One for the X'mas - Mystery Symbols Sudoku

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One for the X'mas - Mystery Symbols Sudoku

Postby simon_blow_snow » Sun Dec 26, 2010 2:02 pm

Merry Christmas all! 8-)

Mystery Symbols Sudoku

Image

Note: this is a straight forward paper solvable Sudoku puzzle (with a simple variant rule, which can be written as a simple sentence).

Note 2: If there was any regional constraint (e.g. diagonals, windows) required to solve the puzzle I would have shown them explicitly. Players shouldn't need to guess the variant rule from thin air.

I will not reveal too much for now but I hope the smart players here will not need any of the extra spoilers and will have solved this by the time I come back a few days after Boxing Day! ;-)
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby David P Bird » Thu Dec 30, 2010 11:55 pm

I can't work out the icons, but using numbers I suggest:
Hidden Text: Show
Code: Select all
123|456|789
564|897|231
978|312|645
---+---+---
897|231|564
312|645|978
456|789|123
---+---+---
645|978|312
789|123|456
231|564|897

This is a form of the most canonical grid so two possible additional rules are:
a) Each box has identical row and column candidate sets
b) The cell sets having the same positions in each box hold one of each digit
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby simon_blow_snow » Fri Dec 31, 2010 11:11 am

David, thanks for trying. I thought this was a very simple puzzle. There is only one simple additional rule, but unfortunately none of you has managed to pick it up.

I don't want to drag this into the new year, so here I will reveal the answer:

The grid is a standard Sudoku grid made up of 9 different symbols. Each symbol has 2 attributes:

1. Square structure: 1-square/2-squares/3x3-squares

2. X structure: no-X/small-X/large-X

To solve the puzzle, you need a very simple extra rule, which can be spotted from the initial givens:

Neighbours have different attributes.

For example, R2C5 is a single square with a small X, so its 4 neighbours, R13C5 and R2C46, must be either 2 squares or 3x3 squares with no X or a large X, as demonstrated in 2 of the initial givens.

With this rule the unique solution should be very easily solved.
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby David P Bird » Fri Dec 31, 2010 1:22 pm

Simon, OK I see how you developed your icons now, but I think I deserve a small modicum of credit.

Your icon attributes can be translated into digits by saying:
Code: Select all
Attribute A:  One Square = 0,   Two Squares = 1,  Nine Squares = 2 
Attribute B:  No X       = 1,   Small X     = 4,  Large X      = 7 
Digit = A + B
If you now compose your grid using digits you'll find that it is the same pattern mine but with the digits renumbered – that is it is a form of the most canonical grid which is derived from a double latin square - the basis of your design.

It would be interesting to see if you can find more than one solution to your puzzle using either of my alternative extra rules in place of yours. I believe they all represent properties of the MC grid and amount to the same thing.

BTW Thanks for the challenge!
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby simon_blow_snow » Fri Dec 31, 2010 3:33 pm

David, even if you apply both of your 2 rules, as well as the "double latin square" concept (which, by the way, has an official name called "Euler Square"), you will still reach no fewer than two solutions:

Code: Select all
+-------+-------+-------+
| 2 6 7 | 5 9 1 | 8 3 4 |
| 9 1 5 | 3 4 8 | 6 7 2 |
| 4 8 3 | 7 2 6 | 1 5 9 |
+-------+-------+-------+
| 3 4 8 | 6 7 2 | 9 1 5 |
| 7 2 6 | 1 5 9 | 4 8 3 |
| 5 9 1 | 8 3 4 | 2 6 7 |
+-------+-------+-------+
| 1 5 9 | 4 8 3 | 7 2 6 |
| 8 3 4 | 2 6 7 | 5 9 1 |
| 6 7 2 | 9 1 5 | 3 4 8 |
+-------+-------+-------+

+-------+-------+-------+
| 8 3 4 | 5 9 1 | 7 2 6 |
| 6 7 2 | 3 4 8 | 5 9 1 |
| 1 5 9 | 7 2 6 | 3 4 8 |
+-------+-------+-------+
| 3 4 8 | 6 7 2 | 9 1 5 |
| 7 2 6 | 1 5 9 | 4 8 3 |
| 5 9 1 | 8 3 4 | 2 6 7 |
+-------+-------+-------+
| 2 6 7 | 4 8 3 | 1 5 9 |
| 9 1 5 | 2 6 7 | 8 3 4 |
| 4 8 3 | 9 1 5 | 6 7 2 |
+-------+-------+-------+


So no, one can only reach a unique solution from my initial givens using my rule, which is also much simpler and easier to describe than any rule proposed by you or other solvers (in other forums).

But you certainly do deserve some credit for being the only player in this webspace to be gutsy enough to try it. Other members don't even have any heart to start it! ;-)
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby David P Bird » Fri Dec 31, 2010 8:22 pm

Simon – yes you're right, my rules do give two possibilities compared to the one of yours. It's because yours works across the edge connections for the corner boxes – something that, like your attributes, went right over my head. Consequently you puzzle is cannier than I gave it credit for!
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Re: One for the X'mas - Mystery Symbols Sudoku

Postby simon_blow_snow » Sat Jan 01, 2011 5:26 am

To officially close the topic, here is the unique solution image for this puzzle:

Unique solution image: Show
Image


Happy New Year to all reading this thread! :-D
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