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Futoshiki Solving Tips

Futoshiki is a simple and fun logic puzzle, that is great when you have a few minutes to spare (for 5x5 puzzles) or considerably longer for large puzzles which are usually 7x7 in size, but sometimes even 8x8 or possibly 9x9.

The key to solving futoshiki is to make the most of the greater than and less than signs (> and <) remembering that the open end always points to the larger number.

So as a first stage you might like to go through and deduce as much as you can from the symbols in the puzzle. In a 5x5 everytime you see a single > next to another cell, then you know the greater cell must be 2,3,4,5 and the smaller must be 1,2,3,4.

Chains are particularly useful: if a>b>c then you know that 'a' must be at '3' for instance, and that 'c' cannot be greater than 3.

Chains where all the cells are in a region are also useful. For instance, if a < b > c is the pattern facing you, and the three cells are in the same region, then you know that 'b' must be at least 3, whilst 'a' and 'c', as stands to reason, cannot be 5. Note that a < b > c where, say, a is in the same row as b and c in the same column, we cannot say that 'b' must be at least three, as 1,2,1 would be a valid solution.

The common rules of sudoku are also useful in futoshiki, particularly when you have placed quite a few numbers then the once-per-row and once-per-column rule are useful.

With the hard futoshiki puzzles in the Guardian, you will also need to look at the sets of possible candidates. For instance, if you know that the candidates for a region are 34, 35, 12345, 12345 and 345 in a 5x5 puzzle then you can see that cells three and four must contain the 1 and the 2, so this can be whittled fown to 34, 35, 12, 12, 345.

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