TECHNIQUES FOR SOLVING FUTOSHIKI PUZZLES

The technique for solving a FUTOSHIKI puzzle is quite similar to that used for SUDOKU puzzles. In particlar, it is recommended that "pencil mark" numbers be entered into the cells of the puzzle to show the numbers which might potentially be the final number for each cell. The solving strategies are then applied to gradually remove these "pencil marks" until there is only one left. This last remaining number in any cell becomes the solution number for that cell.

When specific cells need to be referred to in this discussion, they will be designated as C4-R3 which means the 4th cell in row 3.

For a description of FUTOSHIKI puzzles, refer to  Building Futoshiki Puzzles 

Fundamental Strategy.

   
The most fundamental process of course applies to any "given" numbers which may appear in the puzzle. Such numbers must be removed from the pencil marks within each cell in the same row or column as the given number. This has already been done in the left hand graphic above.

Secondly, the maximum amount of information must be extracted from the "inequality" symbols which appear between certain pairs of cells. As an example, consider the cells C4-R5 and C5-R5. The number which finally appears in C4-R5 must be greater than the one appearing in C5-R5, and this means that the 1 can be removed, because it is not greater than any of the numbers in C5-R5. Using the same reasoning, the 5 can be removed from C5-R5.

This process should be applied to every pair of cells which have an inequality symbol between them. When you find a chain of cells which are linked by inequality symbols, the process must be applied repeatedly until no more pencil marks can be removed. This situation applies to a group of four cells located at the top left corner of the puzzle. The right hand graphic shows the puzzle after all possible pencil marks have been removed.

Subsequent Strategies.

   
Whenever a cell achieves the status of having only a single pencil mark, then that pencil mark becomes the solution for that cell, and appearances of that number must be removed fron cells in the same column or row. This has been done in the right hand graphic above.

From this point on, most of the solution strategies described for  SUDOKU Puzzles  are applicable, and should be studied if you are not familiar with them. As the solution proceeds, and more and more cells are finalised, you will need to return to the inequalities to extract further information which becomes available as the number of pencil marks within the puzzle diminishes.

Astute solvers may find other, more obscure strategies which they can apply. However, the strategies listed here are guaranteed to solve any FUTOSHIKI puzzle created by Magnum Opus.