## Sunday puzzle (multi steps)

Post puzzles for others to solve here.

### Sunday puzzle (multi steps)

Can anyone find a neat solution not necessary in one step.(perhaps as a bonus)
02-03-21-extreme-plus.png (14.8 KiB) Viewed 394 times

Code: Select all
`39.2.57.......7...4....8.....4.5.2.15.....3..9.23..4...6.....82.......7..4.6.....`
urhegyi

Posts: 406
Joined: 13 April 2020

### Re: Sunday puzzle (multi steps)

A mix of different moves, starting with:
Code: Select all
` 3       9       8      | 2      14     5      | 7      14     6       6       25      15     | 149    3      7      | 8      124    59      4       257     157    | 19     6      8      | 159    123    359    ------------------------+----------------------+--------------------- 78      3       4      | 78     5      9      | 2      6      1       5       178     6      | 1478   12478  124    | 3      9      78      9       178     2      | 3      178    6      | 4      5      78     ------------------------+----------------------+--------------------- 17      6       3579   | 1457   1479   134    | 159    8      2       128     58      359    | 158    1289   123    | 6      7      4       1278    4       579    | 6      12789  12     | 159    13     359    `

1. Double ALS at r9c6 and r8c23456, with X-Z values 1 and 2 => -1 r7c456, -1 r9c5, -2 r9c5, -8 r8c1,
2. BUG-lite (type 1) of 178 at r5c259, r6c259 => -1 r5c5, -7 r5c5, -8 r5c5
3. (9=5)r2c9 - (5=9)r3c47 => -9 r3c9
4. (1=7)r6c5 - (7)r45c4 = (7-5)r7c4 = (5)r8c4 - (5=8*)r8c2 - (8)r6c2 = (8)r6c9 - (8=7)r5c9 - (7|8*=1)r5c2 => -1 r5c46, r6c2; stte

Phil
Last edited by pjb on Sun Feb 28, 2021 6:45 am, edited 1 time in total.
pjb
2014 Supporter

Posts: 2310
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Sunday puzzle (multi steps)

.

6 singles to the following
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`;;; Resolution state RS0:   3         9         8         2         14        5         7         14        6            126       125       156       149       13469     7         8         123459    359          4         1257      1567      19        1369      8         159       12359     359          678       3         4         789       5         69        2         69        1            5         178       167       14789     1246789   12469     3         69        789          9         178       2         3         1678      16        4         56        578          17        6         13579     14579     13479     1349      159       8         2            128       1258      1359      1589      12389     1239      6         7         4            1278      4         13579     6         123789    1239      159       1359      359`

whip[1]: c6n3{r9 .} ==> r9c5 ≠ 3, r7c5 ≠ 3, r8c5 ≠ 3
whip[1]: c6n6{r6 .} ==> r6c5 ≠ 6, r5c5 ≠ 6
whip[1]: b9n3{r9c9 .} ==> r9c6 ≠ 3, r9c3 ≠ 3
Code: Select all
`;;; Resolution state RS1:   3         9         8         2         14        5         7         14        6            126       125       156       149       13469     7         8         123459    359          4         1257      1567      19        1369      8         159       12359     359          678       3         4         789       5         69        2         69        1            5         178       167       14789     124789    12469     3         69        789          9         178       2         3         178       16        4         56        578          17        6         13579     14579     1479      1349      159       8         2            128       1258      1359      1589      1289      1239      6         7         4            1278      4         1579      6         12789     129       159       1359      359`

