## Tatooine Double Noon

Post puzzles for others to solve here.

### Tatooine Double Noon

Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . . 1 | 2 . . | . . 3 || . 4 . | . 5 . | . 6 . |+-------+-------+-------+| . 6 . | . 4 . | . 7 . || . . 2 | 3 . . | . . 8 || . . . | . . . | . . . |+-------+-------+-------+| . . . | . . 5 | 1 . . || . 5 . | . 6 . | . 4 . || . . 3 | 9 . . | . . 2 |+-------+-------+-------+...........12....3.4..5..6..6..4..7...23....8..............51...5..6..4...39....2`
mith

Posts: 301
Joined: 14 July 2020

### Re: Tatooine Double Noon

No takers? In that case I'll remove the easy option to make it more interesting for others.

Step 1. Swordfish x 5 (digits 23456):

15x15 {23r348 456r259 \ 2346c167 5c178} => -2346 c167, -5 c178 (=> +9 r6c7)
Step 2. Swordfish: (7)r259\c256 => -7 c256 (=> +7 r1c7,r6c1)

Code: Select all
`.--------------.-----------------.-----------------.| 89  23   56  | 46   1389  189  |  7     1289  45 || 56  789  1   | 2    789   46   |  45   b89    3  || 23  4    789 | 178  5     1389 |  28    6     19 |:--------------+-----------------+-----------------:| 13  6    89  | 158  4     1289 |  23    7     15 || 45  19   2   | 3    179   67   |  46    15    8  || 7   138  45  | 56   128   18   |  9     23    46 |:--------------+-----------------+-----------------:| 89  289  46  | 47   23    5    |  1   ab38'9  67 || 12  5    79  | 18   6     23   | a38    4     79 || 46  178  3   | 9    18    47   |  56    5-8   2  |'--------------'-----------------'-----------------'`

Step 3. XYZ-Wing: (83)b9p42 = (98)r72c8 => -8 r9c8; stte
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: Tatooine Double Noon

Yep, that's the easy option. Curious to see if there's some crazy short option.

There are actually more fish to find before the XYZ-Wing (in fact, SE finds Swordfish on all 9 digits for this one).
mith

Posts: 301
Joined: 14 July 2020

### Re: Tatooine Double Noon

Code: Select all
`(solve-sudoku-grid   +-------+-------+-------+   ! . . . ! . . . ! . . . !    ! . . 1 ! 2 . . ! . . 3 !    ! . 4 . ! . 5 . ! . 6 . !    +-------+-------+-------+   ! . 6 . ! . 4 . ! . 7 . !    ! . . 2 ! 3 . . ! . . 8 !    ! . . . ! . . . ! . . . !    +-------+-------+-------+   ! . . . ! . . 5 ! 1 . . !    ! . 5 . ! . 6 . ! . 4 . !    ! . . 3 ! 9 . . ! . . 2 !    +-------+-------+-------+)`

Many Subsets at the start:

