 crossings and usually falls in four moves, which is short enough to finish in one sitting.
7 to 9
Nine dots and 15 lines. Eight dots have to move on average, so the order you move them in starts to matter.
10 and up
Twelve dots, 21 lines and around 50 crossings on the table at once. This is where the game stops being tidying up.
Grown-ups
The same big board, played against the clock rather than against the puzzle. The shape was always there, and the only question is how fast you see it.
Accessibility
Every dot is a real button with a name of its own, so Enter or Space picks one up and the four arrow keys walk it around: the whole board can be solved from the keyboard alone. Dragging is a shortcut and never a requirement, which matters for a small hand that does not aim well yet and for anyone using an alternative pointer, because tapping a dot and then tapping a destination solves exactly the same board. The area a finger has to hit is larger than the circle it draws. Lines caught in a crossing are drawn thicker as well as in another colour, so the board can be read without telling the two hues apart. There is a clock and it only counts: nothing ends when it moves, and a board left half-finished waits exactly as it was.
Playing together
One dot each
Take turns, one dot per turn. You find out quickly that the other player just opened the crossing you were about to close.
Say it first
Name where the dot is going and why, then move it. A child who can answer is playing the game rather than following their own finger.
Guess the ending
Before the first move, everybody guesses how many dots will end up somewhere new. On the big board it is 11 of 12, and that guess is almost always low.
Read the count out
Call the crossing number aloud after every move. Younger children work out what caused what without anybody explaining it.
Common questions
Is every board really solvable?
Yes, and by construction rather than by checking. The lines are drawn without a single crossing first, and the dots are scrambled afterwards, so a clean picture existed before the board appeared.
Do I have to drag?
No. Tap a dot, then tap where it goes. The arrow keys work too. Dragging is only faster.
What if two dots end up on the same spot?
The lines leaving them meet at that point, and that counts as a crossing. The board will look tidy and refuse to finish, so spread them out.
Is there a time limit?
No. The clock counts and nothing else, and an unfinished board is still there after you close the browser.
Does it cost anything?
It is free, with no ads, no sign-up and no download. It loads in the browser and keeps working with no connection.
Why does the small board feel so easy?
Because one dot is usually caught in 90.7% of its crossings, so moving that dot is most of the answer. Older players should start on the bigger board.
Can I get stuck?
You can feel stuck, because sometimes a dot has to go somewhere that looks worse before the board comes right. No board ever locks, and any move is undone by making another one.