naked-pairs-in-a-column: c8{r4 r5}{n6 n9} ==> r9c8 ≠ 9, r6c8 ≠ 6, r3c8 ≠ 9, r2c8 ≠ 9
singles ==> r6c8 = 5, r6c6 = 6, r4c6 = 9, r4c8 = 6, r5c8 = 9, r5c3 = 6, r2c1 = 6, r3c5 = 6, r2c5 = 3
whip[1]: c5n9{r9 .} ==> r7c4 ≠ 9, r8c4 ≠ 9
whip[1]: c1n1{r9 .} ==> r7c3 ≠ 1, r8c2 ≠ 1, r8c3 ≠ 1, r9c3 ≠ 1
whip[1]: c3n1{r3 .} ==> r2c2 ≠ 1, r3c2 ≠ 1
whip[1]: c1n2{r9 .} ==> r8c2 ≠ 2
Code: Select all
`;;; Resolution state RS2:   3         9         8         2         14        5         7         14        6            6         25        15        149       3         7         8         124       59           4         257       157       19        6         8         159       123       359          78        3         4         78        5         9         2         6         1            5         178       6         1478      12478     124       3         9         78           9         178       2         3         178       6         4         5         78           17        6         3579      1457      1479      134       159       8         2            128       58        359       158       1289      123       6         7         4            1278      4         579       6         12789     12        159       13        359`

From this point on (which some would consider as "no-step"), there are two possibilities:

1) Using SudoRules standard simplest-first strategy, requiring only very simple short reversible chains:
finned-x-wing-in-rows: n8{r9 r4}{c1 c5} ==> r6c5 ≠ 8, r5c5 ≠ 8
whip[1]: c5n8{r9 .} ==> r8c4 ≠ 8
biv-chain[3]: r7c1{n1 n7} - r4n7{c1 c4} - r6c5{n7 n1} ==> r7c5 ≠ 1
biv-chain[3]: r4n7{c1 c4} - b5n8{r4c4 r5c4} - r5c9{n8 n7} ==> r5c2 ≠ 7
biv-chain-rc[3]: r5c2{n1 n8} - r8c2{n8 n5} - r8c4{n5 n1} ==> r5c4 ≠ 1
biv-chain[3]: r9n8{c5 c1} - r8c2{n8 n5} - r8c4{n5 n1} ==> r9c5 ≠ 1
z-chain-rc[3]: r3c4{n9 n1} - r3c7{n1 n5} - r2c9{n5 .} ==> r3c9 ≠ 9
z-chain[3]: r5n2{c5 c6} - b5n1{r5c6 r6c5} - r1c5{n1 .} ==> r5c5 ≠ 4
z-chain-bn[3]: b2n4{r1c5 r2c4} - b5n4{r5c4 r5c6} - b5n1{r5c6 .} ==> r1c5 ≠ 1
Singles+ 1 whip[1] to the end

2) Looking for a 1-step solution
There are:
2 BRT-anti-backdoors: n8r4c4 n7r4c1
3 W1-anti-backdoors: n8r4c4 n7r4c1 n7r3c2
6 S-anti-backdoors: n8r9c1 n5r8c2 n5r7c4 n8r4c4 n7r4c1 n7r3c2 , 4 of which give a 1-step solution:

Code: Select all
`whip[8]: r4n8{c1 c4} - c5n8{r6 r8} - r8c2{n8 n5} - r8c4{n5 n1} - c6n1{r9 r5} - r6c5{n1 n7} - c4n7{r5 r7} - c4n5{r7 .} ==> r9c1 ≠ 8Singles and whips[1] to the endwhip[9]: r2c2{n5 n2} - r3c2{n2 n7} - b4n7{r6c2 r4c1} - r4c4{n7 n8} - r8c4{n8 n1} - c6n1{r9 r5} - r6c5{n1 n7} - c4n7{r5 r7} - c4n5{r7 .} ==> r8c2 ≠ 5sttewhip[9]: r4c1{n8 n7} - c2n7{r6 r3} - c2n2{r3 r2} - c2n5{r2 r8} - r8c4{n5 n1} - c6n1{r9 r5} - r6c5{n1 n7} - c4n7{r5 r7} - c4n5{r7 .} ==> r4c4 ≠ 8sttewhip[9]: c2n7{r6 r3} - c2n2{r3 r2} - c2n5{r2 r8} - c4n5{r8 r7} - c4n7{r7 r5} - r4c4{n7 n8} - r6c5{n8 n1} - r1c5{n1 n4} - c4n4{r2 .} ==> r4c1 ≠ 7stte`

Of course, using so long chains for a puzzle that can be solved in S+W3 is questionable.

