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How many xy-wings needed to solve this sudoku?

 
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peter urhegyi



Joined: 26 Oct 2020
Posts: 28

PostPosted: Sun Sep 24, 2023 10:40 am    Post subject: How many xy-wings needed to solve this sudoku? Reply with quote

Code:

+-------+-------+-------+
| 1 . . | . 8 . | . . . |
| . . 5 | 4 . . | . . 6 |
| . . . | . . 2 | . 7 . |
+-------+-------+-------+
| . . 8 | . 5 . | . 9 . |
| 2 . . | . . 3 | 6 . . |
| . 6 . | 7 . . | . . 1 |
+-------+-------+-------+
| . . . | . . 4 | . . . |
| 7 . . | 9 . . | . . 5 |
| . 3 . | . 1 . | . 8 . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site
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dongrave



Joined: 06 Mar 2014
Posts: 568

PostPosted: Tue Sep 26, 2023 5:38 pm    Post subject: Reply with quote

Thanks for the puzzle peter! I used 3 XY Wings and I double-checked to make sure that they were all necessary.

After basics (Note the 1,5 Hidden Pair in row 3):
Code:
+--------------------+-----------------+------------------+
| 1     2479  234679 | 356   8    5679 | 23459 2345  2349 |
| 389   2789  5      | 4     379  179  | 12389 123   6    |
| 34689 489   3469   | 15    369  2    | 15    7     3489 |
+--------------------+-----------------+------------------+
| 34    147   8      | 126   5    16   | 2347  9     2347 |
| 2     14579 1479   | 18    49   3    | 6     45    478  |
| 3459  6     349    | 7     249  89   | 23458 2345  1    |
+--------------------+-----------------+------------------+
| 5689  12589 1269   | 23568 2367 4    | 12379 1236  2379 |
| 7     1248  1246   | 9     236  68   | 1234  12346 5    |
| 4569  3     2469   | 256   1    567  | 2479  8     2479 |
+--------------------+-----------------+------------------+

Step 1: 16-8 XY Wing at r48c6,r5c4 (-8r6c6, -8r7c4).
Code:
+---------------+-------------+---------------+
| 1    2   7    | 356 8   56  | 3459  34  349 |
| 39   8   5    | 4   379 17  | 123   12  6   |
| 3469 49  3469 | 15  39  2   | 15    7   8   |
+---------------+-------------+---------------+
| 34   7   8    | 16  5   16  | 234   9   234 |
| 2    19  19   | 8   4   3   | 6     5   7   |
| 5    6   34   | 7   2   9   | 8     34  1   |
+---------------+-------------+---------------+
| 8    5   129  | 23  367 4   | 12379 126 239 |
| 7    14  124  | 9   36  8   | 1234  126 5   |
| 469  3   2469 | 25  1   57  | 2479  8   249 |
+---------------+-------------+---------------+

Step 2: 56-1 XY Wing at r14c6,r3c4 (-1r4c4, -1r2c6) or 15-6 XY Wing at r1c6,r34c4 (-6r1c4, -6r4c6).
Code:
+---------------+-------------+-------------+
| 1    2   7    | 5   8   6   | 49  34  39  |
| 39   8   5    | 4   39  7   | 12  12  6   |
| 3469 49  3469 | 1   39  2   | 5   7   8   |
+---------------+-------------+-------------+
| 34   7   8    | 6   5   1   | 24  9   23  |
| 2    19  19   | 8   4   3   | 6   5   7   |
| 5    6   34   | 7   2   9   | 8   34  1   |
+---------------+-------------+-------------+
| 8    5   12   | 3   7   4   | 129 6   29  |
| 7    14  124  | 9   6   8   | 3   12  5   |
| 69   3   69   | 2   1   5   | 7   8   4   |
+---------------+-------------+-------------+

Step 3: 39-4 XY Wing at r24c1,r3c2 (-4r3c1).
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