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Futoshiki or Hutosiki puzzles are great fun...

This puzzle comes under a couple of different names: Futoshiki and Hutosiki, but the principal is the same: you are given a grid of any size - normally 4 x 4 or 5 x 5 and need to deduce where to place the numbers in the grid using logic alone.

Sounds familiar? That's because it is another popular Japanese puzzle that has made its way over to Europe and is now starting to filter into some magazines and newspapers.

Futoshiki is, apparently, Japanese for 'not equal' which gives a clue as to how it works, as you will see later... A valid futoshiki puzzle should have one unique solution, however not all those you will see out there meet this requirement!

The aim of the game is similar to sudoku in that each number (1 - 4 in a 4 x 4 and 1 - 5 in a 5 x 5) must be placed once in each row and column. There are no boxes in this puzzle, so there is no other constraint along those lines.

Most of these puzzles seem to be composed by hand, given the size of the grid this is quite feasible and means that difficulty can be accurately accessed by the compiler; rating computer created puzzles can be quite difficult and is one of the major distinguishers of a good automated puzzle creator over a poorer automated creator tool.

The other element of futoshiki or hutosiki that is very interesting is that there are few stated givens. However, another mathematical relationship is given: the greater than or less than sign is used between some cells to specify whether a number is greater than or less than the number next to it.

Therefore if we see this in a 5 x 5 puzzle: 2 > _ ...

Then we know that the blank cell must be a 1, as the only number between 1 and 5 that 2 is greater than is 1. If it were the other way round, e.g. 2 < then we know that the cell next to it must be either 3,4,5.

Futoshiki is therefore an interesting puzzle as it makes you think about the relationships between the numbers and use that logic to deduce where each number must go. This also means that you need surprisingly few givens, in fact you can create grids where you do not need any givens, as long as you give enough relationships for each cell.

Here is a 4 x 4 simple futoshiki puzzle for you to enjoy:



If you would like to play Futoshiki online, then why not try the online Futoshiki player?

If you want to buy Futoshiki puzzles or virtually any other puzzle, then you can Buy Futoshiki here.
Futoshiki Puzzles
Author: Dan

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Last Updated: Oct 17th 2006

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Questions Dan has Answered:

I want to solve a futoshiki puzzle 7x7. I didnt get the answer. How can I send you the question?

Remember that each row and column must contain 1 - 7 once only and you must obey inequalities. Normally when someone gets a different answer it is because inadvertently they have not met these conditions. If you double checked and yours seems valid then it could be wherever you got the puzzle from was not actually a valid futoshiki puzzle in which case you should let the publisher now - if you type up the puzzle and send it here I can have a look.

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