## New member....lost in a sea of numbers......

Post the puzzle or solving technique that's causing you trouble and someone will help

### New member....lost in a sea of numbers......

| 256 3 4 | 68 9 16 | 1268 7 125 |
| 2569 159 12569 | 47 168 47 | 12689 12568 3 |
| 69 8 7 | 2 3 5 | 1469 16 149 |
-----------------------------------------------------------------------------------
| 1 2 589 | 34589 58 349 | 7 35 6 |
| 45689 459 5689 | 35689 7 12369 | 1239 1235 1259 |
| 3 7 569 | 569 1256 1269 | 129 4 8 |
----------------------------------------------------------------------------------
| 245 45 235 | 1 256 8 | 2346 9 7 |
| 7 145 12358 | 3569 256 2369 | 123468 123568 1245 |
| 289 6 12389 | 37 4 237 | 5 1238 12 |

Hello All!
I'm hoping someone can assist me here. I'm sort of ashamed of all the numbers still on the table, but I'm an intermediate level at best I guess, and learned mostly on my own plus ready AngusJ teachings on pairs/triples/quads (hidden and naked) xy-wing and x-wing, but NOT too clear on the basic x-cycle in actual application (read reasonably good explanation on this site, but haven't had enough practical use).

To get as far as I did on the above (from Rofact International magazine, puzzle # 80 in the offchance someone's done it) I used an x-wing and a naked quad, and then got stuck...

Is there someone who could describe and perhaps demonstrate how to get at least the next number? P.S. And if someone can describe how to get the puzzle info into the posting all nicely aligned that would be great!
EHoward

Posts: 6
Joined: 11 January 2006

First of all: did you read: New topics - How to ask for help? (If you did: was it too unclear on how to format your post?)

This post had a formatted version of the grid. But the next post also has it. So there is no reason for it to be here. (The next post is more useful then this one.)
Last edited by Animator on Wed Jan 11, 2006 7:18 pm, edited 1 time in total.
Animator

Posts: 469
Joined: 08 April 2005

You had some eliminations I couldn't easily see, so starting over, I got to here
Code: Select all
`+---------------------+----------------------+---------------------+| 256    3     4      | 68      9     16     | 1268    7      125  || 2569   159   12569  | 47      168   47     | 12689   12568  3    || 69     8     7      | 2       3     5      | 1469    16     149  |+---------------------+----------------------+---------------------+| 1      2     589    | 34589   58    349    | 7       35     6    || 45689  459   5689   | 345689  7     123469 | 1239    1235   1259 || 3      7     569    | 569     1256  1269   | 129     4      8    |+---------------------+----------------------+---------------------+| 245    45    235    | 1       256   8      | 2346    9      7    || 7      1459  123589 | 3569    256   2369   | 123468  12368  124  || 289    6     12389  | 379     4     2379   | 5       1238   12   |+---------------------+----------------------+---------------------+`

The candidate 1 on row 2 is locked in box 1
Translation: all 1's in box 1 are on row 2. Hence 1 must be in one of those cells. Therefore 1's can be erased from all other cells in row 2.

Then some 1's can be placed (r1c6, r6c5)

Now The candidate 2 on column 6 is locked in box 5.

Do those eliminations to get here:
Code: Select all
`+---------------------+--------------------+---------------------+| 256    3     4      | 68      9    1     | 268     7      25   || 2569   159   12569  | 47      68   47    | 2689    2568   3    || 69     8     7      | 2       3    5     | 1469    16     149  |+---------------------+--------------------+---------------------+| 1      2     589    | 34589   58   349   | 7       35     6    || 45689  459   5689   | 345689  7    23469 | 1239    1235   1259 || 3      7     569    | 569     1    269   | 29      4      8    |+---------------------+--------------------+---------------------+| 245    45    235    | 1       256  8     | 2346    9      7    || 7      1459  123589 | 3569    256  369   | 123468  12368  124  || 289    6     12389  | 379     4    379   | 5       1238   12   |+---------------------+--------------------+---------------------+`

Now after seeing the 4's locked on row 5 in box 4 I got stuck, too.

