The New Sudoku Players' Forum

[FEARDIZ]

Code: Select all

 *-----------*
 |6.4|.9.|...|
 |...|416|.5.|
 |.9.|..8|..3|
 |---+---+---|
 |...|...|5.4|
 |..3|...|1..|
 |9.2|...|...|
 |---+---+---|
 |2..|8..|.7.|
 |.8.|329|...|
 |...|.7.|3.8|
 *-----------*


 *-----------*
 |654|793|281|
 |328|416|759|
 |197|258|643|
 |---+---+---|
 |87.|..2|5.4|
 |543|.87|1.2|
 |9.2|...|8.7|
 |---+---+---|
 |23.|8..|97.|
 |78.|329|41.|
 |4.9|.7.|328|
 *-----------*

 
 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7   + 16   | 169  36   2    | 5    369  4    |
 | 5    4    3    | 69   8    7    | 1    69   2    |
 | 9    16   2    | 156  346  145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3    + 15   | 8    46   14   | 9    7    + 56   |
 | 7    8    56   | 3    2    9    | 4    1    56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*




why does this not work for xy wing
xy=R7c3 xz=r7c9 yz=r4c3

thanks
John[/code]

[Carcul]

Because you don't have any cell that see both r4c3 and r7c9, which is how XY-Wing works.
However, the puzzle can be easily solved using uniqueness (if you take one step back) or using the TILA.

Carcul

[re'born]

Incidentally, an easy solution from your grid:

Code: Select all

  *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169  36   2    | 5    369  4    |
 | 5    4    3    | 69   8    7    | 1    69   2    |
 | 9    16   2    | 156  346  145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3   *15   | 8    46   14   | 9    7   *56   |
 | 7    8   *56   | 3    2    9    | 4    1   *56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


is to note that r7c3=5 > r7c9 = 6 > r8c9 = 5 > r8c3 = 6, forming a deadly pattern. Therefore r7c3 = 1 and the puzzle solves with singles. It should be remarked that this reduction can be made earlier and it will still solve the puzzle. Using one naked pair and several singles you obtain the grid:

Code: Select all

 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169  36   2    | 5    369  4    |
 | 5    4    3    | 69   8    7    | 1    69   2    |
 | 9    16   2    | 156  346  145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3   *156  | 8    46   145  | 9    7   *56   |
 | 7    8   *56   | 3    2    9    | 4    1   *56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


From here the unique rectangle in r78c39 is easier to spot and we immediately set r7c3=1.

[Carcul]

Uniqueness easily solves this puzzle. However, if one don't want to use such an obvious deduction here is another possibility:

Code: Select all

 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169  36   2    | 5    369  4    |
 | 5    4    3    | 69   8    7    | 1    69   2    |
 | 9    16   2    | 156  346  145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3    156  | 8    46   145  | 9    7    56   |
 | 7    8    56   | 3    2    9    | 4    1    56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


=5=[r9c6]-5-[r9c4]=5=[r6c4]-{TILA(1): r7c3|r7c6|r6c6|r6c2|r4c3},
=> r9c6<>5 and it solve the puzzle.

Carcul

[FEARDIZ]

Because you don't have any cell that see both r4c3 and r7c9, which is how XY-Wing works.
However, the puzzle can be easily solved using uniqueness (if you take one step back) or using the TILA.

Carcul

doesn't using the 15 at xy=R7c3 see both r4c3 and r7c9

[Sped]

Code: Select all

 
 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169  36*  2    | 5   (3)69 4    |
 | 5    4    3    | 69*  8    7    | 1    69*  2    |
 | 9    16   2    | 156 (3)46 145  | 8    36*  7    |
 |----------------+----------------+----------------|
 | 2    3    15   | 8    46   14   | 9    7    56   |
 | 7    8    56   | 3    2    9    | 4    1    56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


6-(r4c3)-1-(r7c3)-5-(r7c9)-6

You've spotted an xy wing alright. It allows the exclusion of 6s in all cells that see both r4c3 and r7c9. Unfortunately there are no 6s to exclude in any of those cells.

Now, if you will consider a 4 cell xy chain, which is the same thing as an xy wing but one cell longer:

3-(r4c5)-6-(r5c4)-9-(r5c8)-6-(r6c8)-3

You can exclude 3s in all cells that see both r4c5 and r6c8. r4c8 and r6c5 lose their 3s.

In nice loop notation:

[r4c8]-3-[r4c5]-6-[r5c4]-9-[r5c8]-6-[r6c8]-3-[r4c8] => r4c8<>3
[r6c5]-3-[r6c8]-6-[r5c4]-9-[r5c8]-6-[r6c8]-3-[r6c5] => r6c5<>3

Code: Select all

 
 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169* 36   2    | 5    69*  4    |
 | 5    4    3    | 69*  8    7    | 1    69*  2    |
 | 9    16   2    | 156  46   145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3    15   | 8    46   14   | 9    7    56   |
 | 7    8    56   | 3    2    9    | 4    1    56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


Then there's an easy to spot unique rectangle in r45c4 and r45c8. To avoid a deadly pattern (all 4 cells = 69) r4c4 must be 1.

It's all singles from there.

Simple Sudoku used colors on 1 and 6 and a swordfish on 6 and then an xy wing to solve it. Both the xy chain and the UR are easy to see and save a lot of work compared with Simple Sudoku's way of doing things.

[FEARDIZ]

ok I see my problem I didn't know the exclude had to be buddies with BOTH xz and yz

[kdean63]

Please provide more details on this 'deadly pattern'. What's wrong with r7c3=5 > r7c9 = 6 > r8c9 = 5 > r8c3 = 6? Why can't each of these four cells be either 5 or 6? I don't see why r7c3 must be 1. thanks for some help on this.

is to note that r7c3=5 > r7c9 = 6 > r8c9 = 5 > r8c3 = 6, forming a deadly pattern. Therefore r7c3 = 1 and the puzzle solves with singles. It should be remarked that this reduction can be made earlier and it will still solve the puzzle. Using one naked pair and several singles you obtain the grid:

Code: Select all

 *--------------------------------------------------*
 | 6    5    4    | 7    9    3    | 2    8    1    |
 | 3    2    8    | 4    1    6    | 7    5    9    |
 | 1    9    7    | 2    5    8    | 6    4    3    |
 |----------------+----------------+----------------|
 | 8    7    16   | 169  36   2    | 5    369  4    |
 | 5    4    3    | 69   8    7    | 1    69   2    |
 | 9    16   2    | 156  346  145  | 8    36   7    |
 |----------------+----------------+----------------|
 | 2    3   *156  | 8    46   145  | 9    7   *56   |
 | 7    8   *56   | 3    2    9    | 4    1   *56   |
 | 4    16   9    | 156  7    15   | 3    2    8    |
 *--------------------------------------------------*


From here the unique rectangle in r78c39 is easier to spot and we immediately set r7c3=1.

[underquark]

Allowing:

Code: Select all

56     56
56     56

or any

Code: Select all

XY     XY
XY     XY

would lead to an abiguity over placement of X and Y such that the puzzle would no longer have a unique solution and violate the usual rules of Sudoku:

Code: Select all

X     Y     or   Y     X      are possible here
Y     X          X     Y

Thus when this pattern emerges one can exclude X and Y from the cell that has the extra candidate Z:

Code: Select all

XYZ     XY     becomes     Z      XY
XY      XY                 XY     XY

[keith]

You can read about Unique Rectangles here:

http://forum.enjoysudoku.com/viewtopic.php?t=4204

Keith