How to solve number line puzzles: 8 tips

To solve number line puzzles, count first and draw second. Most boards give way to a few small counting tricks: how far apart two ends sit, and which squares can only belong to one line. We use the rules of Linelet, the puzzle we make, but the same thinking works on most line and path puzzles.

Before you solve number line puzzles: the rules

• Each pair of matching ends shares a number, a shape and a colour.
• Join each pair with one line that covers exactly that many squares, counting both ends. A 4 covers four squares.
• Lines go up, down, left and right. Never diagonally.
• Lines never cross or share a square.
• When the board's finished, every square is used exactly once.
• Some boards have walls: squares that aren't part of the board. Nothing goes through them and they don't need filling.

Since every square gets used once, the numbers on a board always add up to the number of open squares. A five by five board with no walls has 25 squares, so its lines add up to 25. It's a handy check when something feels off.

Tip 1: count the gap

Pick a pair and count the steps between its two ends, moving only across and up or down, like walking city blocks. Add one, because both ends count. That's the shortest line the pair could have.

If the number on the ends matches that shortest length, the line has no room to wander. And if the two ends also sit in the same row or column, it has to be a straight line. Draw it straight away.

Tip 2: the detour rule

This is the most useful fact in the whole game. Every detour from the shortest route adds squares in pairs, because each step away from the target needs a step back. So a line can only be its shortest length, or two more, or four more, and so on.

It works in reverse, too. Say a line is one square too long or too short to land on its far end. No amount of wiggling will fix that, so back up and take a different turn.

Tip 3: start with the lines that have the fewest choices

Short numbers, and numbers that match their gap, have very few possible routes. Draw those first. Every line you place takes squares away from the rest, so the next line has fewer choices too.

Linelet's hints follow the same logic. The first hint points to the unfinished line with the fewest ways to go.

Tip 4: watch the corners

A corner square only touches two other squares. If a corner isn't one of the ends, a line has to pass through it, coming in from one neighbour and leaving by the other.

So both of the corner's neighbours belong to the same line as the corner. That often tells you which line wraps around the edge.

Tip 5: look for squares with only one way in

The corner idea works anywhere on the board. An empty square that isn't an end needs two open neighbours: one to come in, one to go out. If it's down to one, something has gone wrong and a nearby line needs to move. Walls and finished lines create these pinch points, so check around them first.

Tip 6: don't seal off a pocket

Sometimes a line closes off a little group of empty squares. Count what's left inside. The lines that end inside that pocket have to fill it exactly, and if no ends are inside, nothing can ever fill it. The line that sealed it is wrong.

Tip 7: let the walls do some work

On boards with walls, treat each wall like an extra edge of the board. A square beside a wall behaves like an edge square, and a square boxed in by walls behaves like a corner.

Walls can also split a board into rooms, and each room's lines must add up to its size. Walls turn up on more boards as the sizes grow, which we cover in how Linelet boards get harder from beginner to advanced.

Tip 8: what to do when you're stuck

Everyone gets stuck. These moves usually get a board going again.

• Recount one line. Most mistakes are a line that's one square off, so count its squares, both ends included.
• Undo a little. In Linelet, dragging back along your own line erases it back to that point, so you can try a different turn without starting over.
• Test an idea by cutting through. Drag a new line through an old one and the old one is trimmed back, so trying something costs you very little.
• Take a hint that teaches. In the app, hints climb gently: first a pointer to the line worth thinking about, then the first few squares of its route. Both are free on every board, and the one-time purchase adds a third that shows the whole line.
• Turn on Gentle nudge. It's off by default in Linelet's settings. When it's on, it softly marks any line that can no longer reach its other end, using the detour rule from tip 2.

Every Linelet board has exactly one answer, so there's always a reason for each line to sit where it does. We explain why that matters in why a puzzle with exactly one answer feels fairer.

Ready to try the tips? Today's free Linelet puzzle is a small board you can play in your browser. And if you'd like these boards to be a slow, restful habit rather than a race, our guide to logic puzzles for a calm break is a good next read.