Fill the Grid in One Line

How to play Cover Every Cell

Cover Every Cell is a fill the grid one line puzzle. The board is a grid of squares with a few dark walls. Starting from the square marked with a star, you draw a single line that moves from square to neighbouring square. The line must pass through every open square exactly once. Squares you have visited light up in blue, so you can always see what is left.

1. Press on the star square to start your line.
2. Drag up, down, left or right into the next square. Diagonal moves are not allowed.
3. Avoid the dark walls and never enter a square twice.
4. If you hit a dead end, drag back along your line to undo, then try another way.
5. When the last open square lights up, the level is complete.

Tips for covering every square

• Hug the walls and edges. Squares next to the border or a wall have fewer neighbours. Visit them while you are passing, or you may find them cut off later.
• Watch for dead-end squares. An unvisited square with only one free neighbour must be the very last square of your line. If you create two of those, the level cannot be finished from there, so back up.
• Don't split the board. If your line cuts the remaining open squares into two separate areas, you can only ever finish one of them. Keep the unvisited part in one piece.
• Zig-zag in rows. Sweeping back and forth across open areas, like mowing a lawn, is an easy way to cover big rooms without leaving gaps.
• Use the chessboard trick. Picture the grid as a chessboard. Every move switches colour, so if one colour has more open squares, your line must start and end on that colour.

A puzzle with a famous name

Mathematicians call a route that visits every point of a network exactly once a Hamiltonian path, after the Irish mathematician William Rowan Hamilton, who sold a puzzle game based on the idea in the 1850s. Unlike tracing every line of a figure, there is no quick rule that tells you whether such a path exists, which is exactly why these puzzles stay interesting: you have to plan, test and backtrack. A close cousin is the knight's tour on a chessboard, where a knight must visit every square once.

Grid-filling puzzles are a great workout for planning ahead and spotting traps early. They are relaxing on small boards and surprisingly tricky on large ones with many walls.

Levels and difficulty

There are 40 levels. The first ones are small 4 by 4 boards with no walls to learn the controls. The grid then grows to 5 by 5, 6 by 7 and finally 8 by 9 squares, and more walls appear in the middle of the board, where they split rooms and create narrow corridors. Every level comes from a fixed seed, so it is the same puzzle for every player, and every level is guaranteed to be solvable from its star. Your stars are saved on your device.

Why one-line puzzles are so relaxing

There is no timer, no score chasing and no penalty for experimenting. You can grab your line anywhere and carry on from that square, or pull it back one step at a time, so trying an idea costs nothing. The colours along your path shift from blue to green as you go, which makes it easy to see the order you drew in and spot where a route went wrong. Small boards take a minute, the large ones with many walls can keep you busy for a while, and every one ends with that satisfying moment when the final square fills in.

More line puzzles: trace a whole figure without lifting your pen inOne Line Draw Puzzle, or join coloured pairs and fill the board inConnect the Colors.