eleven wrote:This one needs a bit more.
- Code: Select all
+-------+-------+-------+
| 3 . . | 2 . . | 1 . 4 |
| . . . | . 1 7 | . 3 . |
| . . . | 5 . . | . 6 . |
+-------+-------+-------+
| 2 . 8 | 1 . . | 3 . . |
| . 1 . | . . . | . 2 5 |
| . 4 . | . . . | 9 . . |
+-------+-------+-------+
| 1 . . | 3 . 6 | 2 . . |
| . 3 9 | . 2 . | . . . |
| 7 . . | . 8 . | . . . |
+-------+-------+-------+
DBS (123)(456789)
Maybe someone can find a nice symmetry move to finally solve it.
I have 3 different solving paths for this one:
(Since this puzzle has
Block Symmetry, I will use a new technique called
Bludo, which you can read about
here.
)
Path 1After simple Diagonal Symmetry moves and singles:
- Code: Select all
+----------------------+----------------------+----------------------+
| 3 56789 567 | 2 69 89 | 1 #5789 4 |
| 45689 2 456 | 4689 1 7 | 58 3 89 |
| 489 *789 1 | 5 49 3 |#78 6 2 |
+----------------------+----------------------+----------------------+
| 2 5679 8 | 1 45679 459 | 3 47 67 |
| 69 1 67 | 46789 3 489 | 4678 2 5 |
| 56 4 3 | 678 567 2 | 9 -78 1 |
+----------------------+----------------------+----------------------+
| 1 #58 45 | 3 4579 6 | 2 45789 789 |
| 4568 3 9 | 47 2 45 | 45678 1 678 |
| 7 #56 2 | 49 8 1 | 456 459 3 |
+----------------------+----------------------+----------------------+
7 @ b3 locked @ r1c8+r3c7
=> r3c2+r6c8 can't be [77]
r8c2 must be from {58}
=> r39c2 can't be [85]
Block Symmetry: r3c2+r6c8 can't be [87]
Bludo: r3c2+r6c8 can't be [97]
In summary: r3c2+r6c8 can't be [77|87|97]
=> r6c7 can't be 7
Block Symmetry: r3c5<>9, r9c2<>5
Diagonal Symmetry: r5c3<>6, r8c6<>4, r2c9<>8
- Code: Select all
+----------------+----------------+----------------+
| 3 -578 56 | 2 69 89 | 1 *57 4 |
| 458 2 456 | 68 1 7 | 58 3 9 |
| 89 789 1 | 5 4 3 | 78 6 2 |
+----------------+----------------+----------------+
| 2 *59 8 | 1 569 49 | 3 47 67 |
| 69 1 7 | 689 3 489 | 46 2 5 |
| 56 4 3 | 67 567 2 | 9 8 1 |
+----------------+----------------+----------------+
| 1 58 45 | 3 *79 6 | 2 479 78 |
| 48 3 9 | 47 2 5 | 467 1 678 |
| 7 6 2 | 49 8 1 | 45 459 3 |
+----------------+----------------+----------------+
Block Symmetry: r1c8+r4c2+r7c5=[597|759]
=> r1c8+r4c2=[59|75], must have 5
=> r1c2, seeing r1c8+r4c2, can't be 5
Block Symmetry: r4c5<>9, r7c8<>7
Diagonal Symmetry: r2c1<>8, r5c4<>6, r8c7<>4
- Code: Select all
+----------------+----------------+----------------+
| 3 *78 56 | 2 69 89 | 1 -57 4 |
| 45 2 456 | 68 1 7 | 58 3 9 |
| 89 789 1 | 5 4 3 | 78 6 2 |
+----------------+----------------+----------------+
| 2 59 8 | 1 56 49 | 3 *47 67 |
| 69 1 7 | 89 3 489 | 46 2 5 |
| 56 4 3 | 67 567 2 | 9 8 1 |
+----------------+----------------+----------------+
| 1 58 45 | 3 79 6 | 2 49 78 |
| 48 3 9 | 47 2 5 | 67 1 678 |
| 7 6 2 | 49 8 1 | 45 459 3 |
+----------------+----------------+----------------+
Bludo: r1c2+r4c8 can't be [84]
=> r1c2+r4c8=[74|77|87], must have 7
=> r1c8, seeing r1c2+r4c8, can't be 7
All singles from here.
