Lines Strategy: Finding the Line That Can Go First
How to solve arrow puzzles like Lines without mistakes. Read lanes, start at the edges, follow blocking chains and treat the order as a dependency graph.
The line that can go first is the one whose lane is empty: follow its arrow in a straight line to the edge of the shape, and if no other line sits anywhere along that run, it can leave. Start at the outline, where heads pointing outwards have the shortest lanes. Tap every free line, then look at the lines that were waiting on them. In Lines a free line stays free until you tap it, so you never have to worry about the order of free lines.
This guide is for players who know how to play Lines and want to clear bigger shapes faster and without mistakes. It works for most tap-away arrow puzzles too.
The one rule behind every strategy
Every Lines strategy rests on one rule: a line can leave when no other line stands in front of its arrow, all the way to the edge. Call the squares in front of the arrow the line's lane. The lane is straight, even when the line itself is bent, because the head goes straight on and the body follows the path the head took.
Three things follow from that rule, and together they shape how you should play.
A free line stays free. Lines only ever leave the shape; nothing ever moves into a lane. So once a line's lane is empty, it stays empty until you tap that line. You can leave a free line for later without losing it.
The order of free lines does not matter. Because tapping one free line can never block another, any free line is a safe tap. There are no trap moves in Lines. If ten lines are free, you can clear them in any order and end up in the same place.
The only mistake is a blocked tap. You cannot make a Lines puzzle unsolvable by tapping lines in the wrong order. The only thing that goes wrong is tapping a line whose lane is not empty, which counts as a mistake. So every strategy below is really about one question: how do you see, quickly and surely, which lanes are empty?
That makes Lines different from many puzzles. In sudoku or Trail, a wrong move can quietly ruin the rest of the solve. In Lines the puzzle cannot be spoiled by order, and Puzzle Picnic builds each shape so that it can always be cleared. Your job is to read lanes accurately and keep moving.
Edges first
The lines at the outline of the shape are the best place to start, because a head at the edge pointing outwards has the shortest possible lane. Often it has no lane at all: one step and it is outside the shape.
Work round the outline in one direction, clockwise for example, and look at every head you pass. For each one, ask which way it points:
- Pointing out of the shape, at the edge: almost always free. Check the one or two squares beyond it, then tap.
- Pointing along the edge: its lane runs along the outline. Look along the whole run; the edge row or column is often crowded.
- Pointing into the shape: its lane crosses the whole shape. Leave it for later unless the shape is nearly empty.
Watch the outline's shape. Lines puzzles come in shapes such as a heart, a star, a circle, a diamond, a house and a square, and on the curved and pointed ones the edge is uneven. A head near the tip of a star's point has only a short run of squares in front of it, so it frees early. On a heart, a lane that leaves one of the two rounded tops sideways can cross the dip in the middle and run over the other top, so a head that looks like it points out may still have a line in its way.
Edges first is also how the shape comes apart in practice. Each line that leaves the outline opens a little bay, and the heads facing into that bay now point into empty space. The shape clears from the outside in, like peeling an orange.
Follow the arrow to the edge
Most blocked taps come from checking only the first few squares of a lane. The rule says all the way to the edge, and a single square of another line near the far side is enough to block. Make it a habit to run your eye, or a finger just above the screen, along the full lane before every tap you are not sure of.
Three things are easy to miss:
- A tail or a bend. A lane is blocked by any piece of another line, not only by its head. The tail end of a long line is the classic miss, because it does not catch the eye.
- A line across a gap. On a shape with empty patches or a curved outline, a lane can pass through empty squares and then hit another line beyond them. Empty squares do not make a lane clear; only reaching the edge does.
- Two lines in the same lane. If a lane holds two different lines, the line has to wait for both. Clearing the near one is not enough.
In that row, Q is free: its head points right with one empty square before the edge. Tap Q first, and P's lane is then empty all the way. The same pattern, a long empty run with a blocker at the end, appears all over big shapes.
Blocking chains
Most lines in a Lines puzzle are waiting on other lines, and those waits link up into chains. Line D waits for C, C waits for B, B waits for A. The chain tells you the order: A first, then B, then C, then D. Seeing chains is what turns Lines from tapping around into planning.