However, for those who would insist on a 1-step solution starting from the givens, there's one with Forcing-T&E:
FORCING-T&E(BRT) applied to bivalue candidates n7r4c1 and n7r4c4 :
===> 24 values decided in both cases: n1r7c1 n6r2c1 n6r5c3 n9r5c8 n6r4c8 n5r6c8 n9r4c6 n6r6c6 n6r3c5 n3r2c5 n2r2c2 n2r3c8 n3r3c9 n3r9c8 n1r9c7 n2r9c6 n2r8c1 n7r7c5 n1r6c5 n1r5c2 n4r1c5 n2r5c5 n1r1c8 n4r2c8
===> 108 candidates eliminated in both cases: n1r1c5 n4r1c8 n1r2c1 n2r2c1 n1r2c2 n5r2c2 n6r2c3 n1r2c4 n4r2c4 n1r2c5 n4r2c5 n6r2c5 n9r2c5 n1r2c8 n2r2c8 n3r2c8 n5r2c8 n9r2c8 n3r2c9 n1r3c2 n2r3c2 n5r3c3 n6r3c3 n1r3c5 n3r3c5 n9r3c5 n1r3c7 n1r3c8 n3r3c8 n5r3c8 n9r3c8 n5r3c9 n9r3c9 n6r4c1 n9r4c4 n6r4c6 n9r4c8 n7r5c2 n8r5c2 n1r5c3 n7r5c3 n1r5c4 n7r5c4 n9r5c4 n1r5c5 n4r5c5 n6r5c5 n7r5c5 n8r5c5 n9r5c5 n1r5c6 n2r5c6 n6r5c6 n9r5c6 n6r5c8 n9r5c9 n1r6c2 n6r6c5 n7r6c5 n8r6c5 n1r6c6 n6r6c8 n5r6c9 n7r7c1 n1r7c3 n5r7c3 n7r7c3 n1r7c4 n7r7c4 n9r7c4 n1r7c5 n3r7c5 n4r7c5 n9r7c5 n1r7c6 n9r7c6 n1r7c7 n1r8c1 n8r8c1 n1r8c2 n2r8c2 n1r8c3 n5r8c3 n8r8c4 n9r8c4 n1r8c5 n2r8c5 n3r8c5 n2r8c6 n9r8c6 n1r9c1 n2r9c1 n1r9c3 n3r9c3 n9r9c3 n1r9c5 n2r9c5 n3r9c5 n7r9c5 n1r9c6 n3r9c6 n9r9c6 n5r9c7 n9r9c7 n1r9c8 n5r9c8 n9r9c8 n3r9c9
Code: Select all
`CURRENT RESOLUTION STATE:    3         9         8         2         4         5         7         1         6            6         2         15        9         3         7         8         4         59           4         57        17        19        6         8         59        2         3            78        3         4         78        5         9         2         6         1            5         1         6         48        2         4         3         9         78           9         78        2         3         1         6         4         5         78           1         6         39        45        7         34        59        8         2            2         58        39        15        89        13        6         7         4            78        4         57        6         89        2         1         3         59`

stte
denis_berthier
2010 Supporter

Posts: 2206
Joined: 19 June 2007
Location: Paris

### Re: Sunday puzzle (multi steps)

Code: Select all
`*------------------------------------------------*| 3    9   8    | 2     14     5   | 7   14  6   || 6    25  15   | 149   3      7   | 8   124 59  || 4    257 157  | 19    6      8   | 159 123 359 ||---------------+------------------+-------------||b78   3   4    |a78    5      9   | 2   6   1   || 5    178 6    | 1478  1247-8 124 | 3   9   78  || 9    178 2    | 3     17-8   6   | 4   5   78  ||---------------+------------------+-------------|| 17   6   3579 | 1457  1479   134 | 159 8   2   || 128  58  359  | 15-8  1289   123 | 6   7   4   ||c1278 4   579  | 6    d12789  12  | 159 13  359 |*------------------------------------------------*`

Skyscraper : (8) r4c4 = r1c4 - r1c9 = (8) r5c9 => - 8 r56c5, r8c4;

Code: Select all
`*--------------------------------------------------*| 3    9   8    |  2      14     5   | 7   14  6   || 6    25  15   |  149    3      7   | 8   124 59  || 4    257 157  |  19     6      8   | 159 123 359 ||---------------+--------------------+-------------|| 78   3   4    | e78     5      9   | 2   6   1   || 5    178 6    | e1478   1247  c124 | 3   9   78  || 9    178 2    |  3     d17     6   | 4   5   78  ||---------------+--------------------+-------------|| 17   6   3579 | f147-5  1479  b134 | 159 8   2   || 128  58  359  | a15     1289  b123 | 6   7   4   || 1278 4   579  |  6      12789 b12  | 159 13  359 |*--------------------------------------------------*`

(5=1) r8c4 - r789c6 = r5c6 - (1=7) r6c5 - r45c4 = (7) r7c4; => - 5 r7c4; stte

Leren
Last edited by Leren on Sun Feb 28, 2021 9:10 am, edited 1 time in total.
Leren

Posts: 4067
Joined: 03 June 2012

### Re: Sunday puzzle (multi steps)

Same as Leren
Hidden Text: Show
Code: Select all
`Hidden Single: 4 in b9 => r8c9=4Hidden Single: 6 in b9 => r8c7=6Hidden Single: 3 in b4 => r4c2=3Hidden Single: 8 in c7 => r2c7=8Hidden Single: 8 in b1 => r1c3=8Naked Single: r1c9=6Locked Candidates 1 (Pointing): 3 in b9 => r9c3<>3,r9c5<>3,r9c6<>3Locked Candidates 1 (Pointing): 3 in b2 => r7c5<>3,r8c5<>3Locked Candidates 1 (Pointing): 6 in b2 => r5c5<>6,r6c5<>6Locked Pair: in r4c8,r5c8 => r5c9<>9,r6c8<>6,r2c8<>9,r3c8<>9,r6c8<>6,r9c8<>9,Hidden Single: 6 in r6 => r6c6=6Naked Single: r4c6=9Hidden Single: 9 in b6 => r5c8=9Hidden Single: 6 in b6 => r4c8=6Hidden Single: 6 in b4 => r5c3=6Hidden Single: 6 in b1 => r2c1=6Hidden Single: 6 in b2 => r3c5=6Hidden Single: 3 in b2 => r2c5=3Naked Single: r6c8=5Locked Candidates 2 (Claiming): 1 in c1 => r8c2<>1,r7c3<>1,r8c3<>1,r9c3<>1Locked Candidates 2 (Claiming): 2 in c1 => r8c2<>2Locked Candidates 1 (Pointing): 1 in b4 => r2c2<>1,r3c2<>1Locked Candidates 1 (Pointing): 9 in b2 => r7c4<>9,r8c4<>9Skyscraper : 8 in r4c4,r9c5 connected by r49c1 => r56c5,r8c4 <> 8Grouped AIC Type 2: 7r7c4 = r45c4 - (7=1)r6c5 - r5c6 = r789c6 - (1=5)r8c4 => r7c4<>5Hidden Single: 5 in b8 => r8c4=5Naked Single: r8c2=8Hidden Single: 8 in b8 => r9c5=8Hidden Single: 8 in b4 => r4c1=8Full House: r4c4=7Hidden Single: 7 in b8 => r7c5=7Hidden Single: 9 in b8 => r8c5=9Hidden Single: 8 in b5 => r5c4=8Hidden Single: 8 in b6 => r6c9=8Full House: r5c9=7Hidden Single: 7 in b4 => r6c2=7Full House: r6c5=1Full House: r5c2=1Hidden Single: 7 in b1 => r3c3=7Hidden Single: 7 in b7 => r9c1=7Hidden Single: 2 in b7 => r8c1=2Full House: r7c1=1Hidden Single: 2 in b8 => r9c6=2Hidden Single: 1 in b8 => r8c6=1Full House: r8c3=3Hidden Single: 3 in b8 => r7c6=3Full House: r5c6=4Full House: r5c5=2Full House: r1c5=4Full House: r1c8=1Full House: r7c4=4Hidden Single: 1 in b9 => r9c7=1Hidden Single: 4 in b3 => r2c8=4Hidden Single: 2 in b3 => r3c8=2Full House: r9c8=3Hidden Single: 3 in b3 => r3c9=3Hidden Single: 1 in b1 => r2c3=1Hidden Single: 1 in b2 => r3c4=1Full House: r2c4=9Hidden Single: 9 in b3 => r3c7=9Full House: r3c2=5Full House: r2c2=2Full House: r2c9=5Full House: r7c7=5Full House: r7c3=9Full House: r9c3=5Full House: r9c9=9`
yzfwsf

