Q is for Quad

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Q is for Quad

Postby mith » Mon Aug 24, 2020 12:35 am

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 9 . | . . 8 |
| . . 7 | 6 . 5 | . . . |
+-------+-------+-------+
| . . 6 | 4 . . | 5 . . |
| . 3 . | . 2 . | . 1 . |
| . . 4 | . . 7 | 6 . . |
+-------+-------+-------+
| . . . | 9 . 4 | 7 . . |
| . . . | . 3 . | . 5 1 |
| . 2 . | . . . | . . . |
+-------+-------+-------+
.............9...8..76.5.....64..5...3..2..1...4..76.....9.47......3..51.2.......
mith
 
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Re: Q is for Quad

Postby Leren » Mon Aug 24, 2020 1:33 am

My solution included 5 naked quads, 1 X Wing, 1 Swordfish & 1 Jellyfish. Hodoku was similar with 1 less naked quad.

In the usual way of these puzzles I found a MSLS : Base 1238; r289 c347 + r2c6 r8c6 r9c6 r5c7 & r5c34 : 15 Links; 123r2 28r8 138r9 & 8r5 ; 59c3 57c4 49c7 ; => 7 eliminations which eliminates the SF & JF. Wow !

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Re: Q is for Quad

Postby denis_berthier » Mon Aug 24, 2020 1:53 am

mith wrote:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . 9 . | . . 8 |
| . . 7 | 6 . 5 | . . . |
+-------+-------+-------+
| . . 6 | 4 . . | 5 . . |
| . 3 . | . 2 . | . 1 . |
| . . 4 | . . 7 | 6 . . |
+-------+-------+-------+
| . . . | 9 . 4 | 7 . . |
| . . . | . 3 . | . 5 1 |
| . 2 . | . . . | . . . |
+-------+-------+-------+
.............9...8..76.5.....64..5...3..2..1...4..76.....9.47......3..51.2.......


If the most basic whips[1] are applied first, there are fewer quads.

Hidden Text: Show
(solve ".............9...8..76.5.....64..5...3..2..1...4..76.....9.47......3..51.2.......")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
*** Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r5c6 = 6
hidden-single-in-a-block ==> r4c6 = 9
hidden-single-in-a-block ==> r6c4 = 3
hidden-single-in-a-column ==> r1c9 = 5
229 candidates, 1572 csp-links and 1572 links. Density = 6.02%
whip[1]: c9n6{r9 .} ==> r9c8 ≠ 6, r7c8 ≠ 6
whip[1]: r8n6{c2 .} ==> r9c1 ≠ 6, r7c1 ≠ 6, r7c2 ≠ 6
whip[1]: r7n2{c9 .} ==> r8c7 ≠ 2
whip[1]: c7n2{r3 .} ==> r1c8 ≠ 2, r2c8 ≠ 2, r3c8 ≠ 2, r3c9 ≠ 2
whip[1]: c9n7{r5 .} ==> r4c8 ≠ 7
whip[1]: c3n2{r2 .} ==> r3c1 ≠ 2, r1c1 ≠ 2, r2c1 ≠ 2
hidden-single-in-a-row ==> r3c7 = 2
whip[1]: b5n1{r6c5 .} ==> r9c5 ≠ 1, r1c5 ≠ 1, r3c5 ≠ 1, r7c5 ≠ 1
whip[1]: b8n1{r9c6 .} ==> r9c1 ≠ 1, r9c3 ≠ 1
whip[1]: r3n1{c2 .} ==> r1c1 ≠ 1, r1c2 ≠ 1, r1c3 ≠ 1, r2c1 ≠ 1, r2c2 ≠ 1, r2c3 ≠ 1
hidden-single-in-a-column ==> r7c3 = 1
hidden-pairs-in-a-column: c8{n6 n7}{r1 r2} ==> r2c8 ≠ 4, r2c8 ≠ 3, r1c8 ≠ 9, r1c8 ≠ 4, r1c8 ≠ 3
hidden-triplets-in-a-block: b7{r9c1 r8c2 r8c1}{n4 n6 n7} ==> r9c1 ≠ 9, r9c1 ≠ 8, r9c1 ≠ 5, r9c1 ≠ 3, r8c2 ≠ 9, r8c2 ≠ 8, r8c1 ≠ 9, r8c1 ≠ 8
whip[1]: b7n9{r9c3 .} ==> r1c3 ≠ 9, r5c3 ≠ 9
naked-pairs-in-a-row: r5{c3 c4}{n5 n8} ==> r5c7 ≠ 8, r5c1 ≠ 8, r5c1 ≠ 5
whip[1]: c7n8{r9 .} ==> r7c8 ≠ 8, r9c8 ≠ 8
swordfish-in-columns: n3{c3 c6 c7}{r9 r2 r1} ==> r9c9 ≠ 3, r9c8 ≠ 3, r2c1 ≠ 3, r1c1 ≠ 3
jellyfish-in-columns: n8{c3 c4 c6 c7}{r9 r5 r1 r8} ==> r9c5 ≠ 8, r1c5 ≠ 8, r1c2 ≠ 8, r1c1 ≠ 8
naked-quads-in-a-block: b1{r1c1 r1c2 r2c1 r2c2}{n4 n9 n6 n5} ==> r3c2 ≠ 9, r3c2 ≠ 4, r3c1 ≠ 9, r3c1 ≠ 4, r2c3 ≠ 5
whip[1]: r3n9{c9 .} ==> r1c7 ≠ 9
x-wing-in-columns: n5{c3 c4}{r5 r9} ==> r9c5 ≠ 5
naked-quads-in-a-row: r9{c1 c5 c9 c8}{n4 n7 n6 n9} ==> r9c7 ≠ 9, r9c7 ≠ 4, r9c4 ≠ 7, r9c3 ≠ 9
stte
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Re: Q is for Quad

Postby mith » Mon Aug 24, 2020 3:17 am

Yeah, you only need three two or three depending on the ordering of techs (though both SE and Hodoku use four).
Last edited by mith on Mon Aug 24, 2020 4:51 am, edited 2 times in total.
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Re: Q is for Quad

Postby pjb » Mon Aug 24, 2020 3:33 am

Slightly different to leren: Two MSLSs:

16 cell Truths: r3467 c2589; 16 links: 49r3, 7r4, 9r6, 6r7, 158c2, 158c5, 238c8, 23c9
11 eliminations: r3c1<>4, r3c1<>9, r4c1<>7, r6c1<>9, r1c2<>8, r2c2<>5, r1c5<>8, r9c5<>5, r9c5<>8, r9c8<>3, r9c9<>3

16 cell Truths: c2589 r3467, 16 links: 18c2, 18c5, 238c8, 23c9, 49r3, 7r4, 59r6, 56r7
2 eliminations: r67c1<>5

Then 2 naked quads (1238 at r3467c1, 4679 at r1c1258) and one naked triple of 469 at r1c12, r2c2 => stte

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Re: Q is for Quad

Postby rjamil » Mon Aug 24, 2020 1:37 pm

Three (4679) NQ / 9 step STTE solution:

Code: Select all
 +---------------------+------------------+--------------------+
 | 4689-3   4689  238  | 1278  478   1238 | 1349  67     5     |
 | 456-3    456   235  | 127   9     123  | 134   67     8     |
 | 1(3)489  1489  7    | 6     48    5    | 2     (3)49  (3)49 |
 +---------------------+------------------+--------------------+
 | 1278     178   6    | 4     18    9    | 5     2(3)8  2(3)7 |
 | 79       3     58   | 58    2     6    | 49    1      479   |
 | 12589    1589  4    | 3     158   7    | 6     289    29    |
 +---------------------+------------------+--------------------+
 | (3)58    58    1    | 9     568   4    | 7     2(3)   2(3)6 |
 | 467      467   89   | 278   3     28   | 489   5      1     |
 | 47       2     3589 | 1578  5678  18   | 3489  49-3   469-3 |
 +---------------------+------------------+--------------------+
1) SF: 3 @ r347c189 Row wise;
Code: Select all
 +-----------------------+--------------------+------------------+
 | 469-8    469-8   238  | 1278  47-8    1238 | 1349  67     5   |
 | 456      456     235  | 127   9       123  | 134   67     8   |
 | 134(8)9  14(8)9  7    | 6     4(8)    5    | 2     349    349 |
 +-----------------------+--------------------+------------------+
 | 127(8)   17(8)   6    | 4     1(8)    9    | 5     23(8)  237 |
 | 79       3       58   | 58    2       6    | 49    1      479 |
 | 125(8)9  15(8)9  4    | 3     15(8)   7    | 6     2(8)9  29  |
 +-----------------------+--------------------+------------------+
 | 35(8)    5(8)    1    | 9     56(8)   4    | 7     23     236 |
 | 467      467     89   | 278   3       28   | 489   5      1   |
 | 47       2       3589 | 1578  567-8   18   | 3489  49     469 |
 +-----------------------+--------------------+------------------+
2) JF: 8 @ r3467c1258 Row wise;
3) NQ: 4679 @ r1c1258 in Row 1;
4) LC (Type 2 Claiming): 9 @ r1c123;
5) NQ: 4679 @ r1589c1 in Column 1;
6) NS: 5 @ r2c1;
7) NT: 469 @ r1c12 r2c2 in Box 1;
8) X-Wing: 5 @ r67c25 Row wise;
9) NQ: 4679 @ r9c1589 in Row 9; stte

R. Jamil
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