Futoshiki

Futoshiki Instructions:
Here's how to play Futoshiki:
Place the numbers from 1 - n exactly once in each row and column in the puzzle.

Inequality symbols appear between certain neighbouring cells. These must be obeyed by the solution.

Note: inequalities symbols are > (greater than) and < (less than). For instance 5 > 3 > 2 whilst 1 < 4 < 6.

The Fun of Futoshiki

Futoshiki is a fairly-commonly seen variant of the sudoku puzzle, and is another variant that makes use of the fact that one is using numbers to solve these puzzles.

The puzzles are one of the most popular variants because there is one simple extra rule: that where inequalities appear between cells, they must be obeyed. These allow you to narrow down the values that can go in these sets of cells and thus help you to reach the solution.

Futoshiki puzzles are most commonly seen at either 5 x 5 grid size or 7 x 7 grid sizes (other sizes do appear but much less frequently). Because of the additional information provided by the inequalities then, even though there only two regions in these puzzles, there will be fairly few givens in a grid - and indeed there may be none at all given, as one sees with killer sudoku.

As soon as one learns which symbol is which ( > for greater than and < for less than) - if not already familiar with these from doing maths at school - then it is just a case of using this extra information to whittle down the options that is required to solve futoshiki.

Of course, there are some simple rules that these introduce that will be picked up after solving a few puzzles. For instance, if the value in a cell is greater than both the cell to the right of it AND the cell to the left of it (or alternatively above AND below) then the lowest value in the stated cell is 3, given we have this situation in this instance:
x < y > z and we know that the values of all three must differ since they are in the same row or in the same column.

Futoshiki puzzles, although not uncommon, are usually seen published alongside a range of other logic puzzles rather than on their own... we're not aware of any magazines that have ever been published purely of futoshiki for instance.

If you'd like to have a go at solving a futoshiki puzzle, you can play a Sample Online Futoshiki Puzzle using our online puzzle player.

Or, if you'd like to find out how to solve the puzzle, then this video outlines the rules of futoshiki and how to solve the puzzle linked to above:

Last updated: 03 Sep 2019

Back to A - Z of puzzles

Sample puzzle:
start Futoshiki image

Sample solution:
solution Futoshiki image

View a sample Futoshiki PDF

Play Futoshiki Puzzles:

If you like futoshiki, then why not play lots of great futoshiki puzzles online at the futoshiki puzzles section of the Puzzle Club website.

If you like solving on paper, then download an issue of Futoshiki Magazine in PDF format and print off the puzzles to solve at your leisure!

Publish Futoshiki Puzzles:

If you would like to buy or licence Futoshiki puzzles for publication, then please Contact Us >>>

Futoshiki

The Fun of Futoshiki

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