Posts: 337
Joined: 16 April 2019

### Re: Sunday puzzle (multi steps)

After the 'lcls' steps, as Cenoman uses to say, the sudoku state becomes as follows:
Code: Select all
`.-----------------.------------------.---------------.| 3     9    8    | 2     14     5   | 7    14   6   || 6     25   15   | 149   3      7   | 8    124  59  || 4     257  157  | 19    6      8   | 159  123  359 |:-----------------+------------------+---------------:| 78    3    4    | 78    5      9   | 2    6    1   || 5     178  6    | 1478  12478  124 | 3    9    78  || 9     178  2    | 3     178    6   | 4    5    78  |:-----------------+------------------+---------------:| 17    6    3579 | 1457  1479   134 | 159  8    2   || 128   58   359  | 158   1289   123 | 6    7    4   || 1278  4    579  | 6     12789  12  | 159  13   359 |'-----------------'------------------'---------------'`

Now it is possible to get a one-step solution with a forcing net. Maybe this is not a 'nice' solution, but the logical chains can be easily described graphically. I will try to prove that the premise r4c1=7 leads to r7c4=5 and r7c4=4, which is a contradiction. So r4c1=8, and we get a sequence of singles.
See the picture: https://disk.yandex.ru/i/rBJo3ttnB5sQeg
1. The red chain. r4c1=7 => r4c4<>7 (1.1) => r4c4=8 => r6c5<>8 (1.2)
2. The black chains. r4c1=7 => r56c2<>7 => r3c2=7 =>
2.1. r3c2<>5
2.2. r3c3<>2 =>r3c8=2 => r2c8<>2 => r2c2=2 => r2c2<>5 => (because of 2.1) r8c2=5 => r8c4<>5 => r7c4=5 (2.2.1) => r7c4<>7 => (because of 1.1) r5c4=7 =>
2.2.2. r5c4<>4
2.2.3. r6c5<>7 => (because of 1.2) r6c5=1 => r1c5<>1 => r1c5=4 => r2c4<>4 => (because of 2.2.2) r7c4=4 - contradiction with 2.2.1.
Consequently, r4c1<>7, sste.
Bogdan
AnotherLife

Posts: 48
Joined: 07 January 2021
Location: Moscow, Russia

### Re: Sunday puzzle (multi steps)

AnotherLife wrote:Now it is possible to get a one-step solution with a forcing net. [...]

Starting with the same PM, the same elimination was obtained by my last whip[9] instead of this complicated net.
denis_berthier
2010 Supporter

Posts: 2206
Joined: 19 June 2007
Location: Paris

### Re: Sunday puzzle (multi steps)

denis_berthier wrote:whip[9]: c2n7{r6 r3} - c2n2{r3 r2} - c2n5{r2 r8} - c4n5{r8 r7} - c4n7{r7 r5} - r4c4{n7 n8} - r6c5{n8 n1} - r1c5{n1 n4} - c4n4{r2 .} ==> r4c1 ≠ 7

Can you explain your solution graphically?
Bogdan
AnotherLife

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Joined: 07 January 2021
Location: Moscow, Russia

### Re: Sunday puzzle (multi steps)

AnotherLife wrote:
denis_berthier wrote:whip[9]: c2n7{r6 r3} - c2n2{r3 r2} - c2n5{r2 r8} - c4n5{r8 r7} - c4n7{r7 r5} - r4c4{n7 n8} - r6c5{n8 n1} - r1c5{n1 n4} - c4n4{r2 .} ==> r4c1 ≠ 7

Can you explain your solution graphically?

