The New Sudoku Players' Forum

[PeetNeef]

Hello,

I cannot solve the remaining of this puzzle. I want to advance as a Sudoku player, but I am stuck here. Can someone show which techniques I could have been used with an explanation? I learned something new about Unique Rectangles, and I could see some patterns which are probably candidates for a certain Unique Rectangle. However, I don't know how to continue.

Thanks in advance!

I provided a photo below!

https://ibb.co/9hNsHtc

[Leren]

The puzzle .7.1.6.9.....4.....698....29..3..8..3.7...5.1..4..1..31....273.....7.....2.9.8.5.

Code: Select all

*-----------*
|.7.|1.6|.9.|
|...|.4.|...|
|.69|8..|..2|
|---+---+---|
|9..|3..|8..|
|3.7|...|5.1|
|..4|..1|..3|
|---+---+---|
|1..|..2|73.|
|...|.7.|...|
|.2.|9.8|.5.|
*-----------*

This is where you appear to be:

Code: Select all

*------------------------------------------*
| 458-2 7  *258 | 1   *25  6  | 3 9     45 |
| 25    3   1   | 257  4   9  | 6 8     57 |
| 45    6   9   | 8    3   57 | 1 47    2  |
|---------------+-------------+------------|
| 9     1  *26  | 3   *256 57 | 8 467-2 47 |
| 3     8   7   | 26   9   4  | 5 26    1  |
| 26    5   4   | 267  8   1  | 9 267   3  |
|---------------+-------------+------------|
| 1     49  568 | 456  56  2  | 7 3     89 |
| 568   49  568 | 456  7   3  | 2 1     89 |
| 7     2   3   | 9    1   8  | 4 5     6  |
*------------------------------------------*

There is an X Wing in columns in the cells marked * which removes a couple of 2's as shown. This doesn't do much but you should be on the lookout for X Wings as they may solve other puzzles.

Code: Select all

*---------------------------------------*
| 458 7  258 | 1   25  6  | 3 *9    45  |
| 25  3  1   |b257 4   9  | 6 *8   a57  |
| 45  6  9   | 8   3   57 | 1 *4-7  2   |
|------------+------------+-------------|
| 9   1  26  | 3   256 57 | 8  467 *4-7 |
| 3   8  7   | 26  9   4  | 5  26  *1   |
| 26  5  4   |c267 8   1  | 9 d267 *3   |
|------------+------------+-------------|
| 1   49 568 | 456 56  2  | 7  3    89  |
| 568 49 568 | 456 7   3  | 2  1    89  |
| 7   2  3   | 9   1   8  | 4  5    6   |
*---------------------------------------*

This move is called a Skyscraper and is marked in the cells a-b-c-d. I'll explain how this works in words.

Assume cell a is not 7. Then since there are only two 7's in Row 2, cell b must be 7. So cell c is not 7 and since there are only two 7's in Row 6, cell d must be 7.

Similarly, if you start off by assuming cell d is not 7 then you can work backwards and conclude cell a is 7.

So the upshot of all this is that one of cells a or d must be 7. This means that you can remove any 7's in the 6 cells that cells a and d can both see, which I've marked with *'s

There are two of them, and this basically solves the puzzle. You can read about X Wings here and Skyscrapers here.

Leren