Flood It — free colour flood puzzle in your browser

You own one square: the top-left corner. Pick a colour and your square becomes it, along with everything already joined to it, and anything of that colour it now touches joins too. Keep going until all 196 squares are one colour. The catch is the move budget, which is printed before you start and gets tighter every level.

Your score is the number of levels you clear, so a run ends the first time the moves run out. Free, no download, no sign-up, and it plays the same with a thumb as with a mouse.

How to play

• Tap a colour from the row under the board. Your blob turns that colour and grows.
• The blob is outlined in white so you can always see exactly what you own.
• Fill all 196 squares before the move counter hits zero to clear the level.
• Each level gives you fewer moves relative to the board, so the same play that cleared level one will not clear level eight.
• On a desktop the keys 1 to 6 pick the colours, left to right.
• Your score is levels cleared, and your top 5 is kept on this device.

Every board is winnable, and the budget is proof rather than a guess

A move budget is only fair if the board can actually be cleared inside it. So before a board is dealt, it is solved: a greedy player runs over a copy of it, always taking whichever colour grows the blob the most, and the number of moves that takes becomes the basis of the budget. Level one gives you that number plus about 16%, and by level eight the margin is down to 2%. Two things stop that being a trap. The solver is run twice with different tie-breaking and the worse of the two answers is used, because a player who breaks a tie differently can need an extra move on the same board. And there is one spare move at every level on top of that. A budget only the solver's own habits can meet is not a fair budget. A board a greedy run cannot finish in 30 moves is thrown away and a new one dealt.

That has a pleasant consequence: the budget is generous exactly as long as greedy play is good enough, and stops being generous at the point where greedy play stops being good enough. Which is the interesting part of this puzzle, because greedy is not optimal, and the gap shows up in a specific place.

Grabbing the biggest area is the right move early, when the board is mostly strangers and any growth is progress. It becomes the wrong move late. Near the end you are usually not short of squares, you are short of reach: a few pockets of colour survive in different corners and each needs its own move to collect. The move that helps then is the one that touches the most separate pockets, even if it swallows fewer squares this turn, because it sets up a single later move that collects several at once.

The other habit worth building is to look at the far corner. The bottom-right square is the last thing you will reach and the whole board has to be one colour before it counts, so a plan that leaves an awkward colour stranded down there costs you two or three moves at the end. Players who reliably clear the tight levels tend to be steering toward that corner from about halfway.

The puzzle itself is harder than it looks in a formal sense. Deciding the shortest solution to a Flood It board is NP-hard in general, which is why nothing here claims to give you the optimal number, only a number a careful player can beat.

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