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Outlaw from last week

 
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CougChaos



Joined: 03 Apr 2007
Posts: 2

PostPosted: Mon Apr 09, 2007 2:45 pm    Post subject: Outlaw from last week Reply with quote

I don't have it handy but I was wondering about one of the outlaws from last week(April 3rd probably). I think I saved a copy of it but I don't recall where... Smile

In any event I 'solved' it with an educated guess or at least I think it was.

I had solved the puzzle up to the point where it got complicated... then I noticed in the top row that there appeared to be 4 squares that had a quad. However it wasn't a quad because those squares also had other numbers. My educated guess was that in the first row there was only 4 squares where each of the 4 numbers could go. Which meant that the rest could be eliminated. Doing this basically removed the guess that was required to solve the puzzle in another part(If I recall it was a guess where a 2 went into the first box.). Was I just lucky or would this approach work?
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GreenLantern



Joined: 23 Nov 2006
Posts: 91

PostPosted: Mon Apr 09, 2007 9:22 pm    Post subject: Reply with quote

What you are describing is known as a Hidden Quad. If there are only four squares in a unit that 4 different digits appear in, then any other digit in those four squares can be immediately removed. So, you did not guess at all. Good job solving the outlaw. They're pretty tough!
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CougChaos



Joined: 03 Apr 2007
Posts: 2

PostPosted: Tue Apr 10, 2007 9:09 pm    Post subject: Reply with quote

Here was the puzzle:

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

My candidate list for the first row was:
(24678)|1|(2Cool|(457)|3|(4Cool|9|(456)|(2456)

Looking at it now I think did it this way
I was looking at 456 and nearly had a triple. However I couldn't eliminate the 7. Adding the 7 to my group gave me the quad(added 1 new square and allowed me to use the common square.) This solved the 2 and 8 and made the rest easy. If that's a hidden quad then I'm happy and I'm eager to see if I can get it to work again(I still haven't mastered the nice loops/colouring yet though.)
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GreenLantern



Joined: 23 Nov 2006
Posts: 91

PostPosted: Wed Apr 11, 2007 2:38 am    Post subject: Reply with quote

Now that I see more details, I can see that this is not a Hidden Quad at all since you actually have 4 digits in 5 cells (there's a '4' in r1c6). However, the Naked Quad in Box 2 leads to immediate eliminations in r1c3 and r2c5.

It's helpful when posting puzzles to the forum to also include a Candidates Grid in addition to the original puzzle grid. To do this, press the Import/Export button, and then the Export candidates button and copy and paste the text in the window into your post. You should also put "code" tags around the grid to preserve the fixed width formatting. For details on how to do this, see this link.

For example, in your Outlaw, this is the Candidates Grid after some basic techniques have been applied:

Code:
+-------------------------+-------------------------+-------------------------+
| 24678   1       28      | 57      3       48      | 9       456     256     |
| 467     467     39      | 2       57      149     | 8       1456    1356    |
| 248     5       39      | 49      1489    6       | 13      7       123     |
+-------------------------+-------------------------+-------------------------+
| 23589   238     1       | 6       279     239     | 4       589     35789   |
| 349     34      7       | 8       149     5       | 2       169     1369    |
| 234589  2348    6       | 3479    12479   12349   | 1357    1589    135789  |
+-------------------------+-------------------------+-------------------------+
| 2678    9       28      | 1       2458    248     | 567     3       4578    |
| 12368   2368    4       | 359     2589    7       | 156     1589    1589    |
| 1378    378     5       | 349     6       3489    | 17      2       14789   |
+-------------------------+-------------------------+-------------------------+


In this position, the SDXP hint system gives a Multicoloring elimination as the next step. If you have any questions about Coloring, Nice Loops, or any other technique, Paul's Sudoku Solving Guide is a very useful reference, or you can just ask here in the forum.
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