How to Play Futoshiki
Basic Rules
- 1.Fill the grid with digits 1 to N (where N is the grid size). For a 5×5 puzzle, use digits 1-5.
- 2.Each row must contain each digit exactly once.
- 3.Each column must contain each digit exactly once.
- 4.Satisfy all inequality constraints between adjacent cells. The greater than (>) or less than (<) signs show which cell must be larger.
Understanding Inequality Signs
Example:
If you see 3 > ___, the empty cell must contain 1 or 2.
If you see ___ < 4, the empty cell must contain 1, 2, or 3.
Solving Strategies
1. Start with Extreme Values
Look for chains of inequalities. If you see A < B < C < D < E in a 5×5 grid, A must be 1 and E must be 5. Fill these in first!
2. Use Row and Column Elimination
Once a number is placed in a row or column, eliminate it from other cells. Combine this with inequality constraints to narrow down possibilities.
3. Apply Constraint Propagation
If a cell has only one valid value (considering both Latin square rules and inequalities), fill it in. This often unlocks more cells.
4. Use Pencil Marks
Write down possible values for each cell. As you solve, update these marks. When a cell has only one possibility left, that's your answer!
5. Look for Forced Positions
Sometimes a number can only go in one cell in a row or column based on the inequality constraints, even if other values are possible there.
Controls
- Click a cell to select it, then use the number pad or keyboard to enter a digit
- Number keys (1-N) to enter a digit in the selected cell
- Backspace/Delete to clear the selected cell
- P key or Pencil button to toggle pencil mode for noting candidates
- Ctrl+Z / Cmd+Z to undo your last move
- Ctrl+Shift+Z / Cmd+Shift+Z to redo