Path 2 (a step shorter than the one above)
After the first block of moves in
Path 1:
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+----------------+----------------+----------------+
| 3 578 #56 | 2 69 89 | 1 57 4 |
| 458 2 *456 | 68 1 7 | 58 3 9 |
| 89 789 1 | 5 4 3 | 78 6 2 |
+----------------+----------------+----------------+
| 2 59 8 | 1 569 49 | 3 47 #67 |
| 69 1 7 | 689 3 -489 |*46 2 5 |
| 56 4 3 | 67 567 2 | 9 8 1 |
+----------------+----------------+----------------+
| 1 58 45 | 3 79 6 | 2 479 78 |
| 48 3 9 | 47 2 5 | 467 1 678 |
| 7 6 2 | 49 8 1 | 45 459 3 |
+----------------+----------------+----------------+
Bludo: r1c3+r4c9 can't be [57]
=> r1c3+r4c9=[56|66|67], must have 6
=> r2c3+r5c7 can't be [66]
Block Symmetry: r5c6 can't be 4
All singles from here.
Path 3 (no Bludo in this approach)
After simple Diagonal Symmetry moves and singles:
- Code: Select all
+----------------------+----------------------+----------------------+
| 3 56789 567 | 2 69 89 | 1 5789 4 |
| 45689 2 *456 | 4689 1 7 | 58 3 89 |
|*489 789 1 | 5 *49 3 | 78 6 2 |
+----------------------+----------------------+----------------------+
| 2 5679 8 | 1 45679 459 | 3 47 67 |
| 69 1 67 | 46789 3 489 | 4678 2 5 |
| 56 4 3 | 678 567 2 | 9 78 1 |
+----------------------+----------------------+----------------------+
| 1 58 *45 | 3 -4579 6 | 2 45789 789 |
| 4568 3 9 | 47 2 45 | 45678 1 678 |
| 7 56 2 | 49 8 1 | 456 459 3 |
+----------------------+----------------------+----------------------+
Turbot fish (kite):
4 @ r3 locked @ r3c15
4 @ c3 locked @ r27c3
r2c3+r3c1 can't be [44]
=> r3c5+r7c3=[44|45|94], must have 4
=> r7c5, seeing r3c5+r7c3, can't be 4
Block Symmetry: r1c8<>8, r4c2<>6
Diagonal Symmetry: r5c7<>7, r8c1<>5, r2c4<>9
- Code: Select all
+----------------------+----------------------+----------------------+
| 3 56789 567 | 2 #69 -89 | 1 579 4 |
| 45689 2 456 | 468 1 7 | 58 3 89 |
| 489 789 1 | 5 *49 3 | 78 6 2 |
+----------------------+----------------------+----------------------+
| 2 579 8 | 1 @45679 459 | 3 *47 #67 |
| 69 1 67 | 46789 3 489 | 468 2 5 |
| 56 4 3 | 678 567 2 | 9 -78 1 |
+----------------------+----------------------+----------------------+
| 1 58 45 | 3 579 6 | 2 45789 789 |
| 468 3 9 | 47 2 45 | 45678 1 678 |
| 7 56 2 | 49 8 1 | 456 459 3 |
+----------------------+----------------------+----------------------+
Block Symmetry: r3c5+r6c8=[48|97]
4 @ c5 locked @ r34c5
=> r3c5+r46c8 can't be [947]
=> r6c8 can't be 7
Block Symmetry: r9c2<>5, r3c5<>9
Block Symmetry: r1c6+r4c9=[86|97]
6 @ r4 locked @ r4c59
=> r1c56+r4c9 can't be [697]
=> r1c6 can't be 9
Block Symmetry: r4c9<>7, r7c3<>5
All singles from here.
Personally I like the 3rd path the best, but the usage of Bludo in the first 2 paths probably makes them easier.