Apart From Guessing - How to proceed?

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Apart From Guessing - How to proceed?

Postby suzette » Wed Feb 22, 2006 7:30 am

Hi! All,

I am now trying on a diabolical level puzzle, and got stuck at a stage. The hint given says "Either candidate for R1C9 forces 4 into R2C8".

I think this involves guessing, right? I don't think I can be checking every single cells this way, as I won't be able to see the relationship between R1C9 and R2C8 easily.

Is there any other way/lead that I can solve this without guessing? Or, am I missing something simple here (I often find things I missed out are very easily identified!!!).

Original Puzzle:
Code: Select all
. 7 . | . . . | . . .
9 . . | . 2 5 | . . 7
. . 6 | 7 8 4 | . . .
------+-------+------
1 3 . | . . . | 2 7 .
. 4 7 | . . . | . 5 .
. 8 9 | . . . | . 3 6
------+-------+------
. . . | 8 4 9 | 7 . .
7 . . | 1 6 . | . . 4
. . . | . . . | . 1 .


Stuck at:
Code: Select all
48 7   248 | 9 1 3 | 568 2468 25
9  1   348 | 6 2 5 | 38  48   7
35 25  6   | 7 8 4 | 19  29   1239
-----------+-------+-------------
1  3   5   | 4 9 6 | 2   7    8
6  4   7   | 2 3 8 | 19  5    19
2  8   9   | 5 7 1 | 4   3    6
-----------+-------+-------------
35 26  1   | 8 4 9 | 7   26   35
7  59  38  | 1 6 2 | 35  89   4
48 269 248 | 3 5 7 | 68  1    29
suzette
 
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Postby vidarino » Wed Feb 22, 2006 8:34 am

No need to guess.:)

There is an XYZ-Wing in the lower-left box. Consider the 26 and 269 in column 2, plus the 29 in R9C9;
- If R9C9=9, then you'd have a naked pair of 26 in the box, which would make some eliminations, including the 2 in R9C3.
- If R9C9=2, you'd *also* be able to eliminate 2 from R9C3.

So, R9C3<>2 no matter what, and the rest should come naturally from there.:)

Vidar
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Re: Apart From Guessing - How to proceed?

Postby emm » Wed Feb 22, 2006 10:49 am

suzette wrote:The hint given says "Either candidate for R1C9 forces 4 into R2C8". I think this involves guessing, right?

The chains that explain this are

r1c9=2 => r9c9=9 => r8c8=8 => r2c8=4

r1c9=5 => r7c9=3 => r8c7=5 => r8c2=9 => r8c8=8 => r2c8=4

This is not guessing - either option for r1c9 => r2c8=4
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Postby emm » Wed Feb 22, 2006 11:04 am

Another option is the uniqueness technique which cuts a few corners.

There's a unique rectangle at r3c79 and r5c79. The numbers 1,9 share two rows, two columns, and two boxes in those 4 cells and therefore the puzzle could have two solutions - the 1s and 9s could just be switched over to get a second solution. Since we assume the puzzle has only one solution you can remove the 1,9 from the cell that has other candidates ie r3c9 = 23

Then r3c7 = 1 and its just singles from there.
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Re: Apart From Guessing - How to proceed?

Postby Auguste » Wed Feb 22, 2006 4:30 pm

suzette wrote:
Code: Select all
48 7   248 | 9 1 3 | 568 2468 25
9  1   348 | 6 2 5 | 38  48   7
35 25  6   | 7 8 4 | 19  29   1239
-----------+-------+-------------
1  3   5   | 4 9 6 | 2   7    8
6  4   7   | 2 3 8 | 19  5    19
2  8   9   | 5 7 1 | 4   3    6
-----------+-------+-------------
35 26  1   | 8 4 9 | 7   26   35
7  59  38  | 1 6 2 | 35  89   4
48 269 248 | 3 5 7 | 68  1    29

Code: Select all
48 7    248 | 9 1 3 | 568 2468  25
9  1    348 | 6 2 5 | 38  48    7
35 *25  6   | 7 8 4 | 19  *29   1239
------------+-------+--------------
1  3    5   | 4 9 6 | 2   7     8
6  4    7   | 2 3 8 | 19  5     19
2  8    9   | 5 7 1 | 4   3     6
------------+-------+--------------
35 26   1   | 8 4 9 | 7   26    35
7  *59  38  | 1 6 2 | 35  89    4
48 269  248 | 3 5 7 | 68  1     29

the three cells marked with * make a xy-wing leading to
the elimination of 9 in r8c8.
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Postby tarek » Thu Feb 23, 2006 12:16 am

There are some finned fishes attacking r1c8, however the xy wing is still needed:D

Tarek
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Re: Apart From Guessing - How to proceed?

Postby suzette » Thu Feb 23, 2006 2:10 am

Thanks all for the leads. I think I still need to brush up on those techniques! Very useful!

BTW,
em wrote:The chains that explain this are

r1c9=2 => r9c9=9 => r8c8=8 => r2c8=4

r1c9=5 => r7c9=3 => r8c7=5 => r8c2=9 => r8c8=8 => r2c8=4

This is not guessing - either option for r1c9 => r2c8=4


What I meant by 'guessing' is, you won't know which cell(s) to look for the chain unless you start checking one by one, right? That would be too time consuming, wouldn't it? Or, do you have techniques to identify some cells are 'suspecious' that you would start checking its chain?
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Postby absolute beginner » Sun Feb 26, 2006 11:05 pm

how did you get rid of the 3 in r3c7 and the 9 in r9c7?
I always get 139 in r3c7 and 689 in r9c7
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Postby absolute beginner » Sun Feb 26, 2006 11:14 pm

ok, I can see the 3:
rc3c7 = 3 => r2c3 = 3 => r7c1 = 3 => o position for 3 in the
right lower block

but I don't see a solution for 9 in r9c7
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Postby emm » Mon Feb 27, 2006 6:37 am

Code: Select all
*-----------------------------------------------------------*
 | 48    7     248   | 9     1     3     | 568   2468  25    |
 | 9     1     348   | 6     2     5     | 38    48    7     |
 | 35*   25    6     | 7     8     4     | 139   29    1239* |
 |-------------------+-------------------+-------------------|
 | 1     3     5     | 4     9     6     | 2     7     8     |
 | 6     4     7     | 2     3     8     | 19    5     19    |
 | 2     8     9     | 5     7     1     | 4     3     6     |
 |-------------------+-------------------+-------------------|
 | 35*   26    1     | 8     4     9     | 7     26    35*  |
 | 7     59    38    | 1     6     2     | 35    89    4     |
 | 48    269   248   | 3     5     7     | 689   1     29    |
 *-----------------------------------------------------------*


The 3 at r3c7 can be eliminated because of the Xwing of 3s marked *

This leaves a naked pair 19 in column 6 which removes the 9 from r9c7

Do you understand these terms? If not click on Simple Sudoku.
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Postby absolute beginner » Mon Feb 27, 2006 10:16 pm

Thank you!
I didn't know the terms and the link was very usefull.
But the naked pair was primitive, I should have seen it.
My program for solving had a problem - i corrected it
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