Code: Select all
`**************************************************************************************************  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin***  Using CLIPS 6.32-r770***********************************************************************************************261 candidates, 2028 csp-links and 2028 links. Density = 5.98%hidden-pairs-in-a-block: b8{r7c5 r8c6}{n2 n3} ==> r8c6 ≠ 8, r8c6 ≠ 7, r8c6 ≠ 1, r7c5 ≠ 8, r7c5 ≠ 7swordfish-in-columns: n6{c3 c4 c9}{r7 r1 r6} ==> r7c1 ≠ 6, r6c7 ≠ 6, r6c6 ≠ 6, r1c6 ≠ 6, r1c1 ≠ 6swordfish-in-columns: n4{c3 c4 c9}{r6 r7 r1} ==> r7c1 ≠ 4, r6c7 ≠ 4, r6c1 ≠ 4, r1c7 ≠ 4, r1c6 ≠ 4hidden-pairs-in-a-block: b2{r1c4 r2c6}{n4 n6} ==> r2c6 ≠ 9, r2c6 ≠ 8, r2c6 ≠ 7, r1c4 ≠ 8, r1c4 ≠ 7, r1c4 ≠ 1hidden-pairs-in-a-block: b6{r5c7 r6c9}{n4 n6} ==> r6c9 ≠ 9, r6c9 ≠ 5, r6c9 ≠ 1, r5c7 ≠ 9, r5c7 ≠ 5hidden-pairs-in-a-block: b7{r7c3 r9c1}{n4 n6} ==> r9c1 ≠ 8, r9c1 ≠ 7, r9c1 ≠ 1, r7c3 ≠ 9, r7c3 ≠ 8, r7c3 ≠ 7finned-x-wing-in-rows: n5{r5 r2}{c1 c8} ==> r1c8 ≠ 5finned-x-wing-in-columns: n5{c9 c3}{r1 r4} ==> r4c1 ≠ 5biv-chain[2]: r5n5{c1 c8} - c9n5{r4 r1} ==> r1c1 ≠ 5hidden-pairs-in-a-block: b1{r1c3 r2c1}{n5 n6} ==> r2c1 ≠ 9, r2c1 ≠ 8, r2c1 ≠ 7, r1c3 ≠ 9, r1c3 ≠ 8, r1c3 ≠ 7swordfish-in-columns: n3{c2 c5 c8}{r6 r1 r7} ==> r6c7 ≠ 3, r6c1 ≠ 3, r1c6 ≠ 3, r1c1 ≠ 3swordfish-in-rows: n2{r3 r4 r8}{c1 c7 c6} ==> r7c1 ≠ 2, r6c7 ≠ 2, r6c6 ≠ 2, r1c7 ≠ 2, r1c1 ≠ 2hidden-pairs-in-a-block: b1{r1c2 r3c1}{n2 n3} ==> r3c1 ≠ 9, r3c1 ≠ 8, r3c1 ≠ 7, r1c2 ≠ 9, r1c2 ≠ 8, r1c2 ≠ 7hidden-pairs-in-a-block: b6{r4c7 r6c8}{n2 n3} ==> r6c8 ≠ 9, r6c8 ≠ 5, r6c8 ≠ 1, r4c7 ≠ 9, r4c7 ≠ 5swordfish-in-rows: n5{r2 r5 r9}{c7 c1 c8} ==> r6c7 ≠ 5, r6c1 ≠ 5, r1c7 ≠ 5naked-single ==> r6c7 = 9hidden-triplets-in-a-column: c7{n4 n5 n6}{r5 r2 r9} ==> r9c7 ≠ 8, r9c7 ≠ 7, r2c7 ≠ 8, r2c7 ≠ 7naked-triplets-in-a-row: r2{c1 c6 c7}{n5 n6 n4} ==> r2c8 ≠ 5hidden-pairs-in-a-block: b3{r1c9 r2c7}{n4 n5} ==> r1c9 ≠ 9, r1c9 ≠ 7, r1c9 ≠ 1hidden-triplets-in-a-column: c1{n4 n5 n6}{r9 r5 r2} ==> r5c1 ≠ 9, r5c1 ≠ 7, r5c1 ≠ 1finned-x-wing-in-rows: n7{r2 r5}{c2 c5} ==> r6c5 ≠ 7hidden-triplets-in-a-row: r6{n4 n5 n6}{c9 c3 c4} ==> r6c4 ≠ 8, r6c4 ≠ 7, r6c4 ≠ 1, r6c3 ≠ 8, r6c3 ≠ 7naked-pairs-in-a-block: b4{r5c1 r6c3}{n4 n5} ==> r4c3 ≠ 5finned-x-wing-in-columns: n7{c3 c7}{r8 r3} ==> r3c9 ≠ 7whip[1]: c9n7{r8 .} ==> r8c7 ≠ 7swordfish-in-columns: n7{c3 c4 c9}{r8 r3 r7} ==> r8c1 ≠ 7, r7c2 ≠ 7, r7c1 ≠ 7, r3c7 ≠ 7, r3c6 ≠ 7hidden-single-in-a-block ==> r1c7 = 7hidden-single-in-a-column ==> r6c1 = 7naked-pairs-in-a-column: c1{r1 r7}{n8 n9} ==> r8c1 ≠ 9, r8c1 ≠ 8, r4c1 ≠ 9, r4c1 ≠ 8hidden-triplets-in-a-column: c6{n4 n6 n7}{r9 r2 r5} ==> r9c6 ≠ 8, r9c6 ≠ 1, r5c6 ≠ 9, r5c6 ≠ 1finned-x-wing-in-rows: n1{r9 r6}{c2 c5} ==> r5c5 ≠ 1hidden-triplets-in-a-row: r7{n4 n6 n7}{c4 c3 c9} ==> r7c9 ≠ 9, r7c4 ≠ 8naked-pairs-in-a-block: b8{r7c4 r9c6}{n4 n7} ==> r9c5 ≠ 7, r8c4 ≠ 7hidden-pairs-in-a-row: r8{n7 n9}{c3 c9} ==> r8c3 ≠ 8swordfish-in-columns: n8{c3 c4 c7}{r3 r4 r8} ==> r4c6 ≠ 8, r3c6 ≠ 8swordfish-in-rows: n9{r3 r4 r8}{c9 c6 c3} ==> r1c6 ≠ 9naked-pairs-in-a-column: c6{r1 r6}{n1 n8} ==> r4c6 ≠ 1, r3c6 ≠ 1`

At this point, there (at least) two possibilities:

- several (3D) bivalue-chains[3]:
Code: Select all
`biv-chain[3]: b7n2{r7c2 r8c1} - b7n1{r8c1 r9c2} - r5c2{n1 n9} ==> r7c2 ≠ 9biv-chain[3]: r1n2{c8 c2} - r7c2{n2 n8} - c1n8{r7 r1} ==> r1c8 ≠ 8biv-chain[3]: c1n8{r1 r7} - r7n9{c1 c8} - r2c8{n9 n8} ==> r2c2 ≠ 8biv-chain[3]: r2n8{c5 c8} - c7n8{r3 r8} - b8n8{r8c4 r9c5} ==> r1c5 ≠ 8, r6c5 ≠ 8biv-chain[3]: c6n1{r1 r6} - r6c5{n1 n2} - c8n2{r6 r1} ==> r1c8 ≠ 1stte`

- or a single xy-chain[4]:
Code: Select all
`biv-chain-rc[4]: r5c8{n1 n5} - r9c8{n5 n8} - r2c8{n8 n9} - r3c9{n9 n1} ==> r4c9 ≠ 1, r1c8 ≠ 1stte`
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris