🎨 Color Flood

Color Flood: One Color at a Time, and the Number That Tells You How Well You Did

Your flood starts as the top-left square. Pick a color and the flood turns that color and swallows every square of that color it touches. Keep going until the whole board is one color, and then the page tells you how few moves that board could have taken. Color Flood is the game most people know as Flood It or Flood-It!, sometimes Flood Fill or Color Fill. The rules are the same ones; what is different here is that there is no move limit. You always finish, and then you find out.

📏 The Rules, All of Them

• The board is a grid of colored squares. Your flood is the top-left square plus every square of the same color connected to it, side to side or up and down, never diagonally.
• A move is picking a color. Your whole flood changes to that color and takes in every square of that color touching it, and everything connected to those.
• The board is done when every square is one color. Your result is the number of moves that took.
• Picking your flood's own color, or a color not touching it, does nothing and is not a move. This page refuses both and tells you why.
• Undo takes back a move and its count. No limit on undos, and no clock.

🔄 Same Colors as SameGame, the Opposite Idea

The board looks like SameGame, but the two games pull in opposite directions: SameGame removes groups and lets the rest fall, Color Flood removes nothing and grows one group until it is the whole board. The other comparison is with the original Flood-It!, which gave you a fixed number of moves and a loss when they ran out. Here nobody loses. You finish every board, and the popup compares your count with the fewest moves our solver found.

🧅 Count the Layers: the One Idea That Matters

Every region of color sits some number of steps from your flood. The regions touching it are layer 1, the regions touching those are layer 2, and so on. A move only ever takes in layer 1 and moves everything else up by one layer at most, so a region in layer 4 cannot join your flood before your fourth move. That gives two quick floors on your score: at least as many moves as there are layers, and at least one move for every color still on the board. The real floor is sharper than either.

A yellow flood, four colors left, four layers out to the purple corner: either quick count says 4 moves. The answer is 5. Everything from layer 2 outward holds four colors (green, red, blue, purple) and none of it can be touched before move 2, so that is 1 + 4 = 5. The red beyond the green costs a second red.

So for any layer: the moves before it, plus one for each color that still appears in that layer or beyond, and the biggest of those is your floor. In play you don't need the arithmetic, just the habit: look at the far corner, count the colors between you and it, and notice when a color shows up both near you and far away, because that color will cost you twice. The move that helps most is usually the one that shortens the longest path, not the one that paints the most squares.

One more rule falls out of the same picture. When every remaining square of a color already touches your flood, take that color now. It can never cost a move: whatever the best route from here was, it had to use that color somewhere, and playing it first then following that route leaves your flood at least as big at every step.

🪣 Why the Biggest Grab Isn't the Best Move

The natural way to play is to pick whichever color turns the most squares, and it is a trap, because it measures the wrong thing. We played every board in our test set three ways: picking colors at random, grabbing the most squares each move, and picking the move that leaves the fewest layers. On a 12 × 12 board with six colors the random player needs about 30 moves, the grabber about 23 and the layer-counter about 21, against a best route of 18. The grabber's extra moves come from the same mistake every time: it fills a fat region nearby while a thin path to the far corner goes untouched, then pays for the path one color at a time at the end. The layer-counter is still about one move in seven over the best route, because it never looks more than one move ahead. The solver does.

⚠️ Mistakes That Cost Moves

1. Painting instead of traveling. Twenty squares beside you and none toward the far corner is no progress.
2. Leaving a lone square behind. One stray square in the corner the flood reaches last is a whole extra move. Spot it early and sweep it up with a move you were making anyway.
3. Ignoring a color that appears twice. Red near you and red beyond the green is two red moves. Where you can, reach both reds before you play red.

🎚️ Boards, Colors, and What the Numbers Say

For each of the nine combinations we generated 35 boards, found the fewest moves for each, and played them through with the three players above; the random player is a floor and the layer-counter roughly what a careful human does.

Fewest is the typical board, with the range seen, over 35 boards per row; the three players (random picks, biggest grab, layer counting) are averages over the same boards. Proven is how often the background search finished and showed the count could not be beaten.

Doubling the colors and doubling the side of the board cost about the same, each adding roughly three quarters to the move count, but differently: a bigger board puts more layers between you and the far corner, while more colors means more of them turn up twice. The gap between the biggest-grab player and the best route widens with the board, from one move on 8 × 8 Easy to about ten on 16 × 16 Hard. Easy on 8 × 8 is a two-minute game; Hard on 16 × 16 is a long, careful one where even the solver's best route runs to twenty-eight or so.

🔎 How We Know the Fewest Moves, and When We Say So

Two searches run on every board. The first runs before your first move, keeps the forty most promising positions at each step judged by the layer count, and returns a real route. That is why the popup can say it was possible to finish in 15 the moment you finish, and why Watch the solution can play that route on the same board. On most of the boards above it had already found the true minimum.

The second runs in the background while you play, in slices of a few milliseconds between your moves, and it is the one that proves things. It tries every route the layer count cannot rule out, and because that count never promises fewer moves than are really needed, when the search runs out of places to look the shortest route it holds is the shortest there is. Then the popup says the fewest possible was 15. If it has to stop early, which happens mostly on the biggest board with eight colors, the popup says it was possible to finish in 15, and if you then beat the solver's number it tells you so. We checked this search against a plain brute-force search on 70 small boards and the two never disagreed. Flood filling with three or more colors is NP-hard, so the biggest boards will never be proven quickly, and the wording has to carry the difference.

🎮 Playing on This Page

Tap a swatch under the board to flood with that color, or tap any square on the board to pick its color. Keys 1 to 8 pick colors in swatch order, Z undoes and N starts a new game. The swatch with the check mark is your flood's current color; a faded one is a color that is gone from the board. When you finish, Play Again puts the same board back so you can try to shave a move off, and New Game deals a fresh one. Boards are random and there is no daily puzzle, so play as many as you like.

📜 Where Color Flood Came From

The game is Flood-It!, made by the Israeli studio LabPixies around 2006 as a browser gadget and later an iPhone game, before Google bought the studio in 2010. Its grid, corner start and pick-a-color move have been copied many times since: as Flood in Simon Tatham's Portable Puzzle Collection, which sets its move limit at its own solver's count plus a few spare, as Open Flood on Android, and as the daily Color Flood at Ponder Club, whose Double Up likewise prompted our Drop Merge. A 2010 paper by Clifford, Jalsenius, Montanaro and Sach proved that finding the fewest moves is NP-hard with three or more colors, which is why ours proves the count where it can and says so where it can't.

🧒 A First Strategy Game That Looks Like Finger Painting

There is nothing to read and nothing to lose. A four-year-old can play 8 × 8 Easy by tapping the color they like and watching the flood spread, and the strategy arrives on its own: sooner or later a child notices that the far corner is the problem, which is the whole idea of layers without a word of explanation. Undo makes every mistake free, and the popup's two numbers give an older child something precise to chase. Start on 8 × 8 with four colors, move to six when nine moves feels easy, and save 16 × 16 for an afternoon with nowhere to be. 🎨