In Patches, a "forced move" is a placement that is uniquely determined by the existing clues and grid boundaries. Identifying these moves is crucial for efficient puzzle-solving, especially as grids get larger and more complex. Once you spot a forced move, you can place that patch with certainty, simplifying the rest of the puzzle.
Type 1: Corner Clues with Limited Options
Clues in the corners of the grid, especially those whose area is a perfect square, often have very few valid configurations, making their placement forced. Consider a '4' clue at (0,0) in a 2x2 grid:
A '4' can be 1x4, 4x1, or 2x2. In a 2x2 grid at (0,0), it *must* be a 2x2 square as there's no other way to fit it while covering the clue. It takes cells (0,0), (0,1), (1,0), (1,1).
Type 2: Clues Blocked by Adjacent Clues or Boundaries
When a clue is next to a boundary or another already placed patch/clue, one or more of its potential directions for expansion might be blocked, forcing it into a specific shape.
Consider a 4x4 grid with a '2' at (0,3) and a '3' immediately to its left at (0,2):
The '2' at (0,3) can be 1x2 (horizontal) or 2x1 (vertical). However, it cannot extend left to (0,2) because that cell contains another clue ('3'), and each patch must contain *exactly one* clue. Therefore, the '2' is *forced* to extend downwards, taking cells (0,3) and (1,3).
Type 3: Filling Remaining Isolated Spaces
Another common forced move occurs when a portion of the grid becomes isolated, leaving only one logical way to fill it with a remaining clue.
Consider this partial 4x4 grid, where the highlighted '2' clue is the last one to be placed, and the surrounding areas are already filled by other patches (represented by different colors):
In this scenario, the '2' clue at (2,2) has only one available adjacent cell that is not part of another patch: (3,2). It is therefore *forced* to form a 2x1 vertical patch covering (2,2) and (3,2).
Conclusion
Forced moves are your best friends in Patches. By systematically looking for clues that have only one valid placement due to grid boundaries, adjacent clues, or the remaining empty space, you can quickly make progress and reduce the complexity of the puzzle. Practice identifying these situations, and you'll find yourself solving puzzles much more efficiently!