**Play Futoshiki Puzzles Online**

In the following tutorial, basic and advanced techniques for solving Futoshiki puzzles are presented step by step, with accompanying illustrations to show-case the methods on specific board configurations.

The starting point for reaching a solution is the definition of the game itself: Futoshiki requires the user to find out a board where every digit appears once on every row and column, by respecting the board's inequalities. By using this criterion, progress towards a solution can be made by completing, step by step, empty board squares with specific digits because they are the only way to respect the board's restrictions.

If a square's column and row already contain all possible digits, except one, then that square must contain the missing digit. In the example above, the green square must be 4 since it would not be allowed to have any other value as the other possible digits are already found in its row or its column.

Squares that are less than **2** must implicitly have the value **1** as it is the only admissible value on the board which respects that condition. Similarly, squares that are greater than the board size minus 1 must be equal to the board size. In the example above, the only possible value for the green square (less than **2**) is **1**.

Sometimes multiple rules must be used in order to reach a conclusion. This is the case in the example above, where we try to place the value **1** on the second row of the board. The first red square is eliminated due to a **column exclusion** (we already have a **1** on that column), while the second and third red squares are eliminated due to an **exclusion of min values** as those places have 'greater than' inequalities associated with them. Therefore the green square remains the only possible place for placing **1** in that row.

Sometimes, especially on difficult boards, there are no other ways to figure out the correct digit for a square except for diving into the implications of each possibility until a contradiction is reached. In the example above, all red and orange squares are initially blank. We want to figure out if the square A contains **1** or **2**. We assume that it contains **2** and we check to see if we reach a contradiction based on this assumption.

If square A has a **2**, then square B would have a **1** (the only remaining value on the bottom row). Square C can be **1** or **2** as it has a chain of inequalities that requires to have available 2 greater numbers, but now it cannot be 1 due to the column exclusion of square B, so square C is a **2**, and square D is a **3** (the only value between 2 and 4). Due to column exclusions, square E is **1** and square F is **3**.

Now, if we look at the orange squares, we notice the contradiction: if square G were to be **2**, square H would have to be either **3** or **4**, which are not allowed due to a row exclusion. If square G were to be **3**, square H would have to be **4** which is not allowed due to the same reason. As we've ran out of possibilities for square G, it means that we've reached a dead-lock and our initial assumption was wrong: **2** is not a valid move for square A, so we can go ahead and place 1 in it, the only other possible value.

We've shown above how to solve a Futoshiki puzzle successfully by covering a range of techniques that can help you deduce the next move even in difficult situations. The other key ingredient for becoming proficient and fast at solving Futoshiki puzzles is experience: the more you practice, the better and faster you'll become.

If you're up for a challenge, you can play right now a random Futoshiki puzzle by clicking the button below. Good luck!

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