Maybe someone else can see. You are now in the realm of puzzles that are tough, I fear.

Mac
Last edited by QBasicMac on Wed Jan 11, 2006 7:38 pm, edited 1 time in total.
QBasicMac

Posts: 441
Joined: 13 July 2005

This probably requires forcing chains - Simple Sudoku got stuck at the same point as Mac. I've been practising colouring with some 'Expert' puzzles on SS and think I've finally got the hang of it, but forcing chains are something else. This one is too hard for me!
CathyW

Posts: 316
Joined: 20 June 2005

### Thanks for the help!

Thanks much for the help so far! I will see if I can get anywhere further from where you've gotten me and post it if I do. I think I'll likely need to resort to a hidden quad or naked quad along the route...at least that was the case for a similar puzzle from the same magazine...
EHoward

Posts: 6
Joined: 11 January 2006

CathyW wrote:This one is too hard for me!

Even tough on my QBasic program that does T&E to verify a puzzle is valid.

Mac

-34-9--7---------3-87235---12----7-6----
7----37-----48---1-8-977---------6--4-5--
Calling Function with above puzzle

Entering function at level 1
-34-9--7---------3-87235---12----7-6----7----37-----48---1-8-977---------6--4-5--
Locked candidate 1 in box 1
Locked candidate 4 in box 2
Locked candidate 4 in box 4
Locked candidate 1 in row 3
Hidden single 1 in row 1
Hidden single 1 in col 5
Locked candidate 2 in box 5
Naked pair 68 in box 2

Trying pencilmark 1 in cell r9c9
Entering function at level 2
-34-91-7---------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-5-1
Locked candidate 1 in box 1
Locked candidate 4 in box 2
Locked candidate 4 in box 4
Locked candidate 2 in box 5
Naked pair 68 in box 2

Trying pencilmark 2 in cell r9c8
Entering function at level 3
-34-91-7---------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-521
r8c9 = 4
r3c9 = 9
r3c1 = 6
r3c8 = 1
r3c7 = 4
Hidden single 1 in row 5
Hidden single 9 in col 7
Hidden single 2 in box 6
Hidden single 2 in row 6
r1c9 = 5
r1c1 = 2
Hidden single 2 in row 2
Locked candidate 4 in box 4
Locked candidate 3 in box 6
Locked candidate 8 in box 9
Naked pair 45 in row 7
Naked pair 45 in box 7
Naked pair 68 in row 2

Trying pencilmark 3 in cell r9c6
Entering function at level 4
234-91-75------2-368723541912----7-6----7-1-237--12948---1-8-977-------4-6--43521
Hidden single 7 in col 6
Hidden single 7 in row 9
Hidden single 4 in row 2
Hidden single 4 in row 4
Locked candidate 3 in box 6
Locked candidate 9 in box 8
Locked candidate 8 in box 9
Naked pair 45 in row 7
Naked pair 45 in box 7
r8c2 = 1
Hidden single 1 in row 2
Locked candidate 5 in col 3

Trying pencilmark 8 in cell r9c3
Entering function at level 5
234-91-75--14-72-368723541912---47-6----7-1-237--12948---1-8-9771------4-68743521
Singles: 9 5 9 4 5 8 4
Locked candidate 3 in box 6

Trying pencilmark 6 in cell r8c8
Entering function at level 6
234-91-755914-72-368723541912---47-684--7-1-237--1294845-1-8-9771-----64968743521
Singles: 8 3 9 8 6 6 6 5
Result returned to level 5: Invalid Puzzle

Trying pencilmark 8 in cell r8c8
Entering function at level 6
234-91-755914-72-368723541912---47-684--7-1-237--1294845-1-8-9771-----84968743521
Singles: 6 8 8 5 3 5 6
Result returned to level 5: Invalid Puzzle
Result returned to level 4: Invalid Puzzle