This 6x6 square shape has eleven lines. It is small, but it holds a long chain and a keystone, a line that several others are waiting on.
| Line | Arrow points | Lines in its lane | Can go in round |
|---|---|---|---|
| A | Right | None | 1 |
| L | Left | None | 1 |
| M | Left | None | 1 |
| B | Up | A | 2 |
| C | Right | B | 3 |
| E | Up | B, A | 3 |
| D | Up | C, A | 4 |
| K | Right | D, E | 5 |
| X, Y, Z | Down | K, L, M | 6 |
Read the table as a solve. In round 1, A, L and M are free: their heads are at the edge pointing out. In round 2, B can go up now that A has left. In round 3 both C and E can go, since B was in the way of both. In round 4, D's lane up column 4 is clear. In round 5, K's lane along row 4 is clear, because D and E have gone. In round 6, the three lines X, Y and Z can drop out of the bottom.
Two lessons hide in that table:
- A lane waits for its slowest line. X, Y and Z have L and M in their lanes too, and those leave in round 1. It makes no difference: K is in the way until round 5, so X, Y and Z wait until round 6.
- Keystones free groups. K is a single line, but three others wait on it. Spotting a keystone tells you where the big release will come, and which chain to follow to get there.
Three patterns worth recognising
Chains come in a few shapes that repeat across every level, and naming them makes them faster to spot.
The queue. Several lines in one row or column, all pointing the same way, one behind the other. Only the front one can go; then the next becomes the front. Clear a queue from the end its arrows point towards.
The fan. Many arrows pointing at the same long line from one side, like X, Y and Z pointing down at K. Nothing in the fan can move until that one line has gone, so stop looking at the fan and follow the long line's own chain instead.
The face-off. Two heads in the same row or column pointing towards each other. Each head sits in the other's lane, so neither could ever go, which is why you will never find one in a Puzzle Picnic shape. When two heads seem to face each other, look closer: they are in different rows or columns, so their lanes slide past each other.
The order as a dependency graph
The whole puzzle can be pictured as a set of "waits for" arrows between lines: draw a dot for each line, and an arrow from each line to every line in its lane. Mathematicians call that a dependency graph, and putting its dots in an order where every line comes after everything it waits for is called a topological sort. A topological order exists exactly when the graph has no cycles, and there is usually more than one (Wikipedia: Topological sorting).
The classic method for finding one was published by A. B. Kahn in 1962 (ACM Digital Library: Topological sorting of large networks). It is exactly how you play Lines. Take every item that waits for nothing. Remove them. Some items now wait for nothing; take those next. Repeat until everything is gone. In Lines terms: tap every free line, then tap every line that has become free, and so on. The rounds in the table above are Kahn's method by hand.
The theory also explains when a puzzle is stuck. A cycle means two or more lines that wait on each other in a ring, and no line in a ring can ever go first.
Puzzle Picnic builds every Lines shape so that this never happens: each puzzle can be cleared, so its waits never form a ring. That guarantee is what makes the "free lines stay free" rule so useful. There is always at least one line that can go, and every line you take brings the rest closer. Order is the puzzle explains dependencies in more depth, with no maths needed.
Working backwards from a stuck line
When the line you want is blocked, follow its waits backwards until you reach a line that can go now. This is the most useful skill for big shapes, because it turns "I cannot see a move" into a short, certain search.
Take K in the 6x6 shape. You can see it is a keystone, but it is blocked. Ask what is in its lane: D and E. Then ask what is in their lanes:
- K waits for D and E.
- D waits for C and A. E waits for B and A.
- C waits for B. B waits for A.
- A waits for nothing: A can go now.
So the route to K starts with A, then B, then C and E, then D. You have planned five taps, and every one of them is certain. On a real board, you do not need to plan the whole route. Following the waits back one or two steps usually lands on a free line, and tapping it moves the whole chain forward.
When a line leaves, only lines whose arrows pointed into its squares can become free. That gives you a second shortcut: after each tap, look at the arrows aimed at the squares the line just left. If one of them now has an empty lane, it is your next tap. In the 6x6 example, when A leaves the top row, the arrows pointing into its squares belong to B, D and E. Only B's lane is now empty, so B is next.
