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Louise56
Joined: 21 Sep 2005 Posts: 94 Location: El Cajon, California USA

Posted: Sun Oct 16, 2005 3:25 am Post subject: Oct 16 puzzle question 


I'm trying to solve this one and have a question for one of you experts. These are my bottom three, 3x3 boxes
// 359/2/1 389//6
9/6/ 35/7/358 //4
//1 4/6/3589 389/7/238
My question is with the 9's. In row 7 I have a 9 in r7c4 and r7c7. In row 9 I have a 9 in r9c6 and r9c7. These are the only 9's in rows 6 and 9. It looks like an Xwing set up, but in the middle box the 9's are not in the same column. But since they are in the same 3x3 box, it seems like I could treat this like an xwing, but I don't know if I can eliminate the remaining 9's in column 4 or column 6. Does this setup have a name? Thanks! 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Sun Oct 16, 2005 5:30 am Post subject: 


Hi Louise,
That was real a nice question!
I was working a lot on Xwing.
You made a nice discovery. The Xwing that has the same number at intersection of 2 rows and 2 columns (the name cames from the airplains flying in this formation) and having this same number ONLY 2 times in the rows or in the columns  permits us to eliminate the rest of this number from the 2 columns respective 2 rows (if there are any additional such ones).
I think that one of the "generalization" of this Xwing is the technique called "intersectioon of four groups". It is the combination of 4 intersection rows, columns, 3x3 blocks.
* If we have 2 rows and 2 columns  then we speak about the "Xwing".
The other cases are:
* 2 rows, 1 column & 1 block
* 1 row, 2 columns & 1 block
* 2 rows, 2 blocks
* 2 columns, 2 blocks
Let's take an example:
XX
6=6======
XX
=== the sign "=" means no "6"
==6
6==
XX
XX
XX
We have here number 6:
 in row 2 exact twice
 in column 1 exact twice
 in column 3 exact twice
 in 3x3 block (4,1)  (6,3) exact twice
We have the same number 6 at the intersection of four groups:
one row, 2 columns and 1 3X3 block.
We can quickly deduce that from all places marked with "X" the "6" can be eliminated!
For the rest of the cases, I let you draw your own diagrams.
see u, 

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zigzagpython
Joined: 27 Sep 2005 Posts: 4

Posted: Sun Oct 16, 2005 8:02 am Post subject: 


still not understand!!!!
I spent nearly an hour on the sheet
only found 1 in r6c2, 9 in r1c9 and most easily 6 in r8c2
then move no step
help me Mater 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Sun Oct 16, 2005 8:10 am Post subject: 


Hi,
Please post me the initial position.
see u, 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Sun Oct 16, 2005 8:18 am Post subject: 


Hi,
Sorry, now I see which puzzle you have problem with.
080016700
600030005
100890000
320000500
006000200
008000097
000021006
900070004
001460070
6 in r8c2  Unique Horizontal
4 not in r4c6, it is in r4c5 or r5c5 or r6c5 (Column on 3x3 Block interaction)
4 not in r5c6, it is in r4c5 or r5c5 or r6c5 (Column on 3x3 Block interaction)
4 not in r6c6, it is in r4c5 or r5c5 or r6c5 (Column on 3x3 Block interaction)
5 not in r5c4, it is in r5c5 or r6c5 (Column on 3x3 Block interaction)
5 not in r5c6, it is in r5c5 or r6c5 (Column on 3x3 Block interaction)
5 not in r6c4, it is in r5c5 or r6c5 (Column on 3x3 Block interaction)
5 not in r6c6, it is in r5c5 or r6c5 (Column on 3x3 Block interaction)
8 not in r4c6, it is in r4c5 or r5c5 (Column on 3x3 Block interaction)
8 not in r5c6, it is in r4c5 or r5c5 (Column on 3x3 Block interaction)
1 not in r4c8, it is in r4c9 or r5c9 (Column on 3x3 Block interaction)
1 not in r5c8, it is in r4c9 or r5c9 (Column on 3x3 Block interaction)
1 not in r6c7, it is in r4c9 or r5c9 (Column on 3x3 Block interaction)
2 not in r2c8, Hidden Pair 1 8 in r2c7 and r2c8 (in Row)
4 not in r2c7, Hidden Pair 1 8 in r2c7 and r2c8 (in Row)
4 not in r2c8, Hidden Pair 1 8 in r2c7 and r2c8 (in Row)
9 not in r2c7, Hidden Pair 1 8 in r2c7 and r2c8 (in Row)
4 not in r6c2, Nacked Pair 4 5 in r6c1 and r6c5 (same Row)
5 not in r6c2, Nacked Pair 4 5 in r6c1 and r6c5 (same Row)
4 not in r6c7, Nacked Pair 4 5 in r6c1 and r6c5 (same Row)
1 in r6c2  Sole Candidate
and from here on, you can swim alone...
see u, 