Trying pencilmark 9 in cell r9c3
Entering function at level 5
234-91-75--14-72-368723541912---47-6----7-1-237--12948---1-8-9771------4-69743521
r9c1 = 8
Hidden single 9 in row 4
Hidden single 3 in row 4
Hidden single 3 in row 5
Hidden single 9 in row 8
Singles: 6 5 5 6 8 8 6
Result returned to level 4: Invalid Puzzle
Result returned to level 3: Invalid Puzzle

Trying pencilmark 7 in cell r9c6
Entering function at level 4
234-91-75------2-368723541912----7-6----7-1-237--12948---1-8-977-------4-6--47521
Hidden single 7 in row 2
Hidden single 4 in row 2
Hidden single 4 in row 4
Locked candidate 3 in box 6
Locked candidate 8 in box 9
Naked pair 45 in row 7
Naked pair 45 in box 7

Trying pencilmark 3 in cell r9c4
Entering function at level 5
234-91-75---7-42-368723541912-4--7-6----7-1-237--12948---1-8-977-------4-6-347521
Locked candidate 3 in box 6
Locked candidate 9 in box 8
Locked candidate 8 in box 9
Naked pair 45 in row 7
Naked pair 45 in box 7
r8c2 = 1
Hidden single 1 in row 2
Locked candidate 5 in col 3

Trying pencilmark 8 in cell r9c3
Entering function at level 6
234-91-75--17-42-368723541912-4--7-6----7-1-237--12948---1-8-9771------4-68347521
Singles: 9 5 9 4 5 8 4
Hidden single 8 in col 4
Hidden single 8 in row 2
Hidden single 8 in row 4
Hidden single 5 in col 5
Hidden single 8 in row 8
Hidden single 6 in col 8
Singles: 6 6 2 3
Result returned to level 5: Invalid Puzzle

Trying pencilmark 9 in cell r9c3
Entering function at level 6
234-91-75--17-42-368723541912-4--7-6----7-1-237--12948---1-8-9771------4-69347521
r9c1 = 8
Hidden single 9 in row 4
Hidden single 3 in row 4
Hidden single 3 in row 5
Hidden single 9 in row 8
Singles: 5 6 8 6 3 8 8 5 6
Result returned to level 5: Invalid Puzzle
Result returned to level 4: Invalid Puzzle

Trying pencilmark 9 in cell r9c4
Entering function at level 5
234-91-75---7-42-368723541912-4--7-6----7-1-237--12948---1-8-977-------4-6-947521
r9c1 = 8
r9c3 = 3
Hidden single 3 in row 7
Hidden single 6 in row 7
Hidden single 2 in col 5
Singles: 8 6 5 3 5 6
Result returned to level 4: Invalid Puzzle
Result returned to level 3: Invalid Puzzle

Trying pencilmark 9 in cell r9c6
Entering function at level 4
234-91-75------2-368723541912----7-6----7-1-237--12948---1-8-977-------4-6--49521
Singles: 8 3 7
Hidden single 7 in row 2
Hidden single 3 in row 7
Hidden single 4 in row 2
Hidden single 4 in row 4
Hidden single 6 in row 7
Hidden single 2 in col 5
Singles: 8 6 5 3 5 6
Result returned to level 3: Invalid Puzzle
Result returned to level 2: Invalid Puzzle

Trying pencilmark 3 in cell r9c8
Entering function at level 3
-34-91-7---------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-531
Singles: 5 8 6 9 8
Hidden single 5 in col 9
Hidden single 3 in col 7
Hidden single 1 in row 5
Hidden single 3 in row 7
Hidden single 6 in row 7
Singles: 2 8 6 9 2 4 6 9
Result returned to level 2: Invalid Puzzle

Trying pencilmark 8 in cell r9c8
Entering function at level 3
-34-91-7---------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-581
Hidden single 8 in col 1
Hidden single 4 in box 4
Hidden single 4 in col 1
Hidden single 8 in row 8
r7c2 = 5
Hidden single 1 in col 3
Hidden single 1 in row 8
r2c2 = 9
r3c1 = 6
r3c8 = 1
Hidden single 1 in row 5
Hidden single 9 in col 1
Locked candidate 4 in box 2
Locked candidate 2 in box 5
Locked candidate 3 in box 6
Hidden single 2 in row 9
r7c3 = 3
Hidden single 3 in col 7
Hidden single 4 in row 8
r3c9 = 9
r3c7 = 4
Hidden single 9 in col 7
Hidden single 2 in row 6
Naked pair 25 in row 1
Naked pair 68 in box 2

Trying pencilmark 3 in cell r9c6
Entering function at level 4
-34-91-7--91-----368723541912----7-684--7-1--37--129484531-8-97718---3-4962-43581
r9c4 = 7
Hidden single 7 in row 2
Hidden single 4 in col 6
Hidden single 4 in row 2
Naked pair 25 in row 1

Trying pencilmark 2 in cell r8c8
Entering function at level 5
-34-91-7--914-7--368723541912---47-684--7-1--37--129484531-8-97718---324962743581
r7c7 = 6
r7c5 = 2
Hidden single 6 in row 1
Hidden single 8 in row 1
Hidden single 6 in row 2
Hidden single 8 in col 4
Hidden single 3 in row 4
Hidden single 3 in row 5
Hidden single 6 in box 5
Hidden single 2 in row 5
Hidden single 6 in row 6
Hidden single 9 in col 4
Result returned to level 4: Invalid Puzzle

Trying pencilmark 6 in cell r8c8
Entering function at level 5
-34-91-7--914-7--368723541912---47-684--7-1--37--129484531-8-97718---364962743581
r7c7 = 2
r8c6 = 9
r5c6 = 6
r6c4 = 5
Result returned to level 4: Invalid Puzzle
Result returned to level 3: Invalid Puzzle

Trying pencilmark 7 in cell r9c6
Entering function at level 4
-34-91-7--91-----368723541912----7-684--7-1--37--129484531-8-97718---3-4962-47581
r9c4 = 3
Hidden single 7 in row 2
Hidden single 4 in row 2
Hidden single 4 in row 4
Hidden single 8 in row 4
Hidden single 5 in col 5
Hidden single 2 in row 8
r2c5 = 6
r2c8 = 5
r4c8 = 3
Result returned to level 3: Invalid Puzzle
Result returned to level 2: Invalid Puzzle
Result returned to level 1: Invalid Puzzle

Trying pencilmark 2 in cell r9c9
Entering function at level 2
-34-91-7---------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-5-2
r1c9 = 5
Locked candidate 1 in box 1
Locked candidate 4 in box 2
Locked candidate 4 in box 4
Locked candidate 2 in box 5
Naked pair 68 in box 2

Trying pencilmark 1 in cell r9c8
Entering function at level 3
-34-91-75--------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-512
All Singles
Got 234691875516487923987235461129854736648372159375916248452168397791523684863749512
Result returned to level 2: Single Solution

Trying pencilmark 3 in cell r9c8
Entering function at level 3
-34-91-75--------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-532
Singles: 5 8 6 9 8
Hidden single 3 in col 7
Hidden single 3 in row 7
Hidden single 6 in row 7
Hidden single 1 in row 9
Singles: 2 9 6 9 1 4
Result returned to level 2: Invalid Puzzle

Trying pencilmark 8 in cell r9c8
Entering function at level 3
-34-91-75--------3-87235---12----7-6----7----37--1--48---1-8-977---------6--4-582
Singles: 9 6 1 2 5 4 5 1 4 3 7
Result returned to level 2: Invalid Puzzle
Result returned to level 1: Single Solution

Returned from Function with following result
2346918755164879239872354611298547366483
72159375916248452168397791523684863749512
QBasicMac

Posts: 441
Joined: 13 July 2005

Thanks CathyW. I think I'll have some success tomorrow when I'm fresh. The help earlier from all was good too. When I started the puzzle, I was able to use an x-wing based on 7's in R2C4, R2C6,R9C4, R9C6 to elim 7 from R2C2, R2C3, R9C9 at the outset of the puzzle, and using a naked quad based on 1,4,6,9 in R3, columns 1,7,8,9 allowed me to delete 1&6 from C5. Then I got to where I was and got stuck. The help on the locked 1's in box 1 made all the difference, so I'm hoping I can get to the solution. That program you have is interesting and if I get away from the pencil and paper approach, I'll have to check into it.

EHoward
EHoward

Posts: 6
Joined: 11 January 2006

I just checked my solver it solved it without T&E, unfortunately I haven't developed the solver to a level to explain the outcomes so I won't post it, but it looks like one of those puzzles that can be cracked using the nice loops algorithms which should solve it.

I'll post the logic until the point where the nice loops should take ove.
Code: Select all
`*--------------------------------------------------------------------------*| 256     3       4      | 68      9       16     | 1268    7       125    || 2569    159     12569  | 4678    168     1467   | 124689  12568   3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 345689  7       123469 | 1239    1235    1259   || 3       7       569    | 569     1256    1269   | 129     4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     2369   | 123468  12368   124    || 289     6       12389  | 379     4       2379   | 5       1238    12     |*--------------------------------------------------------------------------*Eliminating 1 From r1c7 (Row 3 & Box 3 Box-line interaction)Eliminating 1 From r1c9 (Row 3 & Box 3 Box-line interaction)Eliminating 1 From r2c7 (Row 3 & Box 3 Box-line interaction)Eliminating 1 From r2c8 (Row 3 & Box 3 Box-line interaction)*--------------------------------------------------------------------------*| 256     3       4      | 68      9       1      | 268     7       25     || 2569    159     12569  | 4678    68      467    | 24689   2568    3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 345689  7       23469  | 1239    1235    1259   || 3       7       569    | 569     1       269    | 29      4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     2369   | 123468  12368   124    || 289     6       12389  | 379     4       2379   | 5       1238    12     |*--------------------------------------------------------------------------*Eliminating 2 From r8c6 (Column 5 & Box 8 Box-line interaction)Eliminating 2 From r9c6 (Column 5 & Box 8 Box-line interaction)*--------------------------------------------------------------------------*| 256     3       4      | 68      9       1      | 268     7       25     || 2569    159     12569  | 4678    68      467    | 24689   2568    3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 345689  7       23469  | 1239    1235    1259   || 3       7       569    | 569     1       269    | 29      4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     369    | 123468  12368   124    || 289     6       12389  | 379     4       379    | 5       1238    12     |*--------------------------------------------------------------------------*Eliminating 4 From r2c7 (Row 3 & Box 3 Box-line interaction)*--------------------------------------------------------------------------*| 256     3       4      | 68      9       1      | 268     7       25     || 2569    159     12569  | 4678    68      467    | 2689    2568    3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 345689  7       23469  | 1239    1235    1259   || 3       7       569    | 569     1       269    | 29      4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     369    | 123468  12368   124    || 289     6       12389  | 379     4       379    | 5       1238    12     |*--------------------------------------------------------------------------*Eliminating 4 From r5c4 (Row 4 & Box 5 Box-line interaction)Eliminating 4 From r5c6 (Row 4 & Box 5 Box-line interaction)*--------------------------------------------------------------------------*| 256     3       4      | 68      9       1      | 268     7       25     || 2569    159     12569  | 4678    68      467    | 2689    2568    3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 35689   7       2369   | 1239    1235    1259   || 3       7       569    | 569     1       269    | 29      4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     369    | 123468  12368   124    || 289     6       12389  | 379     4       379    | 5       1238    12     |*--------------------------------------------------------------------------*r2c4 Must only have 47 as valid Candidates (47 is a Hidden Double in Row 2)r2c6 Must only have 47 as valid Candidates (47 is a Hidden Double in Row 2)*--------------------------------------------------------------------------*| 256     3       4      | 68      9       1      | 268     7       25     || 2569    159     12569  | 47      68      47     | 2689    2568    3      || 69      8       7      | 2       3       5      | 1469    16      149    ||------------------------+------------------------+------------------------|| 1       2       589    | 34589   58      349    | 7       35      6      || 45689   459     5689   | 35689   7       2369   | 1239    1235    1259   || 3       7       569    | 569     1       269    | 29      4       8      ||------------------------+------------------------+------------------------|| 245     45      235    | 1       256     8      | 2346    9       7      || 7       1459    123589 | 3569    256     369    | 123468  12368   124    || 289     6       12389  | 379     4       379    | 5       1238    12     |*--------------------------------------------------------------------------*`

tarek

Posts: 2637
Joined: 05 January 2006

I found the locked 4s in box 5, row 4, but had to go to Outback Steakhouse after that.
I'm up to my ears in a VH Pappocom that I really should be able to solve. If I can't find the magic clue, I'll throw myself on the mercy of the court tomorrow.
Hud

Posts: 570
Joined: 29 October 2005

I altered the puzzle to make it symmetric.
Pray I don't alter it further - Darth Vader

This one is interesting.
Code: Select all
`2-4  -9-  -75---  ---  --398-  2-5  ---12-  8--  -3--4-  -7-  -5--7-  --6  -48---  1-8  -977--  ---  ---86-  -4-  5-2`

I couldn't get past here

Code: Select all
`+-----------+----------+------------+| 2   3  4  | 6   9  1 | 8   7  5   || 56  1  56 | 4   8  7 | 9   2  3   || 9   8  7  | 2   3  5 | 14  6  14  |+-----------+----------+------------+| 1   2  69 | 8   5  4 | 7   3  69  || 36  4  8  | 39  7  2 | 16  5  169 || 35  7  59 | 39  1  6 | 2   4  8   |+-----------+----------+------------+| 4   5  2  | 1   6  8 | 3   9  7   || 7   9  1  | 5   2  3 | 46  8  46  || 8   6  3  | 7   4  9 | 5   1  2   |+-----------+----------+------------+`

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

QBasicMac wrote:I altered the puzzle to make it symmetric.
Pray I don't alter it further - Darth Vader

This one is interesting.
Code: Select all
`2-4  -9-  -75---  ---  --398-  2-5  ---12-  8--  -3--4-  -7-  -5--7-  --6  -48---  1-8  -977--  ---  ---86-  -4-  5-2`

I couldn't get past here

Code: Select all
`+-----------+----------+------------+| 2   3  4  | 6   9  1 | 8   7  5   || 56  1  56 | 4   8  7 | 9   2  3   || 9   8  7  | 2   3  5 | 14  6  14  |+-----------+----------+------------+| 1   2  69 | 8   5  4 | 7   3  69  || 36  4  8  | 39  7  2 | 16  5  169 || 35  7  59 | 39  1  6 | 2   4  8   |+-----------+----------+------------+| 4   5  2  | 1   6  8 | 3   9  7   || 7   9  1  | 5   2  3 | 46  8  46  || 8   6  3  | 7   4  9 | 5   1  2   |+-----------+----------+------------+`

Mac

That is because the puzzle has 3 different solutions now (1 for each candidate in r5c9)

tarek

Posts: 2637
Joined: 05 January 2006

tarek wrote:That is because the puzzle has 3 different solutions now (1 for each candidate in r5c9)

Heh - stupid. I forgot about the possibility of multiple solutions.

I should delete the post, but never mind.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

I'm glad I didn't invest too much of my not valuable time on that one, I did FINALLY find a naked triple (that wasn't all that hard) and saved some face on the Pappocom I was having trouble with.
Hud

Posts: 570
Joined: 29 October 2005

Its complicated but that is what I found
Code: Select all
`+----------------------+----------------------+----------------------+| 256    3      4      | 68     9      1      | 268    7      25     | | 2569   159    12569  | 47     68     47     | 2689   2568   3      | | 69     8      7      | 2      3      5      | 1469   16     149    | +----------------------+----------------------+----------------------+| 1      2      589    | 34589  58     349    | 7      35     6      | | 45689  459    5689   | 35689  7      2369   | 1239   1235   1259   | | 3      7      569    | 569    1      269    | 29     4      8      | +----------------------+----------------------+----------------------+| 245    45     235    | 1      256    8      | 2346   9      7      | | 7      1459   123589 | 3569   256    369    | 123468 12368  124    | | 289    6      12389  | 379    4      379    | 5      1238   12     | +----------------------+----------------------+----------------------+first we can  see that R1C7<>6 because we have R1C7=6=>R2C5=6 and that eliminate all the candiates for 6 in R7now we get +----------------------+----------------------+----------------------+| 256    3      4      | 68     9      1      |^28     7     ^25     | | 2569   159    12569  | 47    *68     47     | 2689  ^2568   3      | | 69     8      7      | 2      3      5      | 1469   16     149    | +----------------------+----------------------+----------------------+| 1      2      589    | 34589  58     349    | 7      35     6      | | 45689  459    5689   | 35689  7      2369   | 1239   1235   1259   | | 3      7      569    | 569    1      269    | 29     4      8      | +----------------------+----------------------+----------------------+| 245    45     235    | 1      256    8      | 2346   9      7      | | 7      1459   123589 | 3569   256    369    | 123468 12368  124    | | 289    6      12389  | 379    4      379    | 5      1238   12     | +----------------------+----------------------+----------------------+ Almost Locked x-z rule tell us that r2c7<>8and we get+----------------------+----------------------+----------------------+| 256    3      4      | 68     9      1      |*28     7      25     | | 2569   159    12569  | 47    ^68     47     |*269    2568   3      | | 69     8      7      | 2      3      5      | 1469   16     149    | +----------------------+----------------------+----------------------+| 1      2      589    | 34589  58     349    | 7      35     6      | | 45689  459    5689   | 35689  7      2369   | 1239   1235   1259   | | 3      7      569    | 569    1      269    |*29     4      8      | +----------------------+----------------------+----------------------+| 245    45     235    | 1      256    8      | 2346   9      7      | | 7      1459   123589 | 3569   256    369    | 123468 12368  124    | | 289    6      12389  | 379    4      379    | 5      1238   12     | +----------------------+----------------------+----------------------+here we get R2C8<>8and we get+----------------+----------------+----------------+| 25   3    4    | 6    9    1    | 8    7    25   | | 2569 19   126  | 4    8    7    |^69   25   3    | | 69   8    7    | 2    3    5    | 1469^16   149  | +----------------+----------------+----------------+| 1    2    9    | 8    5    4    | 7    3    6    | | 68   4    68   | 3    7    2    |*19   15   159  | | 3    7    5    | 9    1    6    | 2    4    8    | +----------------+----------------+----------------+| 4    5    23   | 1    26   8    | 36   9    7    | | 7    19   1238 | 5    26   39   | 1346 1268 124  | | 289  6    1238 | 7    4    39   | 5    128  12   | +----------------+----------------+----------------+here we get R5C8<>1 and +----------------+----------------+----------------+| 2    3    4    | 6    9    1    | 8    7    5    | | 5    19   16   | 4    8    7    | 69   2    3    | | 69   8    7    | 2    3    5    | 1469 16   149  | +----------------+----------------+----------------+| 1    2    9    | 8    5    4    | 7    3    6    | | 68   4    68   | 3    7    2    | 19   5    19   | | 3    7    5    | 9    1    6    | 2    4    8    | +----------------+----------------+----------------+| 4    5    23   | 1    26   8    | 36   9    7    | | 7    19   1238 | 5   *26   39   | 1346^168  124  | | 89   6    1238 | 7    4    39   | 5   ^18  ^12   | +----------------+----------------+----------------+now we get R8C9<>2+----------------+----------------+----------------+| 25   3    4    | 6    9    1    | 8    7    25   | | 2569 19   126  | 4    8    7    | 69   25   3    | | 69   8    7    | 2    3    5    | 1469 16   149  | +----------------+----------------+----------------+| 1    2    9    | 8    5    4    | 7    3    6    | | 68   4    68   | 3    7    2    | 19   15   159  | | 3    7    5    | 9    1    6    | 2    4    8    | +----------------+----------------+----------------+| 4    5    23   | 1    26   8    | 36   9    7    | | 7   ^19   1238 | 5    26   39   | 1346 1268 14   | |*289  6    1238 | 7    4    39   | 5   *128 *12   | +----------------+----------------+----------------+and here we get that R9C3<>1+----------------+----------------+----------------+| 25   3    4    | 6    9    1    | 8    7    25   | | 2569 19   126  | 4    8    7    | 69   25   3    | | 69   8    7    | 2    3    5    | 1469 16   149  | +----------------+----------------+----------------+| 1    2    9    | 8    5    4    | 7    3    6    | | 68   4    68   | 3    7    2    | 19   15   159  | | 3    7    5    | 9    1    6    | 2    4    8    | +----------------+----------------+----------------+| 4    5    23   | 1    26   8    | 36   9    7    | | 7    19   1238 | 5    26   39   | 1346 1268 14   | | 289  6    238  | 7    4    39   | 5    128  12   | +----------------+----------------+----------------+from here its easy to solve`
bennys

