SudokuSolver Forum

What's the difference? Is a futoshiki simply a greater-than without box constraints? Or is it just another name for greater-than?

"Futoshiki" in Japanese means "inequation" (as opposed to "equation" in the mathematical sense).

I think you're mostly right, it basically means "greater-than". Then you can add other rules, such as NC (non-consecutive). If you have box constraints, then it can be called "Futoshiki Sudoku" instead of the more "Greater-than Sudoku".

So when people here talk about Futoshiki, are they referring to ANY type of greater-than/less-than sudoku (with or without other constraints, including boxes)? Is Futoshiki just another name for greater-than/less-than puzzles in general? Or does the term Futoshiki refer to ONLY greater-than/less-than puzzles WITHOUT box constraints (but which may or may not have other constraints)?

There is actually a wikipedia article on Futoshiki:

http://en.wikipedia.org/wiki/Futoshiki



If you really want to scrutinize on the terminology, guess you have to start from the most fundamental level.

Firstly we assume we only work with a square grid. The most simple constraint would be no repeats on each row & column. We call this a Latin Square.

On top of this we can add the following constraints, either individually or a multiple of them:

1) Sudoku: divide the grid using rectangular boxes of area same as the width of the grid, such that no repeats are allowed within those boxes. For example, divide a 9x9 grid into nine 3x3 boxes, or 4x4 grid into four 2x2 boxes, or 6x6 grid into six 2x3 boxes, or 12x12 grid into 2x6 or 3x4 boxes.

2) Jigsaw: divide the grid using irregular shaped boxes of area same as the width of the grid. In some extreme cases the cages can even be remote/disjoint (i.e. split into multiple disconnected pieces). Some called them Jigsaw Sudoku but in fact they are just Jigsaw Latin Square. Another name used to call these puzzles is Du-Sum-Oh.

3) Killer cages: regular/irregular shaped cages of various sizes, normally repeats within the cages are not allowed and the sum of digits (if digits are used as symbols) will be indicated. If repeats are allowed, they are repeat cages. If the sum of digits is omitted, they are zero cages. Killer Sudoku are puzzles combining this and (1) above, but Killer Latin Squares are also possible (I believe HATMAN has posted these before).

4) Algebraic cages: similar to killer cages but instead of sums, the differences/products/quotients might be used, with the operator shown or omitted. There are many different variants using this, most famous being KenKen which allows repeats within the cages and limit the minus/divide cages to 2 cells only. Other variants such as Calcudoku, TomTom etc which might disallow repeats within cages or allow larger minus/divide cages (where the largest digit must start the expression).

5) Anti chess piece: same digits cannot be "seeing" each other if they have the moving power of certain chess pieces. Most popular ones include Anti-King (AK) (not diagonally adjacent) & Anti-kNight (AN).

6) Consecutive/non-consecutive: If horizontally/vertically adjacent cells are consecutive, a thick bar will appear between them. If there is no thick bar, it means they must be non-consecutive. More often than not the Non-Consecutive (NC) constraint (where there are no thick bars in the grid at all) is used.

7) Futoshiki or Greater-Than: Inequality signs (<, >) are shown to indicate the relationship between horizontally/vertically adjacent cells.

8) Other geometrically based constraints such as diagonals, asterisks, windows etc.

There are many many more...

Thank you, simon, for the explanation and the link. It's a little confusing, because the puzzle shown in that link as an illustration is clearly NOT a sudoku, nor is there any mention of sudoku in that article.

I've been ignoring any mention of Futoshiki, thinking it referred only to a type of non-sudoku puzzle. However, if some use it to refer (at least part of the time) to greater-than/less-than sudoku puzzles, I guess I'll have to pay more attention.

Would it be correct, then, to say that a Futoshiki is a greater-than/less-than puzzle that may or may not be a sudoku, and that one must specify it as a "sudoku" in order to refer to a greater-than/less-than sudoku?

enxio27, I don't know about you but for me whether a puzzle is Latin Square-based or Sudoku-based is not that important, as long as they stimulate my brain and give me a sense of satisfaction when I finish it.

Most of HATMAN's latest Futoshiki puzzles are NOT Sudoku. But I enjoyed them very much nonetheless. You still have to apply a considerable amount of Sudoku techniques (e.g. singles, subsets, or even x-wings and turbots in the extreme case). Probably the only irrelevant technique is intersection (or locked candidates as called by some), but for me it makes little difference. You still fill in digits inside a square grid.


But to answer your question, yes I think the term "Futoshiki" is completely independent to "Sudoku". Each of them is a "Latin Square" puzzle. If you combine them, you can probably call it a "Futoshiki Sudoku" puzzle.

On the other hand, "Greater Than Sudoku" has a slight and subtle difference to a general "Futoshiki Sudoku" in that, most "Greater Than Sudoku" puzzles do not have any inequality sign between cells of different boxes, such as R3C3-R3C4 and R6C5-R7C5. So while a 9x9 "Futoshiki Sudoku" can have a maximum of 144 signs, a "Great Than Sudoku" only allows a maximum of 108 signs.