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Hutosiki puzzles: how to solve them...

Hutosiki puzzles are still fairly uncommon over in the West, so first an explanation of what they are.

They are a puzzle, also called futoshiki, in which you have a square grid that is either 5 x 5 , 7 x 7 in shape (though other sizes are also possible, these are the most common). It is unclear which name came first - hutosiki or futoshiki - but all you need to know is that when people refer to the one, they also refer to the other - they are the same puzzle! Apparently hutosiki is Japanese for not equal, which as you'll see below is a good tip to exactly what the puzzle is.

You must work out where the numbers from 1 - 5 or 1 - 7 go in the grid, and they can only go once in each row and column - sounds familiar? Well, yes, so far it is like sudoku. But here comes the twist.

There is no need to worry about small boxes - there are none. However there are greater than and less than signs in hutosiki. So if you don't know what these are or how they work, then hutosiki will be hard for you to play.

So, that's the rules. If you want to play a sample hutosiki puzzle online, then try this link:
Hutosiki puzzle

Now, open up that link, and think up some strategies. Here we go:

Hutosiki / Futoshiki Solving Strategies

The first strategy you will use is the most boring, which is going through each cell and working out the possible values given the numbers already placed in its row and column. This is pretty quick here, as there is just one four placed, so we can just knock out a '4' from the 8 squares in its row and column.

That done, we then move onto the greater than and less than signs. For each two cells in such a relationship, we know that the greater than side cannot be a one, and the less than side cannot be a 5. If there are numbers already placed in a row or column, these can be eliminated too.

If there is a chain of three connected cells, then we know that the top value cannot be lower than 3, and the bottom value cannot be higher than three - and therefore the one in the middle can be 4,3,2.

Sometimes we can place cells straight away. Look at the example puzzle: we see the cell next to the given 4 is greater than 4. Only 5 meets that criteria in this hutosiki puzzle, so write it in.

Since we know a chain of three cells must have at least 3 at the top, and 3 is the highest number left in the row, we can write '3' on the other side of the 4 in this hutosiki puzzle. We then write 2 under and 1 under again. Now we can go through and do eliminations again.

Another useful hutosiki solving strategy is to check where a number can go in a row or column.

Top Hutosiki Solving Tip

Usually when you get stuck it is because you have missed an instance of this above rule. There will only be one possible place, for instance, for a '1' in a row or column and placing that will then let you carry on and solve the puzzle easily.

Often at the start of the puzzle there will be only one place in a row or column that a '1' or '5' could go (in a 5 x 5 puzzle) as all but one cell will either be greater than another cell, or all but one cell in the hutosiki will be less than another cell. This means there is only one candidate for that highest or lowest number.

You also need to be disciplined and everytime you place a number remember to knock it out from other candidate cells in that row or column. Pay particular attention to inequalities as when a number is placed you can often solve the inequality or knock a possibility out from both sides of the inequality.

Advanced Hutosiki Tips

Well, this may not be that advanced, but it is one rule that may not occur to you obviously, again this is borrowed from sudoku.

If you have two cells in a region (row or column) that both have the same two candidate numbers, for instance '12' and '12' then you can knock those 1 and 2 out of the other numbers in that region. Imagine we have these 5 candidates in a row or column:
12, 12, 45, 453, 123

Since the 1 and 2 must be placed in those first two cells whichever way round, we know the final cell cannot be 1 or 2. We therefore knock out the 1 and 2, leaving just the 3 as the only candidate for that cell, and so we can place it.

This rule needs to be remembered as in harder puzzles you often have to apply this rule, and without it would not be able to make progress without guessing - and you never have to guess in a proper hutosiki as there is only one valid solution that can be reached through logic alone.

You can play more hutosiki here.

If you have any other tips for solving hutosiki then I'd love to hear them - please send them to me through your profile and I'll add them here. Those are the ones I could think of for now, but if there are any other strategy tips, then please let me know!

Hutosiki Solving Tips

Author: Dan About the Author: More About the Author >>> | My other pages >>> Page Views: 6082 | Page Ranking: 23 Popular Tags: hutosiki, futoshiki, japanese puzzle, solving tips Last Updated: Nov 9th 2006 Ask Dan a Question >>>

Category: Puzzles and Games [More Categories]

Questions Dan has Answered:

Are there any Fotoshiki/Hutosiki solvers online? I\'m stuck on one and wonder if there is an automated system??

If you enter the numbers here and the greater and less than signs I'll solve it for you - not sure of an online solver though; not seen one! Also where is the puzzle taken from?

Programming fotoshiki - how do I write a futoshiki generator program?

First write a sudoku generator. Then amend the program so that you do not have the box constraint (e.g. the 3x3 square regions in 9x9 sudoku). Then finally add an extra rule that will check the relationship between adjacent cells (in terms of which are greater/less than the neighbours). Add in some relationships between cells and then use the extra knowledge this gains to help your program solve the futoshiki puzzle. This new greater/less than rule combined with the standard sudoku solver rules will enable you to create and solve futoshiki puzzles.

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