YAVH (Yet Another Very Hard)

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YAVH (Yet Another Very Hard)

Postby shakers » Tue Apr 26, 2005 12:59 pm

I'm finding the 'Very Hard's quite frustrating - the majority I'm solving in about 40 mins, but every now and again there are some which still stump me!

Can some kind soul please put me out of misery with this one...
Code: Select all
      | 1 3   |     2
  5 3 | 2   7 | 8 9 
      |       |     3
----------------------
2 8   |     6 | 9   
5   4 |   2   | 1   
    9 | 5     |   2 7
----------------------
9     |       |     
    5 | 4     |   7 9
3     |   9 1 |     


Many thanks...
shakers
 
Posts: 93
Joined: 10 March 2005

Postby Animator » Tue Apr 26, 2005 1:05 pm

Can you repost your puzzle? and use * or . for empty cells (a space is rather confusing)
Animator
 
Posts: 469
Joined: 08 April 2005

Postby shakers » Tue Apr 26, 2005 1:14 pm

Animator wrote:Can you repost your puzzle? and use * or . for empty cells (a space is rather confusing)


Certainly; although it's never presented a problem before when I've posted the numbers aligned properly in columns using the code tag. Each to their own, I guess.

Code: Select all
* * * | 1 3 * | * * 2
* 5 3 | 2 * 7 | 8 9 *
* * * | * * * | * * 3
----------------------
2 8 * | * * 6 | 9 * *
5 * 4 | * 2 * | 1 * *
* * 9 | 5 * * | * 2 7
----------------------
9 * * | * * * | * * *
* * 5 | 4 * * | * 7 9
3 * * | * 9 1 | * * *     
shakers
 
Posts: 93
Joined: 10 March 2005

Postby Sue De Coq » Tue Apr 26, 2005 1:21 pm

Here's a reposted puzzle with dots in place (though personally I didn't have a problem with the original):

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


Here's some solver analysis:

The value 1 in Box [3,1] must lie in Row 8.
The value 4 in Box [1,1] must lie in Column 1.
The value 5 in Box [3,3] must lie in Row 9.
The value 7 in Box [1,1] must lie in Column 1.
The value 8 in Box [2,2] must lie in Row 6.
The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.
The cell (7,5) is the only candidate for the value 7 in Column 5.

I think it's safe to ignore the first four observations for immediate purposes. Once we've restricted the position of the 8 in Box 5, we observe that the value 7 can't occupy the cell r4c5, which leaves just a single candidate position in Column 5.

The first four observations help to solve the remainder of the puzzle - which should be very straightforward from here.
Sue De Coq
 
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Joined: 01 April 2005

Postby shakers » Tue Apr 26, 2005 1:40 pm

Sue De Coq wrote:
The value 1 in Box [3,1] must lie in Row 8.
The value 4 in Box [1,1] must lie in Column 1.
The value 5 in Box [3,3] must lie in Row 9.
The value 7 in Box [1,1] must lie in Column 1.
The value 8 in Box [2,2] must lie in Row 6.
The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.
The cell (7,5) is the only candidate for the value 7 in Column 5.

I think it's safe to ignore the first four observations for immediate purposes. Once we've restricted the position of the 8 in Box 5, we observe that the value 7 can't occupy the cell r4c5, which leaves just a single candidate position in Column 5.


Thanks for that - I had already considered the first four points, so it all fell into place very quickly after that.

Just looking at box 5 again, I have the minimum pencilmarks as follows:
(4,4) = 3 7
(4,5) = 1 4 7
(5,4) = 3 7 9
(5,7) = 3 9
(6,5) = 1 4 8
(6,6) = 3 4 8
and am trying to work out the general rule to describe how we know that "The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order" to make sure I don't miss this sort of thing again...
shakers
 
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Joined: 10 March 2005

Postby Guest » Tue Apr 26, 2005 3:10 pm

It's a little easier (to me at least), to note that 3,7 & 9 are the only candidates for (4,4), (5,4) & (5,7) - thus eliminating these digits from the other cells...

