## PUZZLE |

**Futoshiki Puzzle Rules**

The rules of futoshiki puzzles are as follows:

- Place 1-6 once in each row and column for a 6x6 grid, or place 1-N once in each row and column for an NxN grid
- The grid contains inequality symbols: greater than (>) and less than (<). Where present, these relationships between squares must be obeyed. For instance, 2 < 3 and 5 > 2.

Here's what a typical futoshiki puzzle looks like:

You'll notice, as per the rules, there are various greater than and less than symbols between squares. Notice that in various places these chain between cells, so that you know for a series of cells what the relationship between them is. This can be important when solving puzzles (see the solving tips below).

When solving the puzzles, you'll need to use a combination of classic sudoku rules: where can N go in this row or column, and which values can go in this square, together with the additional logic introduced by the inequality symbols.

**Play A Futoshiki Puzzle**

If you'd like to try to solve the puzzle shown above, then you can have a go via our Online Futoshiki Puzzle Player

If you enjoy this puzzle type, you can join our online Puzzle Connoisseur's Club for £12 or $17 a year and play a new futoshiki puzzle every day of the year, together with many other fun and interesting logic puzzles.

**Strategy and Solving Tips for Futoshiki Puzzles**

Here are some tips on solving futoshiki puzzles, using the above puzzle as an example as relevant:

- Be sure to use pencilmarks when solving a futoshiki puzzle to keep track of what can go where. This can help you spot moves more quickly than trying to store all the options in your head. Using our online player, with a keyboard, you can press the spacebar to toggle between big and small numbers.
- To get started you'll normally need to focus on the inequality symbols rather than standard sudoku rules, although this is not always the case. Often at the beginning of a puzzle it is possible to place the smallest or largest number somewhere in the grid, here by looking at the pattern of inequalities in the rows and columns. For instance, look at the fourth column of the example puzzle that begins with 6. In this column we have 6 and 3 as givens. The square above the 3 is greater in value than it, so can't contain 1. The square under it is in a row that already contains 1, and again the square beneath that one is greater in value than it. This means the 1 can only go in one square in that column: the final square of the column, next to the 4 in the final row.
- Pay attention to chains of inequalities as these can be particularly useful. In the sample grid above, there is a chain of four starting at the end of row three. We know that the third square in this chain contains the given three, therefore the square below the given three must contain 2 as there is already a 1 in its row. As for the two squares next to the 3 at the end of row three, we know these must be 4 or 5 and 5 or 6 respectively, so we can pencilmark those two options per square in accordingly.

**Video solve of the example futoshiki puzzle**

If you've had a go at solving the example futoshiki puzzle above, or are simply looking to find out how to solve these puzzles, then the video below solves the example futoshiki step-by-step and walks through the techniques used to solve it, such as those outlined above: