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Puzzle: a cube with Latin squares

  1. Jul 28, 2011 #1
    Imagine a cube wrapped in Latin squares and try to solve the following puzzles. Please be aware the symbols at the borders are shared between neighboring cube's sides.
    Let me know if you like it or not.

    This is rather straightforward:
    moderate_puzzle.png


    This is a bit harder
    hard_puzzle.png
     

    Attached Files:

  2. jcsd
  3. Aug 3, 2011 #2
    Here is the solution to the first one. I used the # symbol for the square, and the capital letter O for the circle. Highlight the text to see the solution.
    Code (Text):
    [color=black]
        #OX+
        X+O#
        O#+X
        +X#O
    #XO++X#OOX#+
    +OX##O+XXO+#
    X+#OO+X##+XO
    O#+XX#O++#OX
        X#O+
        +OX#
        #X+O
        O+#X
        O+#X
        X#+O
        +XO#
        #OX+
    [/color]
     
     
  4. Aug 3, 2011 #3
    Thank you for your interest (I'm really happy about it).
    Your solution is correct. Actually, that particular puzzle does not need a look-ahead; however the other one does.
    I found a number of these puzzles requiring several look-ahead points, those are really very difficult. I can post some of them if there is an interest.
     
  5. Aug 3, 2011 #4
    mioo, excellent puzzles, I hope you present more of the same or others.

    I followed Jimmy Snyder's lead and used # for the box and O for the circle. This is the solution to the second puzzle.


    ....x#+O
    ....+xO#
    ....#OX+
    ....O+#X
    x+#OO+#xX+#O
    +xO##xO++xO#
    #O+XXO+##O+X
    O#x++#XOO#x+
    ....+#XO
    ....xO+#
    ....#+Ox
    ....OX#+
    ....OX#+
    ....#+OX
    ....+Ox#
    ....x#+O


    In solving I use a truncated version of the puzzle where repeating lines are left out except the top and bottom line. This is the solution in the smaller form. An idea I found useful was to use hexadecimal numbers in the blank spaces to represent what was still possible there.
    x=8 #=4 +=2 O=1 . if a box contains a 6 only 4 or 2 are possible, 13 =8,4,1 and so on.
    for those unfamiliar with hexadecimal numbers they go 1 to 9 and then a,b,c,d,e,f and finally
    10=16. using these numbers the possibilities are always one character long. eg.13=d.

    ...x#+O
    ...+xO#
    ...#OX+
    x+#O+#x+#O
    +xO#xO+xO#
    #O+XO+#O+X
    O#x+#XO#x+
    ...xO+#
    ...#+Ox
    ...OX#+
    ...#+OX
    ...+Ox#
    ...x#+O


    thanks again mioo.

    mathal
     
  6. Aug 4, 2011 #5
    mathal, thank you, I'm very impressed by your approach to a solution. Thanks also for your nice words.
    The following two puzzles are more difficult. I'm posting also a plain text version with characters suggested by Jimmy Snyder.
    hard_1250.png
    Code (Text):

             . . . .
             . . O .
             . . . .
             . . . .

    . . . .  . . . .  . . . .
    . . . .  . . . .  . . . #
    . . . +  + . . .  . . X .
    . . . .  . . . .  . . . .

             . . . .
             . . . .
             . O . .
             . . . .

             . . . .
             . # . .
             . . + #
             . . . .
     
    extreme_puzzle.png
    Code (Text):

             . . # .
             . . . +
             . . . .
             . . . .

    . . . .  . . . .  . . + .
    . . . O  O . X .  . . . .
    . . . .  . + . .  . . . .
    . . . .  . . . .  . . . .

             . . . .
             . + . .
             . . . .
             . . . .

             . . . .
             . . . .
             . . X .
             . . # .

     
    I have even more difficult ones, still following a rule about a single solution.
    Good luck
     
  7. Aug 5, 2011 #6
    This is the solution to the first of these new 2. It appears that these puzzles are going to be more challenging- trying different 2 way choices to see if one side fails completely, and then likely ending in loops in the more difficult problems so that either path must be further split and tested. Anyway, I wrote a program yesterday, to deal with as much of the logical simplifications as I could. It will be added to.
    This is the solution to the first puzzle. I'll start on the extreme tomorrow. Thanks again.

    .... +O#X
    .... #XO+
    .... O+X#
    .... X#+O
    +#OX X#+O O#+X
    O+X# #+OX X+O#
    XO#+ +OX# #OX+
    #X+O OX#+ +X#O
    .... OX#+
    .... +#OX
    .... XO+#
    .... #+XO
    .... #+XO
    .... X#O+
    .... OX+#
    .... +O#X

    mathal
     
  8. Aug 5, 2011 #7
    The program I wrote yesterday does speed up the process quite a bit. This is the extreme cube solved. Keep making them harder (for me anyway). Do you have any other types of puzzles, mioo?
    mathal



    ....o+#x
    ....x#o+
    ....+o#x
    ____#x+o
    ox+##x+oo#+x
    +#xoo#x++xo#
    #+oxx+o##+xo
    xo#++o#xxo#+
    ....+o#x
    ....#+xo
    ....ox+#
    ____x#o+
    ....x#o+
    ....#x+o
    ....+ox#
    ....o+#x
     
  9. Aug 6, 2011 #8
    mathal, you are a great mind. Even there is a small mistake (on the 3'rd row), I can see you solved it, just swapped 2 symbols. I have to find something more difficult for you :)
    BTW, I will not catch a deadline with your ciphered text, nice puzzle...
     
  10. Aug 7, 2011 #9
    Thanks mioo. I haven't added a readable 'save' to my program so I just copied the lines using my eye on the screen and a not always dependable mind- Which is why I wrote the program.
    No one else has come up with the solution yet either- to my ciphered text. The second line deciphered is out today. The first line is an almost but not quite giveaway to the solution.
    I welcome any puzzles you have to offer.

    mathal
     
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