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[mith]

Code: Select all

+-------+-------+-------+
| 3 . . | . . . | . . . |
| . . 1 | 4 . . | . . 3 |
| . 5 . | 3 2 . | . 6 . |
+-------+-------+-------+
| . 2 . | . 6 . | . 1 . |
| . . 9 | 8 . . | . . 4 |
| . . . | . . . | 5 . . |
+-------+-------+-------+
| . 6 . | . 5 . | . 2 . |
| 9 . . | . . . | . . . |
| . 7 3 | 9 . . | . . 8 |
+-------+-------+-------+
3..........14....3.5.32..6..2..6..1...98....4......5...6..5..2.9.........739....8

A bonus crossover puzzle! In addition to being a "Tatooine" puzzle, it contains the first 23 digits of π (obviously not in order) as givens.

[pjb]

3 MSLSs +basis, then simple chain. (It can also be solved by eleven consecutive fish+ basics)

15 cell Truths: r3467 c1349
15 links: 1r3, 5r4, 126r6, 1r7, 478c1, 478c3, 7c4, 79c9
11 eliminations: r3c6<>1, r3c7<>1, r4c6<>5, r6c2<>1, r6c5<>1, r6c6<>1, r6c6<>2, r7c6<>1, r7c7<>1, r1c4<>7, r8c4<>7

15 cell Truths: r146 c134 +r1c9 r6c9 r3c1 r7c1 r3c3 r7c3 r7c4
15 links: 256r1, 5r4, 26r6, 1478c1, 478c3, 17c4
5 eliminations: r1c6<>5, r1c6<>6, r1c7<>2, r1c8<>5, r8c4<>1

Naked triplets of 256 at r8c349 => -2 r8c6, -5 r8c8, -6 r8c67
Naked quads of 1789 at r1c56, r2c5, r3c6 => -1 r1c4, -7 r2c6, -8 r2c6, -9 r2c6
Naked quins of 13478 at r7c46, r8c56, r9c5 => -1 r9c6, -4 r9c6

18 cell Truths: r3467 c13469
18 links: 7r3, 57r4, 267r6, 7r7, 148c1, 48c3, 1c4, 3489c6, 9c9
9 eliminations: r4c7<>7, r6c5<>7, r6c8<>7, r7c7<>7, r1c6<>8, r1c6<>9, r8c6<>3, r8c6<>4, r8c6<>8

Naked pairs of 17 at r18c6 => -7 r467c6
Naked triplets of 147 at r7c4, r8c6, r9c5 => -1 r8c5, -4 r7c6, r8c5, -7 r8c5
Naked quads of 1267 at r7c4, r8c46, r9c6 => -1 r9c5
Hidden pairs of 17 at r6c1 and r6c4
Naked triplets of 349 at r4c6, r6c56 => -3 r5c5

(9)r3c7 = (9-8)r3c6 = (8-3)r7c6 = (3-9)r7c7 = (9)r7c9 => -9 r7c7; stte

Phil

[Leren]

Two steps:

Code: Select all

*--------------------------------------------------------------*
| 3     489    26    | 1567 1789   156789  | 124789 45789  25  |
| 26    89     1     | 4    789    56789   | 2789   5789   3   |
| 478   5      478   | 3    2      189     | 1489   6      19  |
|--------------------+---------------------+-------------------|
|a478c  2     a4578c |a57c  6      34579c  | 379-8  1     a79c |
| 56    13     9     | 8    137    25      | 26     37     4   |
| 147-8 134-8  467-8 | 127  13479  123479  | 5      3789   26  |
|--------------------+---------------------+-------------------|
|b148   6     b48    |b17   5     b13478   | 13479  2     b179 |
| 9     148    25    | 1267 13478  1234678 | 13467  3457   56  |
| 25    7      3     | 9    14     1246    | 146    45     8   |
*--------------------------------------------------------------*

ALS XY Wing: (8=9) r4c1349 - (9=3) r7c13469 - (3=8) r4c13469 => - 8 r4c7, r5c123; some basics,

Code: Select all

*------------------------------------------------------*
| 3    489  26   | 1567 178    15678  | 2478  4579  25 |
| 26   89   1    | 4    78     5678   | 278   579   3  |
| 478  5    478  | 3    2      9      | 48    6     1  |
|----------------+--------------------+----------------|
|b478  2   b4578 |b57   6      3457   | 379   1    b79 |
| 56   13   9    | 8    137    25     | 26    37    4  |
|a147 a134 a467  |a127  9      1247-3 | 5     8    a26 |
|----------------+--------------------+----------------|
|c148  6   c48   |c17   5     c1378   | 13479 2    c79 |
| 9    148  25   | 1267 13478  123678 | 13467 3457  56 |
| 25   7    3    | 9    14     126    | 146   45    8  |
*------------------------------------------------------*

ALS XY Wing: (3=4) r6c12349 - (4=9) r4c1349 - (9=3) r7c13469 => - 3 r6c6; stte

Leren

[denis_berthier]

3..........14....3.5.32..6..2..6..1...98....4......5...6..5..2.9.........739....8

Solved using only Subsets (20):

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
*** Using CLIPS 6.32-r773
***********************************************************************************************
225 candidates, 1515 csp-links and 1515 links. Density = 6.01%
hidden-pairs-in-a-block: b7{n2 n5}{r8c3 r9c1} ==> r9c1 ≠ 4, r9c1 ≠ 1, r8c3 ≠ 8, r8c3 ≠ 4
hidden-pairs-in-a-block: b6{n2 n6}{r5c7 r6c9} ==> r6c9 ≠ 9, r6c9 ≠ 7, r5c7 ≠ 7, r5c7 ≠ 3
hidden-pairs-in-a-block: b1{n2 n6}{r1c3 r2c1} ==> r2c1 ≠ 8, r2c1 ≠ 7, r1c3 ≠ 8, r1c3 ≠ 7, r1c3 ≠ 4
whip[1]: b1n7{r3c3 .} ==> r3c6 ≠ 7, r3c7 ≠ 7, r3c9 ≠ 7
x-wing-in-rows: n3{r4 r7}{c6 c7} ==> r8c7 ≠ 3, r8c6 ≠ 3, r6c6 ≠ 3, r5c6 ≠ 3
naked-triplets-in-a-row: r5{c2 c5 c8}{n3 n1 n7} ==> r5c6 ≠ 7, r5c6 ≠ 1, r5c1 ≠ 7, r5c1 ≠ 1
naked-triplets-in-a-column: c1{r2 r5 r9}{n2 n6 n5} ==> r6c1 ≠ 6, r4c1 ≠ 5
naked-triplets-in-a-column: c9{r3 r4 r7}{n1 n9 n7} ==> r8c9 ≠ 7, r8c9 ≠ 1, r1c9 ≠ 9, r1c9 ≠ 7, r1c9 ≠ 1
swordfish-in-columns: n5{c3 c4 c9}{r8 r4 r1} ==> r8c8 ≠ 5, r4c6 ≠ 5, r1c8 ≠ 5, r1c6 ≠ 5
swordfish-in-columns: n6{c3 c4 c9}{r6 r1 r8} ==> r8c7 ≠ 6, r8c6 ≠ 6, r1c6 ≠ 6
hidden-pairs-in-a-block: b2{n5 n6}{r1c4 r2c6} ==> r2c6 ≠ 9, r2c6 ≠ 8, r2c6 ≠ 7, r1c4 ≠ 7, r1c4 ≠ 1
naked-triplets-in-a-row: r1{c3 c4 c9}{n2 n6 n5} ==> r1c7 ≠ 2
swordfish-in-rows: n9{r3 r4 r7}{c9 c6 c7} ==> r6c6 ≠ 9, r2c7 ≠ 9, r1c7 ≠ 9, r1c6 ≠ 9
swordfish-in-rows: n2{r2 r5 r9}{c1 c7 c6} ==> r8c6 ≠ 2, r6c6 ≠ 2
hidden-pairs-in-a-block: b8{n2 n6}{r8c4 r9c6} ==> r9c6 ≠ 4, r9c6 ≠ 1, r8c4 ≠ 7, r8c4 ≠ 1
x-wing-in-columns: n1{c1 c4}{r6 r7} ==> r7c9 ≠ 1, r7c7 ≠ 1, r7c6 ≠ 1, r6c6 ≠ 1, r6c5 ≠ 1, r6c2 ≠ 1
hidden-single-in-a-column ==> r3c9 = 1
jellyfish-in-columns: n7{c1 c3 c4 c9}{r4 r3 r6 r7} ==> r7c7 ≠ 7, r7c6 ≠ 7, r6c8 ≠ 7, r6c6 ≠ 7, r6c5 ≠ 7, r4c7 ≠ 7, r4c6 ≠ 7
naked-single ==> r6c6 = 4
naked-pairs-in-a-block: b5{r4c6 r6c5}{n3 n9} ==> r5c5 ≠ 3
hidden-pairs-in-a-column: c6{n1 n7}{r1 r8} ==> r8c6 ≠ 8, r1c6 ≠ 8
naked-pairs-in-a-block: b8{r7c4 r8c6}{n1 n7} ==> r9c5 ≠ 1, r8c5 ≠ 7, r8c5 ≠ 1
stte