You can find general graphics for whips in the Basic User Manual for CSP-Rules-V2.1: https://github.com/denis-berthier/CSP-Rules-V2.1/blob/master/Docs/2021-BUM-V2.1-r2.pdf, section 1.7
denis_berthier
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### Re: Sunday puzzle (multi steps)

Hi denis:
Can you provide a graphical representation of the specific steps you found in this puzzle? Convenient to compare and see what is the difference with AIC? Thank you .
yzfwsf

Posts: 337
Joined: 16 April 2019

### Re: Sunday puzzle (multi steps)

yzfwsf wrote:Hi denis:
Can you provide a graphical representation of the specific steps you found in this puzzle? Convenient to compare and see what is the difference with AIC? Thank you .

The way whips are written is, in and of itself, a graphical representation. Read the conventions in the BUM and tell me if there is anything in particular that you don't understand.
Graphically, a whip IS the same thing as a bivalue-chain, i.e. a basic AIC and all the elements present in the AIC are present in the whip notation. You need to understand the general nrc notation, the fact that z- and t- candidates are not part of the whip and the reasons why they can be abstracted.
I've met people here who have no sense of abstraction. It's a big problem for them to understand whips.
denis_berthier
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Location: Paris

### Re: Sunday puzzle (multi steps)

Hello,

After basics

Code: Select all
`   1     2    3      4     5      6     7    8    9.------------------+------------------+---------------.|  3     9    8    | 2     14     5   | 7    14   6   | 1|  6     25   15   | 149   3      7   | 8    124  59  | 2|  4     257  157  | 19    6      8   | 159  123  359 | 3|------------------+------------------+---------------|| d78*   3    4    |e78#   5      9   | 2    6    1   | 4|  5     178  6    | 1478  1247-8 124 | 3    9    78  | 5|  9     178  2    | 3     17-8   6   | 4    5    78  | 6|------------------+------------------+---------------||  1-7   6    3579 | 1457  1479   134 | 159  8    2   | 7|  128   58   359  | 15-8  1289   123 | 6    7    4   | 8|ca1278* 4   a579* | 6    b12789# 12  | 159  13   359 | 9'------------------+------------------+---------------'`

1. (7)r9c13=(7)r9c5-(8)r9c5=(8)r9c1-(8=7)r4c1-(7=8)r4c4 => -7 r7c1, -8 r8c4, -8 r56c5

Code: Select all
`   1     2    3      4     5      6     7    8    9.------------------+------------------+---------------.|  3     9    8    | 2     14     5   | 7    14   6   | 1|  6     25   15   | 149   3      7   | 8    124  59  | 2|  4     257  157  | 19    6      8   | 159  123  359 | 3|------------------+------------------+---------------|| d78    3    4    |e78    5      9   | 2    6    1   | 4|  5     178  6    | 1478  12478  124 | 3    9    78  | 5|  9     178  2    | 3     17     6   | 4    5    78  | 6|------------------+------------------+---------------||  1     6    3579 |a45-7  479    34  | 59   8    2   | 7| c28   c58   359  |b15    1289   123 | 6    7    4   | 8| c278   4    579  | 6     12789  12  | 159  13   359 | 9'------------------+------------------+---------------'`

2. (5)r7c4=r8c4-(5=287)b7p457-(7)r4c1=(7)r4c4 => -7 r7c4; lclste

Regards,
jco

Edit: fixed typos and corrected to lclste.
Last edited by jco on Wed Mar 03, 2021 12:01 pm, edited 9 times in total.
JCO
jco

