The New Sudoku Players' Forum

[Carino]

X21 4X7 XX6
364 8x2 1XX
X57 1X6 42X

432 961 XXX
185 724 639
679 583 241

596 248 X1X
743 619 852
218 375 964

so tell me what trick should i use but don't tell me with computer code

[blue]

Code: Select all

+----------+-----------+-------------+
| 89  2  1 | 4  35   7 | 35  89  6   |
| 3   6  4 | 8  59   2 | 1   79  57  |
| 89  5  7 | 1  39   6 | 4   2   38  |
+----------+-----------+-------------+
| 4   3  2 | 9  6    1 | 57  78  578 |
| 1   8  5 | 7  2    4 | 6   3   9   |
| 6   7  9 | 5  8    3 | 2   4   1   |
+----------+-----------+-------------+
| 5   9  6 | 2  4    8 | 37  1   37  |
| 7   4  3 | 6  1    9 | 8   5   2   |
| 2   1  8 | 3  7    5 | 9   6   4   |
+----------+-----------+-------------+

Either "BUG+1" or "XY-Wing".

Of the two, XY-Wing is better to know, but BUG+1 is "easy" when it's available.
XY-Wings can be spotted without pencilmark candiates showing, but for BUG+1, they're (probably) essential.

[Carino]

Thanks my friend
Are x-wings cummon?
Are they normally only used by experienced players?

[Carino]

Code: Select all

+----------+-----------+-------------+
| 89  2  1 | 4  35   7 | 35  89  6   |
| 3   6  4 | 8  59   2 | 1   79  57  |
| 89  5  7 | 1  39   6 | 4   2   38  |
+----------+-----------+-------------+
| 4   3  2 | 9  6    1 | 57  78  578 |
| 1   8  5 | 7  2    4 | 6   3   9   |
| 6   7  9 | 5  8    3 | 2   4   1   |
+----------+-----------+-------------+
| 5   9  6 | 2  4    8 | 37  1   37  |
| 7   4  3 | 6  1    9 | 8   5   2   |
| 2   1  8 | 3  7    5 | 9   6   4   |
+----------+-----------+-------------+

Either "BUG+1" or "XY-Wing".

Of the two, XY-Wing is better to know, but BUG+1 is "easy" when it's available.
XY-Wings can be spotted without pencilmark candiates showing, but for BUG+1, they're (probably) essential.

So if I use the bug +1 I see there is a house with 3 options right? and which number do I need to eliminate? is so confusing

[Leren]

The BUG principle is based on a mathematical fact that a Sudoku puzzle can't have one solution if it is reduced to solved cells plus a number of cells with 2 candidates left where, in each row, column and box where they exist, there are exactly 2 instances of each digit in the bi-value cells. It can either have 0 solutions or 2 solutions but not 1. Because most published Sudoku puzzles are supposed to have exactly one solution the BUG situation should correspond to an invalid solution state.

In the case of a BUG+1 situation, which is what you have here, there will be one cell with three candidates and removing one of them them will reduce you to the unwanted BUG situation. In your puzzle look what would happen if you were to remove 7 from Row 4 Column 9 (r4c9 for short), there would be 2 7's in Row 4, Column 9 and Box 6, 2 8's in Row 1, Column 1 and Box 1 ....... and so on right throughout the puzzle.

Can't have that - no solution. So .... r4c9 must be 7 !!! You can remove 5 and 8 from r4c9 and the puzzle is solved !!!

The mathematics underlying the BUG principle is pretty obscure, but the pattern is easy to spot, particularly BUG +1.

With regard to the XY wing here's how it works for your puzzle.

Code: Select all

*-----------------------------------------------------*
| 89   2    1     | 4    35   7     |b35   89   6     |
| 3    6    4     | 8    59   2     | 1    79  a57    |
| 89   5    7     | 1    39   6     | 4    2    38    |
|-----------------+-----------------+-----------------|
| 4    3    2     | 9    6    1     | 57   78   578   |
| 1    8    5     | 7    2    4     | 6    3    9     |
| 6    7    9     | 5    8    3     | 2    4    1     |
|-----------------+-----------------+-----------------|
| 5    9    6     | 2    4    8     |c37   1   D3-7   |
| 7    4    3     | 6    1    9     | 8    5    2     |
| 2    1    8     | 3    7    5     | 9    6    4     |
*-----------------------------------------------------*

Look at the cells I've marked a, b and c. Suppose cell a (r2c9) was not 7. Then it must be 5. So cell b (r1c7) must not be 5, so it must be 3. So cell c must not be 3, so it must be 7.

You can reverse this argument and assume that cell c is not 7 and conclude that cell a must be 7. The result of all this is that at least one of cells a and c must be 7. They might both be 7 but they can't both not be 7.

Now look at the cell I've marked D (r7c9). It can see both of cells a and c, at least one of which must be 7.

So cell D can't be 7 !!! You can remove 7 from r7c9 and the puzzle is solved !!!

The X and Y refer to the 2 values in the middle cell b. The pincer digit 7 doesn't get a look-in in the name of the move. You might be tempted to call it an XYZ wing with Z = 7 here, but there is another move called XYZ Wing, so you just have to accept the name.

Here's a site that discusses the BUG +1 and XY Wing moves, and a lot of other solving techniques. It's a great teaching site, one of the best, and it has downloadable software, so you can create and solve your own puzzles.

http://hodoku.sourceforge.net/en/techniques.php

Leren

[Carino]

wow thanks leren
I think i understood the bug+1 but the xywing seems a bit confusing do you know all the tricks?
if the puzzle is already locked with only one solution with all these tricks is it always possible to solve?
and are there possibly more tricks that haven't been found yet?

[SteveG48]

Leren knows a lot of tricks, but no one knows them all. The XY-wing is pretty common, so it's a good one to learn. And no, I don't think there is any "trick set" that you can learn that will solve every puzzle.

[Leren]

Carino wrote : I think i understood the bug+1 but the xywing seems a bit confusing

I thought that had explained the XY Wing as best I could - perhaps you can describe what you think is confusing about it and I can try to clarify it for you.

Leren