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Latin Hexagon [Jun. 9th, 2009|05:02 pm]

Fill in the cells with numbers from 1 to 6. No number may appear more than once in any row. The rows are indicated by the red, black, and grey lines.

The second puzzle in the "Too hard to be published" series :-)

I eventually did find a logical path to the solution, but it took a long time.

From: songmonk
2009-06-10 12:55 am (UTC)
If you just presented the puzzle with the instructions, I would have tried it.

But when *you* say it's difficult, that kind of makes me despair before I've even started. :-)
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[User Picture]From: cyrebjr
2009-06-10 07:10 am (UTC)
I solved it! First I placed most of the 6's, then all the 1's, then the rest of the 6's. The rainmaker was the bottommost full gray row.

Let's see if I can format this right:
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From: meowsqueak
2009-06-10 09:28 pm (UTC)
Is that picture the starting configuration, or an example?
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[User Picture]From: cyrebjr
2009-06-11 02:12 am (UTC)
Eh? The picture in the post is a puzzle of the type described. In the solution, every big hexagon (three short sides and three long sides) should contain a single digit as explained in the rules.

Inasmuch as "starting configuration" makes sense, I can't tell how it's different from an "example." Do you mean "is the grid complete?" Because it isn't.
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From: meowsqueak
2009-06-11 02:23 am (UTC)
Right. Ok. Obviously the grid is not complete. Just because you don't understand my question doesn't mean it wasn't clear.

But let me rephrase:

Is the picture an example of a partially completed solution/attempt, or is that the INITIAL CONFIGURATION for the puzzle? Much like a sudoku puzzle has an initial configuration, rather than 81 empty squares.

Or to put it another way - does the puzzle start with a completely blank grid of cells, or with those numbers shown in the picture?
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[User Picture]From: zundevil
2009-06-11 04:28 am (UTC)
This puzzle starts with the numbers shown in the picture. They're the givens, like the 20-some or 30-some digits given at the start of sudoku puzzles. Like all good logic puzzles, these given digits should only lead to one final, completed solution. An entirely blank grid, OTOH, would lead to countless solutions, and wouldn't make for a lot of fun. :)
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From: meowsqueak
2009-06-11 04:36 am (UTC)
Thanks for the clarification.

When I first read the description of the puzzle, I thought the problem was to find a general strategy for filling the grid, such as one might encounter with those puzzles that challenge you to "use every number exactly N times" or knights-move/queens-type puzzles.

That is why I wasn't sure if the picture represented an example of a puzzle underway, but incomplete, or if that was the initial set-up.
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From: lardarsegreg
2009-06-12 07:57 pm (UTC)
Question: is it possible to also have each ring of 6 cells that surround a "hole" 9where the 3 coloured lines are shown), as well as the implicit holes around the edge, contain the numbers 1-6?
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[User Picture]From: onigame
2009-06-19 08:48 am (UTC)
I don't think it is, although I'm not absolutely sure. This is the closest I've gotten:

      4   6   4
    1   5   2   5
      .   .   .
    2   3   1   3
  3   6   4   6   1
    x   .   .   x
  5   2   5   2   3
1   3   1   3   6   2
  .   .   .   .   .
6   4   6   4   1   5
  2   5   2   5   4
    x   .   .   x
  4   1   3   1   6
    5   4   6   4
      .   .   .
    6   2   5   2
      3   1   3
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