Flow Free Rules: Connect & Fill Every Cell

Flow Free is played on a square grid. Colored dots appear in pairs: two red dots, two blue dots, two green dots, and so on. Your task is to draw a path connecting each pair of same-colored dots. The path moves orthogonally (up, down, left, right) from cell to cell. Three constraints govern every puzzle. **(1)** Paths cannot cross each other. A cell can only belong to one color's path. **(2)** Every cell on the grid must be filled by some path. There can be no empty cells when the puzzle is complete. **(3)** Each path must connect exactly two dots of the same color in a single continuous line. The combination of these three constraints is what makes Flow Free challenging. Connecting the dots is usually easy, but filling every cell without any path crossing another requires careful planning. The "fill every cell" rule is the key constraint that transforms a trivial connection problem into a genuine puzzle.

Always start with the **shortest paths**. Identify color pairs that are adjacent or only a few cells apart and connect them first. These short connections are almost always forced (there is only one reasonable path), so you can fill them in confidently without worrying about blocking other colors. Next, identify **bottlenecks**: narrow corridors between walls of dots. If the only way for a color to reach its partner is through a specific corridor, that path is forced. Draw it immediately. Bottlenecks are the most powerful deduction in Flow Free because they resolve large sections of the board at once. **Corner and edge routing** is another essential early strategy. Dots near the edge of the grid have fewer possible paths. A dot in a corner has only two possible directions for its path. A dot along an edge has three. These constrained starting points often force a specific path direction, especially when other colors block the alternatives.

**Color isolation** is the core advanced technique. When you draw a path for one color, it creates a barrier that other colors cannot cross. Use this deliberately: route one color's path to create a "wall" that forces nearby colors into their only possible route. Thinking about colors as walls as well as connections is the key to solving harder puzzles. **Corner routing** means guiding paths along the edges and corners of the grid to keep the interior open for other colors. A path that hugs the boundary uses the minimum number of interior cells, leaving more room for other paths to navigate. Whenever possible, route paths along the perimeter. **Dead-end elimination** means checking whether a proposed path would leave any cells unreachable. If a path creates a pocket of empty cells that no remaining color can reach (because all paths to the pocket are blocked), that path is invalid. Before committing to a route, trace the remaining empty space and confirm every cell is still accessible to some color.

On large grids (8x8, 9x9) with many colors, you will encounter situations where no single path is obviously forced. In these cases, use **constraint propagation**: tentatively assign a path to one color and see what it forces for the others. If a contradiction appears (a color cannot reach its partner), the tentative path was wrong. The **look-ahead method** is systematic constraint propagation. Choose the most constrained color (the one with the fewest possible paths) and mentally trace each option. When an option leads to a contradiction, eliminate it. This process of elimination often reduces multiple colors to a single valid configuration. When you are truly stuck, **restart with a different initial path**. Sometimes the first few paths you draw create an impossible situation for later colors, even if those initial paths seem correct. Starting over with a different strategy for the first one or two colors often reveals the solution quickly.