## Q is for Quad

Post puzzles for others to solve here.

### Q is for Quad

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

Posts: 301
Joined: 14 July 2020

### Re: Q is for Quad

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 !

Leren
Leren

Posts: 3928
Joined: 03 June 2012

### Re: Q is for Quad

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
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: Q is for Quad

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.
mith

Posts: 301
Joined: 14 July 2020

### Re: Q is for Quad

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

Phil
pjb
2014 Supporter

Posts: 2230
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Q is for Quad

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
rjamil

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Joined: 15 October 2014
Location: Karachi, Pakistan

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