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Posers and Puzzles

Posers and Puzzles

  1. 25 Nov '09 23:56
    I came across this site
    http://www.tile-puzzler.com/unsolved_mysteries.asp

    I see number 5351 has never been solved and has been on there since May

    First one to solve it wins!
  2. Standard member TheMaster37
    Kupikupopo!
    26 Nov '09 10:39
    Originally posted by iamatiger
    I came across this site
    http://www.tile-puzzler.com/unsolved_mysteries.asp

    I see number 5351 has never been solved and has been on there since May

    First one to solve it wins!
    I've tried, but it looks impossible to me. Are you supposed to fill the target region completely?
  3. 26 Nov '09 15:40
    Originally posted by TheMaster37
    I've tried, but it looks impossible to me. Are you supposed to fill the target region completely?
    It is an overlapping one.

    See under "Overlap Puzzlers" here:

    http://www.tile-puzzler.com/instructions.asp
  4. Standard member TheMaster37
    Kupikupopo!
    27 Nov '09 11:58
    Originally posted by lausey
    It is an overlapping one.

    See under "Overlap Puzzlers" here:

    http://www.tile-puzzler.com/instructions.asp
    Yes, I was that far. I didn't see a rule about filling the entire field.
  5. 28 Nov '09 17:21
    Originally posted by TheMaster37
    Yes, I was that far. I didn't see a rule about filling the entire field.
    I think if you can fit them all in you will win, whether or not they fit the area.

    But I also suspect that the designer would have designed it to tile exactly, remember that tiles of identical colour can overlay.

    Ok, first one to solve it or prove it is impossible wins.
  6. 28 Nov '09 18:19
    Originally posted by iamatiger
    I think if you can fit them all in you will win, whether or not they fit the area.
    Having done some of the others on this site now (but not this one yet), I think you have to fill the space. You don't have to use all the shapes, but in a well-designed puzzle it'll be necessary.
  7. Subscriber AThousandYoung
    It's about respect
    28 Nov '09 23:19
    When I realized the pieces were connected to other pieces AND that they could overlap I gave up.

    However now I'm having some new thoughts...

    Are all the groups of pieces the same size? All fit in a 4x4 area for example? Hmm.
  8. 29 Nov '09 13:53
    Originally posted by AThousandYoung
    When I realized the pieces were connected to other pieces AND that they could overlap I gave up.

    However now I'm having some new thoughts...

    Are all the groups of pieces the same size? All fit in a 4x4 area for example? Hmm.
    The all fit in a 5x5 area, and if they are all to be used there has to be some significant overlapping.

    I'm in the process of writing a perl program to solve this puzzle, but it is tricky.
  9. 02 Dec '09 22:51
    Kerching!
  10. 03 Dec '09 23:13
    Originally posted by mtthw
    Kerching!
    Wow, nice one! How did you do it?
  11. 04 Dec '09 10:40 / 1 edit
    Originally posted by iamatiger
    Wow, nice one! How did you do it?
    Brute force . I read your previous note and thought writing a program to do it would be interesting.

    (I had tried several times to solve it without help, but never got very far).

    Incidentally, my program did first find a solution that fits all the shapes in and does not fill the shape. That wasn't accepted, so it's definitely filling the shape that is required to solve the problem.
  12. 04 Dec '09 21:02 / 2 edits
    Originally posted by mtthw
    Brute force . I read your previous note and thought writing a program to do it would be interesting.

    (I had tried several times to solve it without help, but never got very far).

    Incidentally, my program did first find a solution that fits all the shapes in and does not fill the shape. That wasn't accepted, so it's definitely filling the shape that is required to solve the problem.
    Well, nice programming!

    I think I might have tried to be a bit too optimal with my approach, I'm trying to keep track of the number of ways each shape can fit in, and the number of shapes that can fit over each uncovered square, and recursively search by placing the shape which can fit in the least positions or which covers a square that that fewest other shapes can cover, and I'm rather tangled up in pointers as a result.
  13. 06 Dec '09 12:50 / 1 edit
    Yeah, I tried to avoid being too clever with mine - thought I'd worry about optimising if I found it was taking too long to solve it.

    The heart of the program is a function that takes a list of shapes to put into the grid. It takes the first shape, tries all possible positions for that shape, and for those positions that fit it calls the same function recursively with a list of the remaining shapes.

    It looked like this (in Java). Sorry about the lack of indenting. Hopefully it makes sense.

    private boolean solveNext(List<Shape> remainingShapes) {
    if (remainingShapes.isEmpty()) {
    // No more shapes to fit, have we filled the grid?
    return layout.isComplete();
    }

    Shape shape = remainingShapes.remove(0);

    for (Shape subShape : shape.getCongruentShapes()) {
    for (int x = 0; x <= layout.getWidth() - subShape.getWidth(); ++x) {
    for (int y = 0; y <= layout.getHeight() - subShape.getHeight(); ++y) {
    if (layout.shapeFits(subShape, x, y)) {
    layout.addShape(subShape, x, y);
    List<Shape> restOfShapes = new LinkedList<Shape>(remainingShapes);
    boolean restFit = solveNext(restOfShapes);
    if (restFit) {
    // Wahay! Problem solved
    return true;
    }
    else {
    // Not possible in this position - remove and carry on
    layout.removeShape(subShape);
    }
    }
    }
    }
    }
    return false;
    }
  14. Subscriber sonhouse
    Fast and Curious
    10 Dec '09 13:45
    Originally posted by mtthw
    Yeah, I tried to avoid being too clever with mine - thought I'd worry about optimising if I found it was taking too long to solve it.

    The heart of the program is a function that takes a list of shapes to put into the grid. It takes the first shape, tries all possible positions for that shape, and for those positions that fit it calls the same function recu ...[text shortened]... layout.removeShape(subShape);
    }
    }
    }
    }
    }
    return false;
    }
    So do we have any results of your work yet? If so, can that program be modified for a general overlapping piece puzzle solution? Good job BTW.
  15. 10 Dec '09 19:17
    I am now wondering about a reverse program: One that would let me make a nice picture out of coloured tiles, and would find the hardest legal puzzle that it was the answer to.