Flood It

Flood It is a strategy puzzle played on a grid of randomly colored cells. The player controls the top-left cell and, on each turn, changes its color. All connected cells of the same color as the origin (the "flood") adopt the new color, expanding the flooded region. The goal is to flood the entire board with a single color within a limited number of moves. The game typically uses a 14x14 grid with 6 colors and allows around 25 moves.

Rules

1. A square grid (commonly 14x14) is filled with randomly colored cells, using 6 colors.
2. The player starts by controlling the top-left cell.
3. On each turn, the player picks one of the available colors.
4. The top-left cell and all cells connected to it (the "flood region") change to the chosen color.
5. "Connected" means cells of the same color that are horizontally or vertically adjacent to the flood region, forming one contiguous group.
6. The flood region grows each time it absorbs adjacent cells of the newly chosen color.
7. The goal is to make the entire board one color within the move limit.

Strategies

• Maximize Absorption: Choose the color that will absorb the most new cells into the flood region. Look at the boundary of the current region and count how many cells of each color are adjacent.
• Look Ahead: Instead of just maximizing the current move, consider two or three moves ahead. A color that absorbs fewer cells now might set up a much larger absorption next turn.
• Prioritize Rare Colors: If a color appears only a few times on the board and those cells are near the flood boundary, absorb them early. This reduces the number of distinct colors remaining.
• Expand Toward the Edges: The bottom-right corner is the farthest point from the origin. Plan your expansion to reach distant corners early rather than over-flooding nearby areas.
• Bridge Strategy: Sometimes choosing a color that creates a "bridge" to a distant cluster of same-colored cells is more efficient than absorbing the largest adjacent group.
• Count Remaining Moves: If you have N moves left and N colors still on the board, you must absorb at least one color per move. Plan accordingly.

Flood It emerged as a casual web and mobile game in the late 2000s, with multiple independent implementations appearing around 2006-2010. The exact origin is difficult to pinpoint, as the concept was developed by several programmers independently. One of the most well-known early versions was a Facebook application that gained millions of users around 2008-2009.

The game's underlying mechanics relate to the mathematical concept of "flood fill," a fundamental algorithm in computer graphics used for filling connected regions of the same color (the "paint bucket" tool in image editors). The algorithm dates back to the early days of computer graphics in the 1960s and 1970s. Flood It essentially gamifies this algorithm by making the player choose the fill color strategically.

From a computational complexity standpoint, Flood It has been well-studied by researchers. In 2010, Clifford, Jalsenius, Montanaro, and Pilkington proved that determining the minimum number of moves to flood a board is NP-hard, even when restricted to just 3 colors. This means that finding the optimal solution for large boards is computationally intractable, and practical play relies on heuristic strategies. Greedy algorithms that always choose the color absorbing the most cells perform reasonably well but are not optimal.

The game has been widely cloned and adapted across platforms, with versions available on iOS, Android, and the web under various names. Its simple rules, satisfying visual progression, and strategic depth make it an enduringly popular casual game. Variants include different grid sizes, hexagonal grids, and versions where the player can start from any cell rather than just the top-left corner.