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h3lix
 Post subject: Embedded Grid Killer
PostPosted: Thu May 13, 2010 1:08 am 
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There is a 4x4 sudoku grid embedded within this 9x9 killer. The embedded grid is made up of all the blue cells (R2468C2468), and behaves as a normal 4x4 sudoku grid (numbers 1-4, 2x2 blocks).

Image

3x3::k:6400:6400:2:3:4:5:6:5127:5127:6400:6400:6411:3596:3596:3596:5153:5127:5127:18:6411:6411:2581:22:23:5153:5153:26:27:2332:6411:2581:4639:32:5153:3618:35:36:2332:38:39:4639:41:42:3618:44:45:2332:7727:48:4639:1586:5957:3618:53:54:7727:7727:57:58:1586:5957:5957:62:5439:5439:7727:3394:3394:3394:5957:5190:5190:5439:5439:74:75:76:77:78:5190:5190:

I'd place the difficulty around MEDIUM, there are a few tricks to get started, but it's fairly straightforward.

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Last edited by h3lix on Thu May 13, 2010 6:55 pm, edited 1 time in total.

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Afmob
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PostPosted: Thu May 13, 2010 7:43 am 
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Thanks for this interesting Killer variant!

Solution:
6 7 2 5 1 8 3 9 4
8 4 5 2 9 3 7 1 6
1 9 3 7 4 6 2 5 8
5 1 8 3 7 2 6 4 9
3 6 4 8 5 9 1 7 2
7 2 9 4 6 1 8 3 5
2 8 7 9 3 5 4 6 1
9 3 6 1 8 4 5 2 7
4 5 1 6 2 7 9 8 3

Like you said, it was pretty straightforward. It might be even solvable without using the candidates grid, I'll give it a try later.
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Ed
 Post subject: Re: Embedded Grid Killer
PostPosted: Thu May 13, 2010 9:32 am 
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Welcome h3lix!

I can't seem to finish it off and get to here. What am I missing? Must be something to do with the embedded grid. Blind. Thanks.
Hidden Text: 
.-------------------------------.-------------------------------.-------------------------------.
| 6         7         2         | 5         1         8         | 3         9         4         |
| 8         4         5         | 2         9         3         | 7         1         6         |
| 1         9         3         | 67        4         67        | 2         5         8         |
:-------------------------------+-------------------------------+-------------------------------:
| 5         1         8         | 34        7         2         | 6         34        9         |
| 3         6         4         | 8         5         9         | 1         7         2         |
| 7         2         9         | 34        6         1         | 8         34        5         |
:-------------------------------+-------------------------------+-------------------------------:
| 2         8         7         | 9         3         5         | 4         6         1         |
| 9         3         6         | 1         8         4         | 5         2         7         |
| 4         5         1         | 67        2         67        | 9         8         3         |
'-------------------------------.-------------------------------.-------------------------------'

Cheers
Ed
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HATMAN
 Post subject: Re: Embedded Grid Killer
PostPosted: Thu May 13, 2010 9:35 am 
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Dan

I solved it and then I looked at expanding the constraint:
1-9: 1276 solutions
1-8: 236
1-7: 50
1-6:6
1-5:2
1-4:2
with this second solution

+-------+-------+-------+
| 6 7 2 | 5 1 8 | 3 9 4 |
| 8 4 5 | 2 9 3 | 7 1 6 |
| 1 9 3 | 6 4 7 | 2 5 8 |
+-------+-------+-------+
| 5 1 8 | 4 7 2 | 6 3 9 |
| 3 6 4 | 8 5 9 | 1 7 2 |
| 7 2 9 | 3 6 1 | 8 4 5 |
+-------+-------+-------+
| 2 8 7 | 9 3 5 | 4 6 1 |
| 9 3 6 | 1 8 4 | 5 2 7 |
| 4 5 1 | 7 2 6 | 9 8 3 |
+-------+-------+-------+
please check for my error?

Maurice
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Afmob
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PostPosted: Thu May 13, 2010 11:08 am 
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Here is what you both are missing:

Spoiler?:
In a 4*4 grid there are four 2*2 blocks where no number can repeat (itself?). Therefore R24C24 must have all numbers of {1234}. So HATMAN's second "solution" is wrong since R2C2 = 4 = R4C4 which is not allowed.

It was a bit confusing that h3lix didn't explictly tell that it is a 4*4 grid with four 2*2 blocks since it could have also been a latin square of size 4 (with four 1*4 and four 4*1 blocks) which would imply two solutions. I think the best way to define a grid is by telling the size of the blocks, so in this case 2*2 Sudoku.
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h3lix
 Post subject: Re: Embedded Grid Killer
PostPosted: Thu May 13, 2010 2:14 pm 
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Thanks Afmob, my apologies for not explaining that clearly. The embedded grid has quadrants.

That's an interesting method for expanding the constraint. I'll experiment and see what else I can do with this variant.

Thanks Ed! It's good to be back.

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Børge
PostPosted: Thu May 13, 2010 3:08 pm 
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Image with udosuk Style Killer Cages:
Image

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Andrew
 Post subject: Re: Embedded Grid Killer
PostPosted: Thu May 13, 2010 5:00 pm 
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I also reached Ed's diagram yesterday evening and was going to check this morning to see whether I'd made a mistake or missed something.

I'd clearly paid more attention to "The embedded grid is made up of all the blue cells (R2468C2468), and behaves as a normal 4x4 grid (numbers 1-4)" and not realised the full implication of the earlier "There is a 4x4 sudoku grid embedded within this 9x9 killer".

As has already been stated, if it's just a normal 4x4 grid then there are two solutions; if it's a 4x4 sudoku grid then there's a unique solution and the solving path would be different and probably shorter. Mine had lots of naked quads and naked quints.

Børge's diagram was an interesting way to colour the cage pattern and emphasise the 4x4 grid. In my Excel worksheet I just coloured the cages and only put candidates 1,2,3,4 in the 4x4 grid.
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h3lix
 Post subject: Re: Embedded Grid Killer
PostPosted: Thu May 13, 2010 6:53 pm 
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The naked quads and quints were a product of the embedded grid and most of my layout was based on them. The quadrant restraint didn't really have much of an impact until the end, so I'm sure our solve paths are very similar.

You may have found an easier starting move, here's how I started

Opening move:
Conflicting combinations in N7 with cage 21/4 and 30/4: 21/4 can only be {3459}

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