Mosaic Tips: Solving 3×3 Count Grids Against the Clock

Updated October 2026

Mosaic gives you a five-by-five board with a number printed on every one of its 25 squares, and 90 seconds to satisfy as many boards as possible. Each number counts the painted squares in the little three-by-three window around it. The rules fit in one sentence, but the game rewards a very specific way of looking at the board, and a few quirks of how this version builds and checks its grids change what the fastest strategy is. This guide covers both the logic and the time management.

What a number actually counts

Every square's number is the count of painted squares in the window made of that square plus its up to eight neighbours. How big that window is depends on where the square sits, and that matters more than anything else on a board this small:

• Corner squares see only a two-by-two window of 4 squares, so their numbers run from 0 to 4.
• Border squares that are not corners see 6 squares, so their numbers run from 0 to 6.
• The nine inner squares see a full window of 9, so their numbers run from 0 to 9.

The most useful habit is to read each number together with its window size. A 5 in the middle is close to even, since there are four blanks among nine. A 5 on the border means only one of six squares stays blank. A 3 in a corner means exactly one of four stays blank. The same digit means very different things in different places, and players who read the digit alone waste time on numbers that are almost fully determined.

Every number is also a statement about blanks. A window of size s with number k has exactly s − k blank squares. Some numbers are easier to work with that way: an 8 in the centre says one blank, a 1 anywhere says one paint.

How the controls and colour hints work

Tapping a square cycles it through three states: blank, painted, crossed out, and back to blank. Painted squares turn blue. The cross is only a note to yourself that a square is definitely blank.

Each number reacts to its window as you play. It is outlined in red when the window already holds more painted squares than the number, or when too few squares are left unpainted and uncrossed to ever reach it. It turns green when the painted count matches exactly and every other square in its window has been crossed out, so nothing undecided remains. A red number therefore means a mistake somewhere in that window, and a green number means that window is finished.

One detail changes how you should play: the board counts as solved the moment every number matches the painted squares. Crosses play no part in that check. You never have to cross anything out to finish a board.

Spend taps wisely: when to bother with crosses

Because of the three-step cycle, a cross costs two taps on that square, and a square painted by mistake also costs two more taps to clear. Over a 90-second game those taps add up. A good rule of thumb is to cross out squares only when the mark will save you thinking time later:

• Cross out the windows of 0s, because those blanks are the starting point for nearby deductions and it is easy to lose track of them.
• Cross out a square when it is the reason a neighbouring number is forced, so the red check can confirm your reasoning.
• Skip crosses on squares whose neighbouring numbers are already satisfied without them. Paint what must be painted and move on.

The green hint only appears on fully crossed windows, so if you skip crosses you lose some green feedback. Faster players accept that trade and use the red outline as their main safety net.

Finding forced squares quickly

Start with the numbers that decide a whole window. A 0 makes all of its window blank. A number equal to its window size makes all of it painted: a 4 in a corner, a 6 on the border or a 9 in the middle. These are less common than you might think. In our simulation of the game's own board generator, about 72 percent of boards had at least one such number, and a corner showed 0 or 4 roughly one time in five. The other boards have no free opening at all. So learn the second tier of forced situations as well:

• Exhausted windows. Once a number already sees as many painted squares as it asks for, every other square in its window is blank.
• Tight windows. Once a number needs exactly as many more paints as there are undecided squares left in its window, all of those squares are painted.
• Neighbour differences. Two side-by-side inner squares have windows that overlap in six squares. Each window also has one column of three squares the other lacks. The difference between the two numbers equals the difference between those two private columns. If the left number is 3 more than the right one, the left column must be fully painted and the right column fully blank. A difference of 2 still forces a lot.

Move outward from whatever you settle. Each decided square shrinks the undecided part of up to nine windows, and on a five-by-five board one firm square usually forces another within a step or two.

Why you never need to guess

This version builds each board by painting every square at random with even odds, keeping the board if it has between 3 and 22 painted squares, and printing the counts. Before showing it, the game tries to solve the board with exactly the two kinds of reasoning described above: single windows that are already decided, and the difference between two overlapping windows. A board is only used if those steps settle every one of the 25 squares; otherwise it is thrown away and a new one is drawn. That makes every board you see a single-solution puzzle. In our simulation of the generator, about 29 percent of boards fall to single windows alone, and the other 71 percent need the overlap step at least once.

That has a practical consequence. When you reach a point where nothing seems forced, a deduction is still there, and it is almost always a pair of neighbouring windows whose numbers differ by a lot. Compare the numbers of side-by-side squares around the undecided area before you try anything else. A guess can still work, but a wrong one costs two taps to undo plus the time to notice the red outline, which is usually slower than finding the pair.

Managing the 90 seconds

The clock starts when you press Start and runs on real time, so it does not pause if you switch apps. The time box turns red for the last 15 seconds. After each solved board the grid flashes for just under half a second before the next one appears, and taps during that flash are ignored, so do not try to rush the first tap of the new grid. There is no skip button: the only way past a board is to solve it, and New starts the whole 90 seconds again from zero.

A steady routine beats bursts of speed:

1. Look at the four corners and the border first, because their windows are small and their numbers decide the most.
2. Paint every forced square you can find before you think about the middle.
3. Use neighbour differences on any pair of inner squares whose numbers are far apart.
4. When nothing is forced, compare neighbouring numbers: the overlap step always finds the next square.

Your best score is saved on your device. Any game with at least one solved board can be sent to the Hall of Fame from the end card.

Common mistakes

The most frequent error is reading a number without its window. A border 4 is not a middle 4. Another is forgetting that a square counts in its own window: a 1 on a square you have just painted is already satisfied, and the rest of its window is blank. The third is over-marking. Crossing out every blank square looks tidy, but it can double the taps a board needs, and the game never asks for it. Keep the crosses for the places where they help you think, and let the painted squares do the scoring.