Trace Strategy: Forced Squares, Parity and the Shrinking Clock

Updated October 2026

Trace hands you a small grid with a few blacked-out squares and a yellow dot in one corner of a cell. From that dot you must draw a single line that steps through every open square exactly once. A board takes seconds when you see the route and a long time when you guess, and the clock gets shorter after every board. This guide covers how the boards are built, the counting tricks that reveal the route, and how to pace a run against a budget that keeps shrinking.

How each board is made

Every puzzle is created by the game walking a random route through an empty grid, one orthogonal step at a time, until it has covered a fixed number of squares. Whatever the route never touched becomes a wall. That has two useful consequences. First, every board has at least one answer, and that answer begins on the marked cell. Second, the walls carry no message: they are simply the leftovers of a random walk, so they can sit anywhere, including in the middle of the board or alone in a corner.

The board size follows a short ladder. Boards one and two are 5×5 with 5 walls, leaving 20 squares to visit. Boards three and four are 6×6 with 6 walls and 30 open squares. From board five onward every grid is 7×7 with 9 walls and 40 open squares, and it stays that size for the rest of the run. The game checks only that your line covers every open square, so if you find a different route from the one the generator used, it still counts.

The controls, and the rewind tap

Your line already sits on the start cell when the board appears, and it cannot be undone past that cell. Drag a finger through neighbouring squares to extend it; diagonal moves are ignored. Sliding back onto the square you just left removes one step, which is the cheapest way to fix a small mistake. You do not have to drag at all: tapping a square next to the end of the line extends it by one, and tapping the previous square takes one step back.

Tapping a square your line has already passed through cuts the line back to that square, keeping everything drawn before it, and tapping the start cell clears the line completely. Tapping an empty square that is not next to the end of the line does nothing. That makes the rewind tap the fastest fix when you spot a mistake several steps back: touch the last square you are sure of and carry on drawing from there. When you start a new stroke after lifting your finger, put it down on the bright end of the line, on the square right next to it, or on the square you want to rewind to.

Checkerboard counting

Picture the grid coloured like a chessboard. Each step of your line moves to a square of the other colour, so the line alternates light, dark, light, dark. Every board here has an even number of open squares (20, 30 or 40), which means the finished route uses exactly as many light squares as dark ones, and the last square you visit is always the opposite colour to the start.

That gives you a quick test while drawing. If the empty squares you still need to visit include, say, three more light squares than dark ones, the route you are on cannot work, however you continue. You can also use it to rule out finishing spots: a pocket that could only be your last square is worthless if it is the same colour as the start cell.

Squares that decide the route for you

Count the open neighbours of each square, ignoring walls and the grid edge. A square with only one open neighbour can be entered but never left, so it must be the very end of your line. In our simulation of 3,000 boards of each size, roughly one board in ten had such a square (about 15 percent at 5×5 and about 10 percent at 6×6 and 7×7). When you see one, you know where you are heading before you draw anything.

Squares with exactly two open neighbours are almost as strong. Unless that square is the end, the line must arrive from one neighbour and leave through the other, so both connections are fixed. In the same simulation about a quarter to a third of the non-start squares had only two open neighbours, so on a typical board several short segments are already decided. Corners next to a wall, squares squeezed between two walls, and the dead-end strips that random walks love to leave along an edge all belong in this category. Trace those forced segments with your eyes first; they often join up into a long chain that leaves only one sensible way through the middle.

Avoiding the stranded square

Most failed attempts end the same way: a single empty square, or a small cluster, has been cut off from the rest. Before each turn of your line, look at what the move closes off. A good rule is to keep the unvisited area in one piece. If a move would split the empty squares into two separate regions, you would have to finish one region and then somehow cross into the other, which is impossible because you cannot pass back over your own line. A split of the empty area is always fatal, so undo it at once.

Edges and walls are your friends here. Running along a wall uses up squares that would otherwise become awkward later, while cutting through the middle of an open area tends to leave narrow corridors on both sides. When there is a choice, sweep a row or column fully before turning, and take dead-end strips the moment you pass their entrance unless you plan to end in one.

Pacing the shrinking clock

Each board has its own countdown. The first board gets 60 seconds, and every board you clear takes 1.5 seconds off the next one: board 10 gets 46.5 seconds, board 20 gets 31.5, board 30 gets 16.5 and board 40 gets only 1.5. There is no floor, so a run cannot go past 40 boards. Spare seconds do not carry over, and the countdown keeps running on real time even if you switch apps. After a clear there is a short pause of about 0.6 seconds before the next grid appears, and its clock starts only when it is shown.

The early boards are generous, so use them to practise reading the board before you draw. On the 7×7 boards, the budget in the thirties works out to well under half a second per square, and the boards themselves stay just as hard. By then, a short look for forced segments and the likely finishing square pays off more than drawing quickly and resetting. The value turns to tenths of a second under ten seconds, which is your cue to commit to the best route you have.

The New button doubles as a finish line. If you have cleared at least one board, pressing it during a run ends the run and shows your total, which you can then save to the Hall of Fame. If you have not cleared anything yet, it simply deals a fresh first board.

A routine for every board

1. Find the start dot and note its colour on the imaginary chessboard; your route ends on the other colour.
2. Look for any square with a single open neighbour. If there is one, that is your destination.
3. Mark the forced two-neighbour squares and connect them into chains.
4. Draw along walls and edges, finishing dead-end strips as you reach them.
5. Before each turn, check that the remaining empty area is still one connected region.
6. If you get stuck, tap the last square you trust to rewind the line to it, or tap the start cell if the whole plan is wrong.

Score is the number of boards cleared, and your best is stored on your device. Fast, clean reading of forced squares is what separates a run that stops at fifteen from one that reaches the thirties.