How To Solve Futoshiki Puzzles

Discover the numbers hidden inside the board’s empty cells. Each cell is filled with a number between 1 and the board size (usually between 4 and 9). Like Sudoku, each number appears only once in each row and column. Unlike Sudoku, the puzzle contains “inequality symbols” of less than (<) and greater than (>) that must be obeyed. For example, <2 would mean the number before the 2 must be less than 2, and >3 means the number before the 3 must be greater than 3.

Puzzle

Here is a typical Futoshiki puzzle grid. The grid size can be smaller or larger and varies in difficulty.

Like Sudoku, each number appears only once in each row and column. Unlike Sudoku, the puzzle contains “inequality symbols” of less than (<) and greater than (>) that must be obeyed.

Solution

The solution to the puzzle is shown here.

Notice that numbers 1 to 9 appear only once in each row and column. Further, note that all inequalities have been met according to the symbol between the squares. For instance, in row one, we see 2<3, indicating that 2 is less than 3.

Some Common Strategies

  • Look for rows or columns that contain all but one number and fill in the missing number.

  • Chain of Inequalities: Look for long chains of inequality symbols that are the same (all < or all >). In the sample puzzle above, the first row contains six in a row. Since the first seven cells share less than (<) symbols, you now know that the highest number in the sequence, in this case, 9, must be in either of the right two cells. Another example is the 9 in row two. If, in your analysis, you discovered the 9, you will be able to follow the chain to fill in the remaining numbers from the 9 in row two to the 8 to 2 in row one.

  • Forced Minimum and Maximum numbers: Squares that have a <2 must be 1. Squares that have an 8< must be 9.