Big shapes: a scanning routine
On the larger levels the strategies stay the same, but you need a routine so nothing is missed. Lines shapes get bigger at each level: Easy is 11 squares across, Medium 15, Hard 19 and Expert 23, with longer, more tangled lines at each level.
| Level | Shape size | What to expect | Focus on |
|---|---|---|---|
| Easy | 11 squares across | Short lines, many free at once | Lane reading; edges first |
| Medium | 15 squares across | Longer lines, more waiting | Short chains |
| Hard | 19 squares across | Long bent lines, longer chains | Working backwards; keystones |
| Expert | 23 squares across | The longest, most tangled lines | A full routine and patience |
A routine that works on Hard and Expert:
- Sweep the outline once. Go round the whole shape and tap every head that points out with an empty lane. Do not stop to think about the inside yet.
- Look where lines just left. After the sweep, check the arrows pointing into the gaps you made. Tap the ones with empty lanes.
- Sweep again. The outline has changed shape. New heads now face open space.
- Find the keystones. Long lines sit in many lanes, simply because they cover many squares. When a big group of lines is stuck, look for the long line lying across their lanes, and work backwards to it.
- Take a breath before a long lane. Lanes across the full width of an Expert shape are where blocked taps happen. Check the far end twice.
The game shows how many lines you have freed so far and how many are left, so you always know how far you have come. There is no timer pressing you, and a big shape can take as long as you like. Solving big Lines puzzles has more on staying calm on Expert.
Hints, the Grid and staying clean
Lines has a hint and three power-ups, and each one is a different kind of help. A clean solve, with no mistakes, hints or power-ups, earns more points for your picnic, so it is worth knowing when each tool is worth it.
- Hint. You get three free hints a day. A hint lights up a line that can go now, with a green glow. Use it when you have swept the outline twice and still see nothing.
- Grid. Shows every line's way out until the next line leaves: green lanes are clear, red ones run into another line. It is the best teacher, because it shows you every lane you would have had to check by eye.
- Hammer. Smashes any line you tap, even a blocked one. On a puzzle that can always be cleared, it is never needed to finish, but it can break a long wait.
- Magnet. Pulls up to three lines out for you.
Power-ups come from a shared stock that refills a little every day, and any solve that uses a hint or a power-up is marked as assisted. Undo brings back the last line you freed, but hints and mistakes stay counted, so it does not rescue a clean solve.
If you are learning, there is a good case for using the Grid once or twice early on. Compare what it shows with what you expected. The lanes you misjudged are the ones to practise reading.
Frequently asked questions
Which line should I tap first in an arrow puzzle?
Tap a line whose lane, the straight run from its arrowhead to the edge, holds no other line. The easiest to find are heads at the outline pointing outwards. After that, look at the lines whose arrows pointed into the squares that just emptied.
Can I get stuck in Lines by tapping lines in the wrong order?
No. Lines only ever leave, so a free line stays free until you tap it, and tapping one free line never blocks another. Puzzle Picnic builds every shape so it can be cleared, so there is always at least one line that can go.
Why can't I find a free line?
There is always one while lines remain, so look again at the full length of each lane, especially near the far edge, where tails and bends are easy to miss. Pick a blocked line you would like to move and follow its waits back: the chain ends at a free line. A hint also lights up a line that can go now.
What is a dependency graph in a puzzle?
It is a picture of which pieces wait for which. In Lines, each line waits for the lines in its lane. Putting the lines in an order where each comes after everything it waits for is a topological sort, and Kahn's 1962 method of repeatedly taking whatever is free is exactly how you clear a shape.
Does the order of free lines matter for my time?
Only a little. The fastest habit is to clear every free line you can see in one pass, then look at what those departures freed. Stopping to choose between free lines costs more time than it saves.
Where to go next
On your next few shapes, say each lane to yourself before every tap you are not sure of, and use rounds: sweep, then check where lines left, then sweep again. Once that is automatic, move up a level. For the basics, read how to play Lines. For why the genre feels so satisfying, see arrow and untangle puzzles explained, and for more on Hard and Expert, solving big Lines puzzles. Every Lines guide is on the Lines topic page, and a shape to try is on the Lines page.