Fill the grid so every number counts its numbered neighbours, equal numbers never touch and all numbers join into one group. Every board is unique and solvable by logic — beat each level's shrinking clock.
Tap a square to select it, then tap 1, 2, 3, 4 or ✕ on the pad below to write a number or mark the square as empty; ⌫ clears it. Tapping the selected square again cycles it through 1, 2, 3, 4, ✕ and blank, which is the quickest way to enter values. Solve the board before the bar above it runs out.
A finished board follows three rules. Every number equals how many of its four neighbours (up, down, left, right) also hold a number, so a 1 touches exactly one other number and a 4 is surrounded on all sides. Two equal numbers may never sit side by side. And all the numbers must join into one connected group — you can walk from any number to any other through numbered squares. The bold numbers are given and cannot be changed; the empty squares you leave (or mark with ✕) are simply empty.
Each number has its own colour, so two equal numbers touching are easy to spot. A number turns red when it breaks a rule — it touches an equal number, it already has more numbered neighbours than its value, or too few of its neighbours are still open to reach its value. It gets a small green tick once all its neighbours are decided and the count is right. The line under the board tells you what is wrong.
Levels 1 and 2 are 5 × 5 boards, levels 3 to 6 are 6 × 6 and from level 7 every board is 7 × 7. The first level gives you 2 extra numbers and the second 1; after that each board keeps only the numbers you need. Level 1 gives you 160 seconds and every level after it has 4 seconds less, with no minimum, so level 40 has only 4 seconds and no game can go past it. The clock only runs while a board is on screen and keeps running if you switch apps.
When the time runs out the game ends and the solution is shown. Your score is the number of levels you cleared; players with the same number of levels are ranked by their total solving time, to a tenth of a second. Every board is generated fresh, has exactly one solution and can be solved by deduction alone, without guessing.
Start from the extremes. A given 4 means all four of its neighbours are numbered, and a number in a corner can never be more than 2, on an edge never more than 3. A given 1 next to a square that must be numbered (for example the only way out for a neighbouring 4) means every other neighbour of that 1 is empty — mark them with ✕ straight away, because empty squares are just as useful as numbers for the next step.
Think in counts, not just values. For any number, count the neighbours that are already numbered and the ones still open. If the numbered ones already reach its value, every open neighbour is empty; if numbered plus open is exactly its value, every open neighbour must be numbered. Most of each board falls to this one check repeated around the grid, and the colour of each number makes the next candidate easy to see.
Use the touching rule to break deadlocks. When a numbered square's value is still undecided, list the values it could take and strike out any that a neighbour already has: a square that could be 2 or 3 but sits next to a finished 2 must be a 3, which tells you how many of its open neighbours are filled. The connection rule is the other lever — a square that is the only bridge between two parts of the numbers must be numbered, and a pocket of squares walled off by ✕ marks can never hold a number.
On the clock, speed comes from rhythm rather than rushing: sweep the board once for 4s, corners and edges, then follow the chain of forced squares from wherever you just wrote. The selected-square cycle (tap again for the next value) is faster than the pad once you know the answer. From level 7 every board is 7 × 7 and each level is 4 seconds shorter, so the boards you clear early in 2 to 3 minutes must eventually fall in well under a minute.