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

Posted: Sat Sep 03, 2005 7:23 pm Post subject: September 3, 2005 


Samgj called this puzzle "hard," but I thought it qualified for a "very hard" rating.
I was getting nowhere until I noticed the XWing formation in rows 6 and 7, on the number 1. After that things started falling into place.
Did anyone notice a simpler way to solve this particular puzzle? dcb
PS I just got Linux (SuSE 9.3) up and running on my dualboot machine. This is my first post as a Linux user. I stayed up too late getting that done ... maybe I'm just a bit tired. 

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Guest

Posted: Sat Sep 03, 2005 8:53 pm Post subject: 


I struggled with this one, and on checking with the sudoku drawer it rated it as very hard. I got it to work, but not sure how. I have yet to understand some of the terminology used, so cannot help in how I solved it.
Great website, I am thoroughly addicted. 

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

Posted: Sat Sep 03, 2005 11:29 pm Post subject: 


It would seem that the gradings MAY be set by reference to the need to
use particular computeroriented techniques (eg the so called methods A
through F). I find that I can solve the "very hard" examples fairly
consistently but I get stuck on the 'Medium' examples.
This seems to be a difference of approach. I use TWO solution grids and
put the contents of these in the cells. The standard grid (123456789 with
impossibilities removed) is at top left and the second grid at bottom left.
Thus, I like to use the LARGE print!!
The second grid consists of marks where a particular number MUST be in
one of two places within a block of nine (ie the other seven cells have
been excluded). The virtue of this is that when a cell containing values
of the second grid is resolved to a different number, it is IMMEDIATELY
possible to resolve the cell containing the paired item, (eg if value 6 must
be in A1 or C3 and value 7 must be in A1 or B3 then resolving A1 leads
immediately to the resolution of C3 and B3  unless the value in A1 is
either 6 or 7, in which case the new information is the removal of the
pair mark and the usual removal of a possible value in the standard grid).
My methodology is to mark up the pairs first using "look and see" logic
working primarily on groups of three blocks in a rectangle (eg the first
three columns for nine rows). This process is used on the three column
groups, then the three row groups and then all rows/columns with six
or more resolutions are inspected. Then this process is repeated in
greater detail (the first scan is relatively superficial).
Where the pairs are in a horizontal or vertical line, the existence of a
third entry of the same number in the row/column leads to some good
"new" information and a resolution. This is much easier to spot than the
search for combinations in the more complex rules (eg trying to find an
example of F is wearying on a manual scan but fairly clear using the
secondary grid).
Having exhausted the two scans and row/column checks (plus the
consistency of each block), I then revert to the standard method of
determining the remaining possibilities. However the second grid can
assist in eliminating what would otherwise look like feasible numbers.
Very often this will split a row/column into two groups (eg 56,56 and
78,89,79 by shewing say 567 in the first cell to be impossible as the third
and fifth cells form a pair. If 567 were possible then there would be one
big group 56789 rather than two subgroups 56 and 789).
Any cells resolved, I mark by a circled number as otherwise the chart
looks like a veritable mass of numbers.
Can anyone else point me to ways of solution that do not depend on
eagleeyed spotting of patterns in the way that computers would approach
the solution grid? I marvel at people who can hold vast arays of helpful
information in shortterm memory in order to resolve a cell. Am I unusual
in needing a lot of "aidememoire" marks?
Alan Rayner BS23 2QT 

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chobans
Joined: 21 Aug 2005 Posts: 39

Posted: Sun Sep 04, 2005 3:09 am Post subject: Re: September 3, 2005 


David Bryant wrote:  Samgj called this puzzle "hard," but I thought it qualified for a "very hard" rating.
I was getting nowhere until I noticed the XWing formation in rows 6 and 7, on the number 1. After that things started falling into place.
Did anyone notice a simpler way to solve this particular puzzle? dcb 
I didn't have to use any XWing formation to solve this one. Just a simple methods and I was able to solve it. So I think you probably missed one crucial step somewhere. If you retrace it and then post the grid where you got stuck at then maybe that'll better help to understand what the problem was. 

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geoff h
Joined: 07 Aug 2005 Posts: 58 Location: Sydney

Posted: Sun Sep 04, 2005 6:34 am Post subject: 3 September Puzzle 


Yes, I agree with previous  I didn't really find this puzzle difficult.
The key was identifying the 4's in r1c1 and r1c3  these were the only possibilities for Nr4 in Row 1. Therefore, you could exclude the remainder of the 4s in the first block. The puzzle is easily solvable from there.
Cheers. 