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zigzagpython
Joined: 27 Sep 2005 Posts: 4

Posted: Sun Oct 16, 2005 9:44 am Post subject: 


thx for yr tips
'5' in either r4c5 or r5c5
'1' in eihter r4c9 or r5c9
they are important tips and main numbers blocking my going
need more training la
but next week will be very busy.
loads work and have a test from my part time studying in the coming weeks:cry:
got little bit injury from yesterday's rugby match.
see you master 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Sun Oct 16, 2005 2:52 pm Post subject: Here's another tip 


zigzagpython wrote:  thx for yr tips
'5' in either r4c5 or r5c5
'1' in eihter r4c9 or r5c9
they are important tips and main numbers blocking my going

This is a _very_ tough puzzle. Here's what I found that let me solve it.
In column 9, "1" can only appear in r4c9 or r5c9. So we can eliminate "1" from r4c8, r5c8, & r6c7.
Because of the {4, 5} pair in row 6, the "4" in column 8 must lie in the middle right 3x3 box  that is, in r4c8 or r5c8. Now there is an "XWing" on "4"  in r2c6, r3c6, r2c7, & r3c7. So we can eliminate other possible "4"s in rows 2 & 3.
That's probably enough of a hint for now. dcb 

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junior Guest

Posted: Sun Oct 16, 2005 4:59 pm Post subject: Re: Here's another tip 


David Bryant wrote:  zigzagpython wrote:  thx for yr tips
'5' in either r4c5 or r5c5
'1' in eihter r4c9 or r5c9
they are important tips and main numbers blocking my going

This is a _very_ tough puzzle. Here's what I found that let me solve it.
In column 9, "1" can only appear in r4c9 or r5c9. So we can eliminate "1" from r4c8, r5c8, & r6c7.
Because of the {4, 5} pair in row 6, the "4" in column 8 must lie in the middle right 3x3 box  that is, in r4c8 or r5c8. Now there is an "XWing" on "4"  in r2c6, r3c6, r2c7, & r3c7. So we can eliminate other possible "4"s in rows 2 & 3.
That's probably enough of a hint for now. dcb 
I can't see the Xwing on "4". I only see the naked couple [1,8] in r2c6 and r2c7 and the naked couple [4,5] in r6c1 and r6c5, so 4 becomes the sole candidate for r3c7. Am I wrong? 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Sun Oct 16, 2005 5:28 pm Post subject: Re: Here's another tip 


Junior wrote:  I can't see the Xwing on "4". I only see the naked couple [1,8] in r2c6 and r2c7 and the naked couple [4,5] in r6c1 and r6c5, so 4 becomes the sole candidate for r3c7. Am I wrong? 
No, you're not wrong. "4" in r3c7 is correct. But I think you may be forgetting the {4, 5, 8} triplet that must appear in column 5, in the middle center 3x3 box. Since there's a "4" at r9c4, that triplet tells you that the "4" in column 6 must go either at r2c6 or at r3c6  hence at r2c6, since you already have the "4" at r3c7, somehow. dcb 

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Louise56
Joined: 21 Sep 2005 Posts: 94 Location: El Cajon, California USA

Posted: Sun Oct 16, 2005 6:18 pm Post subject: 


Thanks Someone for an excellent explanation. This was my favorite puzzle to date! I'm always looking for patterns and shortcuts. 

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scorpio56xxl
Joined: 16 Oct 2005 Posts: 7 Location: Bonn, Germany

Posted: Sun Oct 16, 2005 7:14 pm Post subject: 


Hi Louise,
I have the same problem as you but I come to another conclusion. Since
in r3c5 there is a nine so there could not be one in r4c5  r6c5. So the nines in the middle box goes in r4c4/r5c4 and r4c6/r5c6. Box number 8 and 9 the last one contains possible nines as you described. So there couldn't be a nine in r9c9. Since there is a nine in box 7 which intersects r9, box 6 which intersects c9 and an intersection between the boxes 8 and 9 the nine for the last column must be placed in r1c9. But I could't see that you can eleminate the nines in the middle box. I 'm looking forward to getting your answer. Thanks in advance. 

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Louise56
Joined: 21 Sep 2005 Posts: 94 Location: El Cajon, California USA

Posted: Mon Oct 17, 2005 12:22 am Post subject: 


Hi Scorpio,
I don't remember all the steps I took to solve the puzzle. I do remember finding a 7/9 pair in r4c6 and r5c6 and that helped me to elimate the 9 in r9c6. That put a 9 in r7c4 and a 9 in r9c7. I hope that helps! 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Mon Oct 17, 2005 7:29 pm Post subject: "Nishio" worked on this puzzle 


Louise56 wrote:  Thanks Someone for an excellent explanation. This was my favorite puzzle to date! I'm always looking for patterns and shortcuts. 
I thought this was an excellent puzzle. Interestingly, I spotted a "Nishio" pattern at a very early stage, and I'm wondering if anyone else noticed it.
After entering a "6" at r8c2 and a "1" at r6c2 the puzzle looked like this to me:
Code: 
. 8 . . 1 6 7 . 9
6 . . . 3 4? 4? . 5
1 . . 8 9 4? 4? 6 1/8
3 2 . . 4/8 7/9 5 . .
. . 6 . . . 2 . .
4/5 1 8 . 4/5 2/3 3/6 9 7
. . . . 2 1 . . 6
9 6 . 3/5 7 . . . 4
. . 1 4 6 . . 7 . 
I'm not very good at spotting "hidden pairs." But because of the {4, 5, 8} triplet in r4c5, r5c5, & r6c5, plus the {3, 6} pair at r6c7, it was apparent that the "4"s in columns 6 and 7 had to appear in the little square marked 4? above. This meant I could eliminate the possibility of a "4" in r2c2, r2c3, r2c4, r3c2, & r3c3. After doing that I found a triplet {2, 7, 9} in row 2, and that uncovered the "hidden pair" in the top right 3x3 box. It also let me enter a few more numbers in the top right region of the puzzle. Now my grid looked like this:
Code: 
2/4/5 8 . . 1 6 7 2/3 9
6 7/9 2/7/9 2/7 3 4 1/8 1/8 5
1 . . 8 9 . 4 6 2/3
3 2 . . 4/8 7/9 5 . 1/8
. . 6 . 4/5/8 3/7/9 2 . 1/3/8
4/5 1 8 . 4/5 2/3 3/6 9 7
. . . . 2 1 . . 6
9 6 2? 3/5 7 . . 2? 4
2/5/8 . 1 4 6 . . 7 2/3/8 
This was when I spotted the "Nishio" pattern. Clearly there are only two places to put a "2" in column 1, and in column 9. You have to look more closely, but it's also clear that there are only two places to put a "2" in the top right, the bottom left, and the bottom right 3x3 boxes. The chain of connected "2"s makes the "Nishio" pattern.
Consider what would happen if r1c1 = 2. Then r9c1 is not 2, and r8c3 = 2. But then r8c8 is not 2, and r1c8 = 2. But this is impossible  we can't have two "2"s in the first row. So we must place "2" at r9c1, r8c8, and r3c9.
I've entered another puzzle that uses "Nishio" in the other puzzles forum, in case you're interested. dcb 

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alanr555
Joined: 01 Aug 2005 Posts: 194 Location: Bideford Devon EX39

Posted: Mon Oct 17, 2005 9:14 pm Post subject: Re: "Nishio" worked on this puzzle 


Code: 
> Interestingly, I spotted a "Nishio" pattern at a very early stage, and I'm
> wondering if anyone else noticed it.
2/4/5 8 . . 1 6 7 2/3 9
6 7/9 2/7/9 2/7 3 4 1/8 1/8 5
1 . . 8 9 . 4 6 2/3
3 2 . . 4/8 7/9 5 . 1/8
. . 6 . 4/5/8 3/7/9 2 . 1/3/8
4/5 1 8 . 4/5 2/3 3/6 9 7
. . . . 2 1 . . 6
9 6 2? 3/5 7 . . 2? 4
2/5/8 . 1 4 6 . . 7 2/3/8
> This was when I spotted the "Nishio" pattern.
Thank you for this explanation of "Nishio".
It would seem to add significance to my promotion of Mandatory Pairs
if I have understood the technique correctly.
Essentially I understand a "Nishio" to be a CLOSED chain of Mandatory
Pairs where the pairs can be in ANY region or line (row/column). The
values MUST toggle along the chain being alternately the value and not
the value. Thus the determination of ANY value within the chain will
immediately resolve half the members of the chain  BRILLIANT!
I solved this puzzle in just under an hour elapsed time after I retired to
bed about 00.30 local time on Monday morning. Often I fall asleep over
them but managed to complete this one. It was not amenable to a full
solution using Mandatory Pairs (cf my submission on that method) and
so I switched to candidate profiles after squeezing the information out
of the Mandatory Pairs data. However, I left such data present and found
that having done so was very useful later. I did not need any advanced
techniques other than finding congruent groups. (eg row 2 turned into
1/8 and 2/4/7/9 and row 6 into 1/4/5 and 2/3/6 and column 6 into 5/8
and 2/3/4/7/9). Success then depends upon finding an "entry" into the
congruent group to isolate one or more entries. Counting within a line
or a region is, of course, one form of entry. In this regard the quality
of "mutual reception" in Mandatory pairs makes "counting" much easier.
The rule about eliminating stragglers when all the occurrences of a
digit within a line are in one region (and vice versa) does not need any
searching with Mandatory Pairs as the pairs generally highlight such
anyway. This I find that M/P is an excellent prelude to the more detail
process of candidate profiling  making the latter MUCH easier in terms
of the tedious compilation involved.
Now that I have a comprehension of the Nishio, I can add it to the M/P
techniques and, hopefully, reduce solution times slightly. So thank you,
again, for clarifying the technique.
Alan Rayner BS23 2QT  [/code] 

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Blackfoot
Joined: 18 Oct 2005 Posts: 1

Posted: Tue Oct 18, 2005 2:49 pm Post subject: Re: "Nishio" worked on this puzzle 


David Bryant wrote: 
Code: 
. 8 . . 1 6 7 . 9
6 . . . 3 4? 4? . 5
1 . . 8 9 4? 4? 6 1/8
3 2 . . 4/8 7/9 5 . .
. . 6 . . . 2 . .
4/5 1 8 . 4/5 2/3 3/6 9 7
. . . . 2 1 . . 6
9 6 . 3/5 7 . . . 4
. . 1 4 6 . . 7 . 

I'm new to all this so forgive me.
I just don't see how you get the 1 in R6C2.
I see a 1 at R4C9 or R5C9
I see a 1 at R5C2 or R6C2
But I also see a 1 at R4C4,R5C4,R6C4.
The only this I can think is that I've missed something in R6C4.
Thanks in advance 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Tue Oct 18, 2005 3:28 pm Post subject: How to place the "1" at r6c2 


There's no need to apologize  all of us were new to this at some point.
Concentrate on row 6. With the {4, 5} pair placed in r6c1 and r6c5, there are only four numbers left  {1, 2, 3, 6}  to fill in the four open positions in the row (that is, the values {1, 2, 3, 6} must occupy the cells r6c2, r6c4, r6c6, & r6c7 in some order).
Now look at r6c2. It has to be a "1", a "2", a "3", or a "6." It clearly can't be either a "2" or a "6" because those values already appear in column 2. And it can't be a "3", either, because there's already a "3" in the middle left 3x3 box. So it has to be a "1." dcb
PS I have some trouble with this idea still  it's easy to eliminate possibilities by looking up and down columns, or left and right across rows. It's a bit harder to remember to look all around the 3x3 box for additional numbers that can safely be eliminated from a list of possibilities. One set of eye motions comes naturally  I have to work at the other one. Maybe crossed eyes would help! 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Tue Oct 18, 2005 3:53 pm Post subject: 


Hi,
just take a look again at the steps that I
Posted: Sun Oct 16, 2005 9:18 am
that should answer your question about placing the "1".
see u, 

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