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 Post subject: My Avatar
PostPosted: Mon Aug 18, 2008 4:41 pm 
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I've been silently waiting for people to notice but it seems nobody picked up on the puzzle behind my avatar. Or all of you thought it was a Ludo board or something? :rambo:

Or perhaps most people here have been so used to using digits for Killers etc they forget the fundamental principle of the basic Sudoku and the symbolic representation of logic? :ugeek:

Anyway, I must admit this puzzle is not my own creation. But it's really a fascinating puzzle, and is of great value to many hardcore vanilla players (wink wink ;) Børge, enxio27). :alien:

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 Post subject: Re: My Avatar
PostPosted: Thu Aug 28, 2008 11:21 pm 
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Vanilla but not Plain Vanilla

I'd assumed that the arrows were directional consecutive and that each colour was a number, but I've not had the time to try that out.

T'man w'Hat


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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 1:51 am 
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Remapping
> as 1
Yellow as 2
Green as 3
Red as 4
Grey? as 5
Blue as 6
< as 7
v as 8
^ as 9

Yields a very difficult but solvable vanilla grid of ER 11.2

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


I'm sure knowing Matt there is more to it than that. :)

Compared to a Windoku only the corner group is disjoint. The other 8 windoku groups contain 1 repeated digit. Applying that rule makes it much easier to solve but I'm sure it's a red herring.

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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 2:19 am 
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udosuk wrote:
I've been silently waiting for people to notice but it seems nobody picked up on the puzzle behind my avatar. Or all of you thought it was a Ludo board or something? :rambo:

Or perhaps most people here have been so used to using digits for Killers etc they forget the fundamental principle of the basic Sudoku and the symbolic representation of logic? :ugeek:

Anyway, I must admit this puzzle is not my own creation. But it's really a fascinating puzzle, and is of great value to many hardcore vanilla players (wink wink ;) Børge, enxio27). :alien:


Ok, I admit it didn't look like a standard sudoku to me (combo of disjoint and non-consecutive?), and knowing your penchant for off-the-wall puzzles, I just left it alone. :lol:

So tell us about the puzzle. . .


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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 3:34 am 
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Like Glyn described it is a plain vanilla sudoku with an Explainer Rating of 11.2 (hence I posted this thread here).

This would normally implies that a bunch of forcing chains/nets are needed to crack it.

However, given the information that it has a unique solution and the observation of a very special thing about the puzzle allow the player to solve it much more easily. :ugeek:

Once in a while we encounter a puzzle which enlightens us to learn some brilliant new tricks. This is one such example.

I'm sorry I'm quite busy these days to post much. But given some more "fun time" in the future I'll explain in more details. Or would other experts do it for me before that? ;)

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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 8:52 pm 
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I should have recognised this one :doh: as I gave the penultimate step when solving it using symmetry on the Players' Forum.

This is a reflection about column 5 of a reduced form of the Mauricio 37 clue grid. The 5's are removed from Boxes 1,3,7 and 9.

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


The cool thing is Matt's use of the arrow symbols for the corners giving a clue to the transformation of digits under a 90 degree rotation that was used to solve the 37 clue version.

The cycles are {>,v,<,^} and {Green,Blue,Red,Yellow}. Grey transforms to Grey.
Numerically shifting the start point rather than relabelling the cycles are {6,7,8,9} and {1,2,3,4} with 5 transforming to itself.

Now to look for a Uniqueness trick rather than the forcing chain RW used there, and which I assume Matt has found. :applause:

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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 10:22 pm 
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Glyn wrote:
Now to look for a Uniqueness trick rather than the forcing chain RW used there, and which I assume Matt has found. :applause:


Boy, sounds as though this one is beyond my skill level! :pallid:


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 Post subject: Re: My Avatar
PostPosted: Fri Aug 29, 2008 10:47 pm 
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Glyn wrote:
Now to look for a Uniqueness trick rather than the forcing chain RW used there, and which I assume Matt has found. :applause:
I think there is a way to do it without chains, but I haven't formulated it too well (yet). Give me some time, or let's work at it together! :dance:

Note that 2 different sets of symmetry-based moves can be applied here - 90 degrees rotation and 180 degrees rotation.

Also note that all symmetry-based moves are also uniqueness-based. If uniqueness is not established it's not logically correct to apply any symmetry-based analysis. :idea:


enxio27 wrote:
Boy, sounds as though this one is beyond my skill level! :pallid:
Nothing is beyond your "skill level", unless you lost all your learning power/heart. :ugeek:

For me hard puzzles are those requiring deep levels of hypothetical analysis (i.e. "Ruudiculous-level" or those with 3.0-4.0 rating), without any alternative. If there are shortcuts to get to the solution (with sound logic of course) then the puzzle becomes an easy one, and everyone can do it (with proper learning).

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 Post subject: Re: My Avatar
PostPosted: Sat Aug 30, 2008 9:54 am 
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enxio27

These are the forcing moves that RW used translated to this shape of the puzzle.

If r2c4=9 => r4c8=6,r8c6=7,r6c2=8 (using symmetry)
=> r3c4=7 => r3c2=6 => r3c1=4 => r1c8=4
No place for a 7 in column 8. => r2c4<>9

If r2c6=9 => r6c8=6,r8c4=7,r4c2=8 (using symmetry)
=> r2c4=6 => r3c4=1 => r1c7=1
=> r4c8=7 => r2c7=7 => r4c7=2 => r8c7=8
No candidate left for r8c6 => r2c6<>9

Therefore r3c4=9,r4c7=6,r7c6=7,r6c3=8 (using symmetry)

Then singles.

The symmetry made it much simpler than the spaghetti that Sudoku Explainer needed to draw for every step of its conventional solution though it still a forcing net.

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 Post subject: Re: My Avatar
PostPosted: Sat Aug 30, 2008 7:11 pm 
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udosuk wrote:
enxio27 wrote:
Boy, sounds as though this one is beyond my skill level! :pallid:
Nothing is beyond your "skill level", unless you lost all your learning power/heart. :ugeek:

Not learning power or heart, just limited time to get into new techniques enough to grasp them. I'm still working on XY-wings right now. ;)


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