Hitori

UPDATE: After some debate with udosuk (see comments), I’ve decided to adopt the rule that every cell must be either black or white, it can’t be left “undecided”. I’ve changed the original puzzle accordingly so you can download it now.

At the end of last year, I announced that I will be introducing more types of number-logic puzzles on this site.
First up – HITORI puzzles.

Goal:
Eliminate duplicate numbers from each row and column by shading them black.

Rules of Hitori:

1. Two black cells must not touch each other horizontally or vertically. Diagonally is Ok.
2. All white cells must constitute one continuous area. In other words, there must be a path between any two white cells, without crossing “the wall” of black cells. Think of it as a maze.

Hitori puzzles can be of any size, from a tiny 4×4 (or even 3×3) to any size you can imagine. Today I’m presenting you a rather large one, 15×15 in size.

You can read how to solve Hitori by following that link.

Hitori 15×15 for February 7, 2009.

(click to download or right-click to save the image)

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sudoku variants and other puzzle books

To see the solution to this puzzle click here

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7 Comments

  1. udosuk
    Posted February 9, 2009 at 2:29 pm | Permalink

    I’ve finished this puzzle, but found that there are 5 cells which could be black or white.

    These include:
    r6c10=5
    r9c7=2
    r10c7=14
    r10c8=10
    r13c8=1

    Of course, r9c7+r10c7 & r10c7+r10c8 can’t be both black. But the fact that some of the cells in the solution grid can be either way gives me a sense of incompleteness. Is there a rule that says if a cell can be black or white then it must be white? 😕

  2. Posted February 10, 2009 at 12:47 pm | Permalink

    I’m aware of that. When I was building my Hitori solver/generator it occurred to me that there is some ambiguity regarding the rules. Eventually I resolved it by adopting what seems to be a general consensus: the only goal is to eliminate duplicates by filling them black. And that’s it. Circling white cells is only used to help you out while solving, it is actually not a mandatory part of the solution.

    Of course, if you convince me that the standard of Hitori is to also circle all cells that aren’t black, I will easily change my software to adopt that rule. 🙂

  3. udosuk
    Posted February 10, 2009 at 10:56 pm | Permalink

    For me, the focus is not whether “circling all cells is mandatory”, but whether “the solution is unique”. For all logic puzzles, uniqueness of solution is a very important aspect.

    It’s obvious your given solution is not the unique solution for the given puzzle (under the rules you specified). Because if say, r6c10=5 is shaded black, we get another valid solution (note that it can be shaded black because originally we have two 5s on r6, so technically both of them are “duplicate numbers”).

    Take the example puzzle in the following page:

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

    In the solution grid, all white cells can’t be shaded black, so the solution is “absolutely unique”. I think it should be a desired standard for your puzzle too. 💡

    So if possible, please change your software to adopt that “rule”. Thanks! :mrgreen:

  4. Posted February 11, 2009 at 12:36 am | Permalink

    udosuk, even though I disagree that the solution was not unique (remember, the goal is only to eliminate duplicates, by shading DUPLICATE numbers black; once you fill in one duplicate, the second one is no longer duplicate), I decided to avoid any ambiguity and have changed my algorithm accordingly.

    I’ve uploaded a new version of the same puzzle. I believe this time there aren’t any uncertainties – please let me know if you agree or not.

  5. udosuk
    Posted February 11, 2009 at 3:16 am | Permalink

    Thank you very much for changing your puzzle/algorithm! 🙂

    Perhaps a big part of the “debate” is the interpretation of the word “duplicate”. But the very fact that such an ambiguity can occur is enough reason for the change.

    Anyway, thanks again for the change, and hopefully you’ll create/sell more great puzzles/books in the future! :mrgreen:

  6. zvifr
    Posted February 11, 2009 at 2:45 pm | Permalink

    Shouldn’t you mention in the rules that a number can’t appear in a row or column more than once.

  7. Posted February 11, 2009 at 8:13 pm | Permalink

    Well, that is mentioned as the goal of Hitori puzzles. 🙂

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