Flip Tiles

Twenty-five two-sided tiles in a five-by-five grid. Select one and it turns over — and so does every other tile sharing its row, and every other tile sharing its column. Nine tiles move at once, and no move is ever local. Get the whole grid onto one face, filled ● or open ○, and either one counts as a win.

The board keeps the books for you. Every tile shows how many times you have selected it, and running tallies down the two edges show how many selections have landed in each row and each column. Those three numbers are the entire law of the game: a tile is showing its dealt face turned over once for each of the three counts that is odd. Read them and the puzzle is arithmetic. Ignore them and it is guesswork with a move budget.

It runs entirely on your device: 0 network requests, works offline. No ads, no account, nothing to buy, and no betting, money or prizes of any kind.

1. Focus the board — click it, or press Tab until it is focused.
2. Move the cursor with the arrow keys (or W A S D). It stops at the edges rather than wrapping, so you never lose your place mid-thought.
3. Press Enter (or Space) to select the tile under the cursor. It turns over, along with its whole row and its whole column. Clicking or tapping a tile does the same thing.
4. Watch the three counts. The word under each tile is whether that tile has been selected an odd or an even number of times. The tally beside each row and above each column is the same reading for the whole line.
5. Spend the budget carefully. The counter at the top is moves used against moves allowed. The allowance is the shortest possible solution for this exact board, worked out before you saw it, plus three spare.
6. Finish on either face. All filled wins. All open wins. One is usually much nearer than the other, and working out which is the first real decision of the board.

How do you solve a puzzle where selecting a tile flips its whole row and column?

Stop thinking about order and start thinking about sets. Selecting a tile twice puts everything back exactly as it was, and two selections done in either order give the same board — so a solution is never a sequence, it is just a set of tiles, each one selected once. That collapses the problem enormously.

From there, use the rule the board prints for you. A tile turns over once for every selection in its row, once for every selection in its column, and once more if it is itself selected — so what decides its final face is three parities, nothing else. Pick how many selections each row will get (odd or even) and how many each column will get, and every single tile of the answer is then forced: select tile (column b, row a) exactly when its dealt face is wrong for your target and the row and column parities do not already fix it between them. Choose the parities, check the choice against itself, and the set falls out. The game does exactly that when it prints your move allowance — it walks all 1,024 parity choices, which is why the number it gives you is the true minimum and not an estimate.

One shortcut is worth knowing. Selecting all five tiles of any single row turns the entire board over. So the two winning faces are never more than five moves apart, and if you can see a short route to one face you can always price the other.

Is every board actually solvable?

Yes, and by construction rather than by luck. Each board starts as a finished, uniform grid and has a handful of selections applied to it in reverse. Those same selections, made again in any order, undo it — so a solution provably exists before you ever see the board. That matters more here than in most puzzles of this shape: on a five-wide grid, most randomly shaded boards cannot be made uniform at all, so a generator that shaded tiles at random and hoped would hand out impossible puzzles most of the time. This one never can.

Where does the move allowance come from?

From a solver, not a designer. Before the board is dealt, the game works out the exact fewest selections that finish it — checking both winning faces and keeping the cheaper — and your allowance is that number plus three. So the budget is always achievable and always tight. Boards whose true minimum is under three or over six are thrown away and redrawn, because one is not a puzzle and the other is bookkeeping.

Why does selecting the same tile twice cost me two moves if it changes nothing?

Because the budget is there to make you plan. The arithmetic really does cancel — the board returns exactly to where it was — but the two moves are gone, and that gap is the whole lesson. Work the set out first, then press. The counts printed on the tiles are there so that a tile you have already selected an even number of times is visibly doing nothing for you.

Is there any money, betting or in-app purchase in this?

None, and there never will be. No currency, nothing to buy, no hints to unlock for a fee, no prizes, no advertising.

Does it work offline, and can I play it without a mouse?

Both. Once the page has loaded once, the whole game — the board generator and the solver that sets your allowance — is on your device, and no server is involved in play at any point. Arrow keys move, Enter or Space selects, and nothing needs a pointer. Every tile announces its face, its own selection count and the parities of its row and column in words, and the two faces are drawn as ● and ○ — so nothing on the board depends on telling two colours apart.

Five by five, so twenty-five tiles and a nine-tile cross per selection. The solver is exhaustive rather than clever: it walks all 1,024 row-and-column parity assignments for each of the two target faces, and because each valid solution turns up under exactly one assignment that finds every one of them without ever testing the 33,554,432 possible selection sets. The minimum it reports is therefore proven rather than sampled. Boards are built from four to six reverse selections and kept only when that measured minimum lands between three and six, which puts every allowance between six and nine moves. There is one puzzle per seed, no timer, and no difficulty setting — the spread comes from the seed and is stated on the board as the shortest possible solution.

Light Grid is the neighbourhood version of the same algebra — a press moves five tiles instead of nine, which makes it local where this one is not. Signal Flip drops the grid entirely and publishes an arbitrary wiring diagram instead. Grid Paint is the other tile puzzle here that is solved by counting rather than by trying.

Bookmark this page (Ctrl+D, or ⌘D on Mac) or install the app — it works offline the next time you need it.