Posts: 93
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### Re: Sunday puzzle (multi steps)

Hi Denis,
I think that yzfwsf and Another Life would like to see the example whip[9] explained in detail. I think there are many members of this forum [me included] who would appreciate a visual explanation. If I am correct, the visuals [for this example puzzle] would be many. One will need the grid with candidates displayed in all 4 ways [rc, rn cn, bn] and for each of the 9 parts of the whip[9]. So, I think there might be as many as 36! grids.
I think you may say I am wrong and you will say I should read the BUM. All I can say is that I have tried to read and study the BUM since you first advised us to do so. Indeed, even the notation for whip[1] still eludes me. On pg 16, one reads r3n4{c5 .} => r4c6 ≠ 4. What does the dot . mean? I would appreciate an explanation that is specific to the 9x9 Sudoku and not the 'general' case.
Perhaps you will argue that we all need to 'see' things in 3D. Well, 3D displays are not easy to reconcile. XSudo is amazing but not for the faint of heart.
Regards Gordon
ghfick

Posts: 133
Joined: 06 April 2016

### Re: Sunday puzzle (multi steps)

ghfick wrote:Hi Denis,
I think that yzfwsf and Another Life would like to see the example whip[9] explained in detail. I think there are many members of this forum [me included] who would appreciate a visual explanation. If I am correct, the visuals [for this example puzzle] would be many. One will need the grid with candidates displayed in all 4 ways [rc, rn cn, bn] and for each of the 9 parts of the whip[9]. So, I think there might be as many as 36! grids.
I think you may say I am wrong and you will say I should read the BUM. All I can say is that I have tried to read and study the BUM since you first advised us to do so. Indeed, even the notation for whip[1] still eludes me. On pg 16, one reads r3n4{c5 .} => r4c6 ≠ 4. What does the dot . mean? I would appreciate an explanation that is specific to the 9x9 Sudoku and not the 'general' case.
Perhaps you will argue that we all need to 'see' things in 3D. Well, 3D displays are not easy to reconcile. XSudo is amazing but not for the faint of heart.
Regards Gordon

The only grid you need to see to understand whips is the standard one. And the only thing you have to understand is a whip looks like a bivalue-chain, i.e. a basic AIC: z- and t- candidates and the associated links don't belong to the whip and don't have to be displayed.
In
Code: Select all
`whip[9]: c2n7{r6 r3} - c2n2{r3 r2} - c2n5{r2 r8} - c4n5{r8 r7} - c4n7{r7 r5} - r4c4{n7 n8} - r6c5{n8 n1} - r1c5{n1 n4} - c4n4{r2 .} ==> r4c1 ≠ 7`
,
- is a link, what you would call a "weak link"
{ } is the content of a csp-variable, which would be translated as a "strong link" in AIC notation. Unfortunately, AIC notation is totally inconsistent, as it makes a difference between bivalue and bilocal.

Making AIC notation consistent, you could write the previous whip as:
whip[9]: c2n7(r6=r3) - c2n2(r3=r2) - c2n5(r2=r8) - c4n5(r8=r7) - c4n7(r7=r5) - r4c4(n7=n8) - r6c5(n8=n1) - r1c5(n1=n4) - c4n4(r2=.) ==> r4c1 ≠ 7
(the "." denotes the absence of a candidate)

r3n4{c5 .} => r4c6 ≠ 4 is for Sudoku !!
denis_berthier
2010 Supporter

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Location: Paris

### Re: Sunday puzzle (multi steps)

If 7r4c1 is true then it leads to no 4 possible in c4, so it can be removed.
Starting at Blue point (false) and follow the manual added blue line.
Note that blue point was group 7r56c2 = 7r3c2 .., but gets reduced to a single in the end.
Note that 7r4c4 was already excluded at start of chain.
Note that . refers to 4r57c4
Another name could be something like "unit contradiction in net".
creint

Posts: 271
Joined: 20 January 2018

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