- #1
Puzzle: a cube with Latin squares
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Discussion Overview
The discussion revolves around puzzles involving a cube wrapped in Latin squares, focusing on solving these puzzles and sharing solutions. Participants explore various strategies and approaches to tackle the challenges presented by the puzzles, with some puzzles being described as straightforward while others are noted to be more difficult and requiring advanced techniques.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants express enjoyment and interest in the puzzles, with one participant offering to post more challenging versions.
- A participant shares a solution to the first puzzle, using specific symbols to represent elements of the puzzle.
- Another participant describes a method involving hexadecimal numbers to represent possibilities in the puzzle, suggesting a unique approach to solving it.
- There is mention of the need for look-ahead strategies in solving the more difficult puzzles, indicating varying levels of complexity.
- One participant notes the use of a program to assist in solving the puzzles, highlighting the computational aspect of the problem-solving process.
- Participants acknowledge minor errors in each other's solutions, indicating an ongoing refinement of their approaches.
- There is a request for more challenging puzzles, reflecting a desire for continued engagement with the topic.
Areas of Agreement / Disagreement
Participants generally agree on the enjoyment of the puzzles and the correctness of some solutions, but there are multiple competing views on the best methods for solving the more complex puzzles. The discussion remains unresolved regarding the optimal strategies and the difficulty levels of the puzzles.
Contextual Notes
Some solutions involve assumptions about the symbols used and the methods of representation, which may not be universally understood. The complexity of the puzzles varies, and certain strategies may depend on individual interpretations of the rules.
Who May Find This Useful
Individuals interested in logic puzzles, mathematical reasoning, and problem-solving techniques may find this discussion engaging and informative.
- #2
Jimmy Snyder
- 1,137
- 21
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:
#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]- #3
mioo
- 4
- 0
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.
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.
- #4
mathal
- 77
- 0
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
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
- #5
mioo
- 4
- 0
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.
I have even more difficult ones, still following a rule about a single solution.
Good luck
The following two puzzles are more difficult. I'm posting also a plain text version with characters suggested by Jimmy Snyder.
Code:
. . . .
. . O .
. . . .
. . . .
. . . . . . . . . . . .
. . . . . . . . . . . #
. . . + + . . . . . X .
. . . . . . . . . . . .
. . . .
. . . .
. O . .
. . . .
. . . .
. # . .
. . + #
. . . .
Code:
. . # .
. . . +
. . . .
. . . .
. . . . . . . . . . + .
. . . O O . X . . . . .
. . . . . + . . . . . .
. . . . . . . . . . . .
. . . .
. + . .
. . . .
. . . .
. . . .
. . . .
. . X .
. . # .Good luck
- #6
mathal
- 77
- 0
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
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
- #7
mathal
- 77
- 0
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
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
- #8
mioo
- 4
- 0
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...
BTW, I will not catch a deadline with your ciphered text, nice puzzle...
- #9
mathal
- 77
- 0
mioo said:
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