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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

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

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

dongrave

Joined: 06 Mar 2014
Posts: 572

Posted: Tue Sep 26, 2023 5:38 pm Post subject:

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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