The New Sudoku Players' Forum

[WayneO]

Hello,
This is my first “Post”, so I do something wrong, or forget something,..please tell me.

I am stuck on this puzzle and hoping someone can help me.

This puzzle is from the Platinum Magazine Group Inc. “SUDOKU #04

Difficulty Level =”HARD”, Puzzle #2

*-----------*
|3..|..4|...|
|98.|36.|4.7|
|.5.|...|..1|
|---+---+---|
|.7.|24.|...|
|1..|793|..2|
|...|.58|.9.|
|---+---+---|
|8..|...|.7.|
|2.3|.71|.45|
|...|4..|..6|
*-----------*




*--------------------------------------------------------------------*
| 3 2 7 | 589 1 4 | 56 568 89 |
| 9 8 1 | 3 6 25 | 4 25 7 |
| 4 5 6 | 89 28 7 | 2389 238 1 |
|----------------------+----------------------+----------------------|
| 5 7 9 | 2 4 6 | 138 138 38 |
| 1 4 8 | 7 9 3 | 56 56 2 |
| 6 3 2 | 1 5 8 | 7 9 4 |
|----------------------+----------------------+----------------------|
| 8 169 4 | 56 23 259 | 1239 7 39 |
| 2 69 3 | 68 7 1 | 89 4 5 |
| 7 19 5 | 4 238 29 | 12389 1238 6 |
*--------------------------------------------------------------------*
Thank You,
WayneO

[Steve R]

Well, I see nothing wrong.

You could try two eliminations:
- 9 from r7c6 and r9c7 using the XY-wing for (23) pivoted on r7c5 with pincers r9c6 and r7c9
- 8 from r4c7 using the XY-wing for (39) pivoted on r7c9 with pincers r4c9 and r8c7.

Steve

[daj95376]

If you're familiar with Unique Rectangles, then look for the UR Type 1 in <56> to quickly solve your puzzle.

If you're not familiar with Unique Rectangles, then you need to search for an XY-Wing, a Locked Candidate (1), and another XY-Wing.

Good Luck!

[udosuk]

For one thing, you could have used the code tags to properly display your grids:

Code: Select all

 *-----------*
 |3..|..4|...|
 |98.|36.|4.7|
 |.5.|...|..1|
 |---+---+---|
 |.7.|24.|...|
 |1..|793|..2|
 |...|.58|.9.|
 |---+---+---|
 |8..|...|.7.|
 |2.3|.71|.45|
 |...|4..|..6|
 *-----------*

 *--------------------------------------------------------------------*
 | 3      2      7      | 589    1      4      | 56     568    89     |
 | 9      8      1      | 3      6      25     | 4      25     7      |
 | 4      5      6      | 89     28     7      | 2389   238    1      |
 |----------------------+----------------------+----------------------|
 | 5      7      9      | 2      4      6      | 138    138    38     |
 | 1      4      8      | 7      9      3      | 56     56     2      |
 | 6      3      2      | 1      5      8      | 7      9      4      |
 |----------------------+----------------------+----------------------|
 | 8      169    4      | 56     23     259    | 1239   7      39     |
 | 2      69     3      | 68     7       1     | 89     4      5      |
 | 7      19     5      | 4      238    29     | 12389  1238   6      |
 *--------------------------------------------------------------------*

Method: Enclose your grids with [code] and [/code].

To solve the puzzle from your state you can use a technique called XY-Wing (as Steve R pointed out):

Code: Select all

 *--------------------------------------------------------------------*
 | 3      2      7      | 589    1      4      | 56     568    89     |
 | 9      8      1      | 3      6      25     | 4      25     7      |
 | 4      5      6      | 89     28     7      | 2389   238    1      |
 |----------------------+----------------------+----------------------|
 | 5      7      9      | 2      4      6      |-138    138   A38     |
 | 1      4      8      | 7      9      3      | 56     56     2      |
 | 6      3      2      | 1      5      8      | 7      9      4      |
 |----------------------+----------------------+----------------------|
 | 8      169    4      | 56    B23    -259    | 1239   7    AB39     |
 | 2      69     3      | 68     7       1     |A89     4      5      |
 | 7      19     5      | 4      238   B29     | 12389  1238   6      |
 *--------------------------------------------------------------------*

Consider the cells marked A.
r7c9 must be one of two possible digits.
As a result, at least one of r4c9 and r8c7 must contain a certain digit.
Therefore, that digit can be eliminated from r4c7.

Consider the cells marked B.
r7c5 must be one of two possible digits.
As a result, at least one of r7c9 and r9c6 must contain a certain digit.
Therefore, that digit can be eliminated from r7c6.

After these two moves the rest would be very easy.

[WayneO]

Dear udosuk,

I’m sorry to write you back, but I’m “new” to the XY-Wing, and I just can’t understand it.

Can you PLEASE tell me why, on the first set of numbers (A), why do you “single out”r4c7, and NOT r4c8 ??????

Thank you,
WayneO

[udosuk]

Can you PLEASE tell me why, on the first set of numbers (A), why do you “single out”r4c7, and NOT r4c8 ??????

Code: Select all

 *--------------------------------------------------------------------*
 | 3      2      7      | 589    1      4      | 56     568    89     |
 | 9      8      1      | 3      6      25     | 4      25     7      |
 | 4      5      6      | 89     28     7      | 2389   238    1      |
 |----------------------+----------------------+----------------------|
 | 5      7      9      | 2      4      6      |-138    138   A38     |
 | 1      4      8      | 7      9      3      | 56     56     2      |
 | 6      3      2      | 1      5      8      | 7      9      4      |
 |----------------------+----------------------+----------------------|
 | 8      169    4      | 56     23     259    | 1239   7     A39     |
 | 2      69     3      | 68     7       1     |A89     4      5      |
 | 7      19     5      | 4      238   B29     | 12389  1238   6      |
 *--------------------------------------------------------------------*

Consider the cells marked A.
r7c9 must be one of two possible digits, 3 or 9.
As a result, at least one of r4c9 and r8c7 must contain a certain digit, 8.
Therefore, that digit, 8, can be eliminated from r4c7.

r4c8 is irrelevant because it isn't affected by r8c7.

To explain it even more plainly:

r7c9 must be 3 or 9.
If r7c9=3, r4c9=8 => r4c7<>8.
If r7c9=9, r8c7=8 => r4c7<>8.
Therefore r4c7 cannot be 8.

And to see it in the opposite way (the "trial-and-error" approach):

Suppose r4c7=8.
Then r7c9=3 and r8c7=9.
Then r7c9 cannot be 3 or 9.
Then we have no valid number to put in r7c9 => Contradiction.
Therefore r4c7 cannot be 8.

See the logic now?

[hrcjcr]

If you're familiar with Unique Rectangles, then look for the UR Type 1 in <56> to quickly solve your puzzle.

Good Luck!

Has there been any work done on unique other shapes; such as parallelograms or trapezoids?

[wapati]

If you're familiar with Unique Rectangles, then look for the UR Type 1 in <56> to quickly solve your puzzle.

Good Luck!

Has there been any work done on unique other shapes; such as parallelograms or trapezoids?

Think fins. (trapezoid)

In the UR sense they are rare, but do occur.


Parallelograms suggests unique loops.

I am far from expert, btw.