So, the general rule is "when N cells have only N candidates between them, those N candidates may be eliminated from the other cells in the unit". N is 3 in this case. This is what's come to be known as Milo's rule 2.
Guest
 

Postby Doc » Wed Apr 27, 2005 9:42 am

Sue De Coq wrote:Here's some solver analysis:

The value 1 in Box [3,1] must lie in Row 8.
The value 4 in Box [1,1] must lie in Column 1.
The value 5 in Box [3,3] must lie in Row 9.
The value 7 in Box [1,1] must lie in Column 1.
The value 8 in Box [2,2] must lie in Row 6.
The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.
The cell (7,5) is the only candidate for the value 7 in Column 5.



I'm fairly new to this, although having some success, but am confused by the above.

Why must the value 1 in Box [3,1] lie in Row 8? There is also a candidate in row 9.
Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

I'll start with those two for now - I'm obviously missing something!

Thanks in advance,

Chris.
Doc
 
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Joined: 27 April 2005

Postby shakers » Wed Apr 27, 2005 10:10 am

Doc wrote:
Sue De Coq wrote:Here's some solver analysis:

The value 1 in Box [3,1] must lie in Row 8.
The value 4 in Box [1,1] must lie in Column 1.
The value 5 in Box [3,3] must lie in Row 9.
The value 7 in Box [1,1] must lie in Column 1.
The value 8 in Box [2,2] must lie in Row 6.
The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.
The cell (7,5) is the only candidate for the value 7 in Column 5.



Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

I'll start with those two for now - I'm obviously missing something!


I don't have the fully pencilmarked puzzle to hand, but... If you look at where 4 could go in column 1, it should only appear in box 1 (albeit in two cells). This means you can eliminate the possible 4s from column 2 in box 1.

Applying this logic should, if I recall, explain the first five statements in the original post.
shakers
 
Posts: 93
Joined: 10 March 2005

Postby Doc » Wed Apr 27, 2005 10:22 am

Thanks, Shakers.

I live and learn in the Sudoku world!

With that new bit of logic, and x-wings under my belt, things should all start making a bit more sense.

Cheers,

Chris.
Doc
 
Posts: 2
Joined: 27 April 2005

Postby Guest » Wed Apr 27, 2005 10:41 am

Doc wrote:
Sue De Coq wrote:Here's some solver analysis:

The value 1 in Box [3,1] must lie in Row 8.
The value 4 in Box [1,1] must lie in Column 1.
The value 5 in Box [3,3] must lie in Row 9.
The value 7 in Box [1,1] must lie in Column 1.
The value 8 in Box [2,2] must lie in Row 6.
The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.
The cell (7,5) is the only candidate for the value 7 in Column 5.



I'm fairly new to this, although having some success, but am confused by the above.

Why must the value 1 in Box [3,1] lie in Row 8? There is also a candidate in row 9.
Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

I'll start with those two for now - I'm obviously missing something!

Thanks in advance,

Chris.



The basics are; that each Box,Row and Column, contain the numbers 1-9.

We see that there is already a 1 in Row 9, cell(9,6) in the original starting grid, this precludes a value of 1 appearing any where else on Row 9.
Comparing where the value 1 can be placed in Boxes [3,1][3,3] should help you.

As for the number 4 in Column 1-Look to the basics.
Guest
 

Solution

Postby Guest » Wed May 11, 2005 4:34 pm

It took me ages, but here is the solution...

If you want to try to work it out yourself don't look at the grid below, but put in a 1 in col 3, row 4. This was an either / or 1 for that box and I had to take a leap of faith to get it all to work out.





896 134 752
453 267 891
712 859 643

281 746 935
574 923 168
639 518 427

948 375 216
165 482 379
327 691 584
Guest
 

Postby Animator » Wed May 11, 2005 6:15 pm

Euhm, does that mean you guessed a number? as in, filled in one you weren't 100% sure of?

Since that is something you shouldn't do...
Animator
 
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