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How to Play Futoshiki

Basic Rules

  1. 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. 2.Each row must contain each digit exactly once.
  3. 3.Each column must contain each digit exactly once.
  4. 4.Satisfy all inequality constraints between adjacent cells. The greater than (>) or less than (<) signs show which cell must be larger.

Understanding Inequality Signs

A < B
means A is less than B (A must be smaller)
A > B
means A is greater than B (A must be larger)

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