## Apart From Guessing - How to proceed?

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### Apart From Guessing - How to proceed?

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    192  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

Posts: 5
Joined: 20 February 2006

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
vidarino

Posts: 295
Joined: 02 January 2006

### Re: Apart From Guessing - How to proceed?

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
emm

Posts: 987
Joined: 02 July 2005

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.
emm

Posts: 987
Joined: 02 July 2005

### Re: Apart From Guessing - How to proceed?

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    192  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     192  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.
Auguste

Posts: 1
Joined: 19 February 2006

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

Tarek

tarek

Posts: 2761
Joined: 05 January 2006

### Re: Apart From Guessing - How to proceed?

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?
suzette

Posts: 5
Joined: 20 February 2006

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
absolute beginner

Posts: 22
Joined: 26 February 2006

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
absolute beginner

Posts: 22
Joined: 26 February 2006

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.
emm

Posts: 987
Joined: 02 July 2005

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
absolute beginner

Posts: 22
Joined: 26 February 2006

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