- Code: Select all
+-------+-------+-------+
| 9 . . | 4 . . | 7 . . |
| . 6 . | . 3 . | . 5 . |
| . . 1 | . . 8 | . . 4 |
+-------+-------+-------+
| 2 . . | 8 . . | 1 . . |
| . 3 . | . 4 . | . 7 . |
| . . 7 | . . 9 | . . 5 |
+-------+-------+-------+
| 5 . . | 6 . . | 2 . . |
| . 2 . | . 8 . | . 9 . |
| . . 6 | . . 1 | . . 3 |
+-------+-------+-------+
+-------------------+-------------------+-------------------+
| 9 58 2358 | 4 1256 256 | 7 12368 1268 |
| 478 6 248 | 1279 3 27 | 89 5 1289 |
| 37 57 1 | 2579 25679 8 | 369 236 4 |
+-------------------+-------------------+-------------------+
| 2 459 459 | 8 567 3567 | 1 346 69 |
| 168 3 589 | 125 4 256 | 689 7 2689 |
| 1468 148 7 | 123 126 9 | 3468 23468 5 |
+-------------------+-------------------+-------------------+
| 5 14789 3489 | 6 79 347 | 2 148 178 |
| 1347 2 34 | 357 8 3457 | 456 9 167 |
| 478 4789 6 | 2579 2579 1 | 458 48 3 |
+-------------------+-------------------+-------------------+
Is this the best Swordfish puzzle ever?
Count them -- Six Swordfish existing in the opening position -- and no other simpler moves are possible! No naked or hidden singles, no naked or hidden sets of any size, no locked candidates, no x-wings, xy-wings, no Unique Rectangles or loops, no xy-type forcing chains of any size.
SF 1s in rows: r2c49-r5c14-r8c19
SF 1s in columns: r67c2-r16c5-r17c8
Both make the same 4 exclusions: r1c9, r6c14, r7c9 <>1
SF 2s in rows: r3c458-r6c458-r9c45
SF 2s in columns: r12c3-r125c6-r125c9 [EDIT -- corrected typo]
Both make the same 4 exclusions: r1c58, r2c4, r5c4 <>2
SF 3s in rows: r1c38-r4c68-r7c36
SF 3s in columns: r38c1-r68c4-r36c7
Both make the same 4 exclusions: r3c8, r6c8, r8c36 <>3
A methodical solver is likely to find one of the swordfish in 1s, then in 2s, then in 3s. However, it is both sufficient and necessary to make the exclusion r8c3<>3 to move the puzzle into an "all singles" state.
The exclusion r8c3<>3 can also be made by (Simple Sudoku-Style) Multiple Colors on 3s:
- Code: Select all
+-------------------+-------------------+-------------------+
| 9 58 +2358 | 4 1256 256 | 7 -12368 1268 |
| 478 6 248 | 1279 3 27 | 89 5 1289 |
|-37 57 1 | 2579 25679 8 | 369 236 4 |
+-------------------+-------------------+-------------------+
| 2 459 459 | 8 567 x3567 | 1 o346 69 |
| 168 3 589 | 125 4 256 | 689 7 2689 |
| 1468 148 7 |o123 126 9 | 3468 23468 5 |
+-------------------+-------------------+-------------------+
| 5 14789 3489 | 6 79 347 | 2 148 178 |
|+1347 2 *34 |x357 8 3457 | 456 9 167 |
| 478 4789 6 | 2579 2579 1 | 458 48 3 |
+-------------------+-------------------+-------------------+
If the cells marked "+" are true (equal to 3), then the cell marked "*" does not equal 3.
If the cells makred "+" are false, then "-" are true, "o" are false and "x" are true -- and "*" does not equal 3.
This exclusion can also be made by Nishio. Most rate this tactic as more advanced than Swordfish, however, die-hard pen+paper solvers who use Nishio regularly *might* solve the puzzle without using pencil marks by noticing that if r8c3=3 the rest of the 3's cannot be placed.
