Futoshiki
![An example of a 5x5 Futoshiki puzzle ...](/Images/godic/202501/14/Futoshiki15340.png")
![... and its solution](/Images/godic/202501/14/Futoshiki25340.png")
![The first step to solve the puzzle is to enumerate possible values based on inequalities and non-duplication within rows and columns. Then AB elimination may be usable to narrow down the range of possibilities. As shown here, the top and bottom positions in the center column must contain 5 and 3, so these can be excluded from the second and fourth positions.](/Images/godic/202501/14/Futoshiki1b5340.png")
![Logical deduction within the inequalities can restrict the range of possibilities. As shown here, a 2 in the upper left corner requires a 1 in the second position due to the first inequality; but a 1 in the second position allows only a 3 in the fifth position ... and so on, until we conclude two 4s would need to be placed in the same column.
Likewise a 3 in the upper left corner would require the top row to be 3 2 5 4 1 and the bottom again to be 1 2 3 4 5 - leading to the same contradiction.
Only a 5 is permissible in the top left corner, from which we deduce 5 4 3 2 1 at top and 1 2 5 4 3 at bottom. The remainder of the solution is simple elimination.](/Images/godic/202501/14/Futoshiki1c5340.png")
Futoshiki(不等式futōshiki), or More or Less, is a logic puzzle game from Japan. Its name means "inequality". It is also spelled hutosiki (using Kunrei-shiki romanization).
The puzzle is played on a square grid, such as 5 x 5. The objective is to place the numbers 1 to 5 (or whatever the dimensions are) such that each row, and column contains each of the digits 1 to 5. Some digits may be given at the start. In addition, inequality constraints are also initially specified between some of the squares, such that one must be higher or lower than its neighbour. These constraints must be honoured as the grid is filled out.