This is a hard one

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This is a hard one

Postby ohanian » Sun May 21, 2006 7:55 am

This sudoku is quite hard.

Code: Select all
 
  1 0 0   0 7 0   0 0 5
  0 2 0   0 0 0   0 6 0
  0 0 3   0 0 0   4 0 0
 
  0 0 0   4 0 3   0 0 0
  6 0 0   0 5 0   0 0 4
  0 0 0   2 0 6   0 0 0
 
  0 0 9   0 0 0   7 0 0
  0 1 0   0 0 0   0 8 0
  7 0 0   0 3 0   0 0 9
 
*-----------*
|1..|.7.|..5|
|.2.|...|.6.|
|..3|...|4..|
|---+---+---|
|...|4.3|...|
|6..|.5.|..4|
|...|2.6|...|
|---+---+---|
|..9|...|7..|
|.1.|...|.8.|
|7..|.3.|..9|
*-----------*

ohanian
 
Posts: 2
Joined: 20 May 2006

Postby Sped » Sun May 21, 2006 12:36 pm

Code: Select all
 *-----------*
 |1..|.7.|..5|
 |.2.|...|.6.|
 |..3|...|4..|
 |---+---+---|
 |...|4.3|...|
 |6..|.5.|..4|
 |...|2.6|...|
 |---+---+---|
 |..9|...|7..|
 |.1.|...|.8.|
 |7..|.3.|..9|
 *-----------*


This is another invalid puzzle, as it has multiple solutions. Simple Sudoku says "too many solutions to count"

One of the solution paths takes us here:
Code: Select all
 *-----------------------------------------*
 | 1   4   6   | 3   7   2   | 8   9   5   |
 | 9   2   5   | 8   4   1   | 3   6   7   |
 | 8   7   3   | 9   6   5   | 4   1   2   |
 |-------------+-------------+-------------|
 | 2   9   7   | 4   8   3   | 1   5   6   |
 | 6   8   1   | 7   5   9   | 2   3   4   |
 | 35  35  4   | 2   1   6   | 9   7   8   |
 |-------------+-------------+-------------|
 | 35  35  9   | 6   2   8   | 7   4   1   |
 | 4   1   2   | 5   9   7   | 6   8   3   |
 | 7   6   8   | 1   3   4   | 5   2   9   |
 *-----------------------------------------*


The puzzle is almost finished, but look in r6c1, r6c2, r7c1 and r7c2. Those four cells are all 3,5 and occupy 2 rows, 2 columns, and 2 boxes. That's a deadly pattern.

The puzzle can be solved two ways from there:

Code: Select all
 
 *-----------*
 |146|372|895|
 |925|841|367|
 |873|965|412|
 |---+---+---|
 |297|483|156|
 |681|759|234|
 |354|216|978|
 |---+---+---|
 |539|628|741|
 |412|597|683|
 |768|134|529|
 *-----------*
 and
 *-----------*
 |146|372|895|
 |925|841|367|
 |873|965|412|
 |---+---+---|
 |297|483|156|
 |681|759|234|
 |534|216|978|
 |---+---+---|
 |359|628|741|
 |412|597|683|
 |768|134|529|
 *-----------*


Whenever you see a deadly pattern like that you will know the puzzle has multiple solutions. If you can safely assume that there is a unique solution then you can sometimes make exclusions based on the knowledge that a deadly pattern cannot be there.

See "Unique Rectangles"
Sped
 
Posts: 126
Joined: 26 March 2006

Re: This is a hard one

Postby JPF » Sun May 21, 2006 1:12 pm

ohanian wrote:This sudoku is quite hard.
Code: Select all
*-----------*
|1..|.7.|..5|
|.2.|...|.6.|
|..3|...|4..|
|---+---+---|
|...|4.3|...|
|6..|.5.|..4|
|...|2.6|...|
|---+---+---|
|..9|...|7..|
|.1.|...|.8.|
|7..|.3.|..9|
*-----------*

Sped wrote:This is another invalid puzzle, as it has multiple solutions. Simple Sudoku says "too many solutions to count"

Try this one.
Easy, but valid...
Code: Select all
 1 . . | . 7 . | . . 6
 . 2 . | . . . | . 4 .
 . . 3 | . . . | 8 . .
-------+-------+-------
 . . . | 4 . 2 | . . .
 6 . . | . 5 . | . . 1
 . . . | 8 . 6 | . . .
-------+-------+-------
 . . 8 | . . . | 4 . .
 . 3 . | . . . | . 2 .
 7 . . | . 9 . | . . 5



JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France


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