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

Posted: Sun Sep 04, 2005 7:35 pm Post subject: Re: 3 September Puzzle 


geoff h wrote:  Yes, I agree with previous  I didn't really find this puzzle difficult.
The key was identifying the 4's in r1c1 and r1c3  these were the only possibilities for Nr4 in Row 1. Therefore, you could exclude the remainder of the 4s in the first block. The puzzle is easily solvable from there.
Cheers. 
Thanks, Geoff! You put your finger on my mental block.
I had in fact noticed that the "4" in the first row had to go in either r1c1 or in r1c3, since those two cells are the only candidates for a "4" in the first row  see the grid below. But then I failed to make the connection that immediately allows one to place a "5" in r2c1. Duh!!! :oops:
Anyway, here's as far as I got before resorting to the "XWing" to complete this puzzle:
Code: 
4/5/7 9 3/4/5 2/3/5 2/3/5 8 1 6 2/5/7
4/5 3/4/5/8 1 7 2/3/5/6/9 3/4/5/6/9 4/5/9 2/4/8/9 2/5/8
2 4/5/7/8 *6* 5/9 1 4/5/9 4/5/7/9 4/7/8/9 3
3 1/2/5/7 8 4 2/5/9 1/5/9 5/7/9 1/7/9 6
1/4/5/7 1/4/5/7 9 3/5/6/8 3/5/6/8 1/3/5/6 2 1/3/5/7 1/5/7
6 x1/2/5x 2/5 2/3/5/9 2/3/5/9 7 8 x1/3/9x 4
8 x1/2/3/5x 2/3/5 3/5/6 4 3/5/6 3/7 x1/2/3/7x 9
1/4/5/9 1/3/4/5 3/4/5 3/5/8/9 *7* 2 6 1/2/3/4/8 1/8
4/9 6 7 1 3/8/9 3/9 3/4 5 2/8

The two values I had managed to locate at this point are marked with * in the grid above  the four cells representing the "XWing" are marked with the letter x. I proceeded as follows  since the value "1" must either appear in r6c2 and in r7c8, or else in r7c3 and in r6c8, one can eliminate the other possible "1"s in columns 2 and 8 to arrive at the following grid.
Code: 
4/5/7 9 3/4/5 2/3/5 2/3/5 8 1 6 2/5/7
4/5 3/4/5/8 1 7 2/3/5/6/9 3/4/5/6/9 4/5/9 2/4/8/9 2/5/8
2 4/5/7/8 *6* 5/9 1 4/5/9 4/5/7/9 4/7/8/9 3
3 2/5/7 8 4 2/5/9 1/5/9 5/7/9 7/9 6
1/4/5/7 4/5/7 9 3/5/6/8 3/5/6/8 1/3/5/6 2 3/5/7 1/5/7
6 x1/2/5x 2/5 2/3/5/9 2/3/5/9 7 8 x1/3/9x 4
8 x1/2/3/5x 2/3/5 3/5/6 4 3/5/6 3/7 x1/2/3/7x 9
1/4/5/9 3/4/5 3/4/5 3/5/8/9 *7* 2 6 2/3/4/8 1/8
4/9 6 7 1 3/8/9 3/9 3/4 5 2/8

In this grid it's immediately obvious that r4c6=1, since that's the only cell in row 4 that can contain the value "1". And it's possible to solve the puzzle with this additional number  that's how I did it the other day.
What Geoff has pointed out is that I should have been looking at the upper left corner, like this:
Code: 
4/7 9 3/4 2/3/5 2/3/5 8 1 6 2/5/7
5 3/8 1 7 2/3/6/9 3/4/6/9 4/9 2/4/8/9 2/8
2 7/8 *6* 5/9 1 4/5/9 4/5/7/9 4/7/8/9 3
3 1/2/5/7 8 4 2/5/9 1/5/9 5/7/9 1/7/9 6
1/4/7 1/4/5/7 9 3/5/6/8 3/5/6/8 1/3/5/6 2 1/3/5/7 1/5/7
6 1/2/5 2/5 2/3/5/9 2/3/5/9 7 8 1/3/9 4
8 1/2/3/5 2/3/5 3/5/6 4 3/5/6 3/7 1/2/3/7 9
1/4/9 1/3/4/5 3/4/5 3/5/8/9 *7* 2 6 1/2/3/4/8 1/8
4/9 6 7 1 3/8/9 3/9 3/4 5 2/8

This second method is clearly much simpler  the next move (a "1" in r8c9) pops out once one recognizes the {2,8} pair in r2c9 and r9c9. dcb :shock:
PS Interestingly, when I applied Geoff's insight to rework this puzzle I found that the pair of "1"s that are part of the XWing formation I had relied on earlier popped up almost immediately  that is to say that Geoff's method and mine led to almost the same solution pathway, except that his was a lot easier to notice than mine was. 

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Guest Too Guest

Posted: Thu Sep 08, 2005 5:46 am Post subject: 


Anonymous wrote:  I struggled with this one, and on checking with the sudoku drawer it rated it as very hard. I got it to work, but not sure how. I have yet to understand some of the terminology used, so cannot help in how I solved it.
Great website, I am thoroughly addicted. 
I manage to do Sudokus from several sources without knowing or understanding any of the complicated names that people refer to. The explanations seem to often make it unecessarily more complicated and confusing. Just follow straight forward logic! When I get stuck I put it down, and later on, on a fresh look it is apparent where the mental block was! Usually obviious and quite uncomplicated. 

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Guest

Posted: Sat Sep 17, 2005 6:41 am Post subject: 


You could've cleaned up the 9th row while you were filling out your code.
#2 can ONLY go in row nine, column nine (Pretty obvious if you look strictly at the structure of the ninth row.)
. . . which in turn means that #8 can ONLY go in row nine, column five.
Do that, and you'll find out that things will go MUCH easier with the puzzle.
BTW. . . I thought this puzzle was tougher than the 94 "very hard" puzzle. 

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