Posts: 156
Joined: 28 September 2005

Starting from here ...
Code: Select all
` . 3 4 | . 9 . | . 7 .  . . . | . . . | . . 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 . | . . . | 7 . 6  . . . | . 7 . | . . .  3 7 . | . . . | . 4 8 -------+-------+------ . . . | 1 . 8 | . 9 7  7 . . | . . . | . . .  . 6 . | . 4 . | 5 . . `

... using relatively simple tactics including naked pairs and locked candidates, I come to here:
Code: Select all
` . 3 4 | . 9 1 | . 7 .  . . . | . . . | . . 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 . | . . . | 7 . 6  . . . | . 7 . | . . .  3 7 . | . 1 . | . 4 8 -------+-------+------ . . . | 1 . 8 | . 9 7  7 . . | . . . | . . .  . 6 . | . 4 . | 5 . .    256     3       4       |+68      9       1       |x268     7       25        2569    159     12569   | 47     -68      47      | 2689    2568    3         69      8       7       | 2       3       5       | 1469    16      149      -------------------------+-------------------------+-------------------------  1       2       589     | 34589   58      349     | 7       35      6         45689   459     5689    | 35689   7       2369    | 1239    1235    1259      3       7       569     | 569     1       269     | 29      4       8        -------------------------+-------------------------+-------------------------  245     45      235     | 1      +256     8       |-2346    9       7         7       1459    123589  | 3569    256     369     | 123468  12368   124       289     6       12389   | 379     4       379     | 5       1238    12      `

Multi-coloring 6s aka turbofish (marked with plus and minus) eliminate the 6 from r1c7.

Code: Select all
`  256     3       4       | 6[8]    9       1       |[2]8     7       2[5]        2569    159     12569   | 47     [6]8     47      | x2689x  256[8]  3         69      8       7       | 2       3       5       | 1469    16      149      -------------------------+-------------------------+-------------------------  1       2       589     | 34589   5[8]    349     | 7       35      6         45689   459     5689    | 35689   7       2369    | 1239    1235    1259      3       7       569     | 569     1       269     | 2[9]    4       8        -------------------------+-------------------------+-------------------------  245     45      235     | 1       256     8       | 2346    9       7         7       1459    123589  | 3569    256     369     | 123468  12368   124       289     6       12389   | 379     4       379     | 5       1238    12      `

Ok -- this step is pretty complex. I think it could be replaced with Almost Locked Sets -- but at this point, I can follow that tactic but cannot find it on my own.

-- r4c5=8 => r2c5=6 => r1c4=8 => r1c7=2 => (r1c9=5 AND r6c7=9)

-- (r2c5=6 AND r1c7=2 AND r1c9=5) => r2c8=8

-- (r2c5=6 AND r1c7=2 AND r2c8=8 AND r6c7=9) leave no candidate available for r2c7.

Therefore, r4c5 cannot be 8 and must be 5.

After this, there are a lot of hidden and naked singles, then:

Code: Select all
` . 3 4 | 6 9 1 | 8 7 .  . . . | 4 8 7 | . . 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 9 | 8 5 4 | 7 3 6  . 4 . | 3 7 2 | . . .  3 7 5 | 9 1 6 | 2 4 8 -------+-------+------ 4 5 . | 1 . 8 | . 9 7  7 . . | 5 . . | . . .  . 6 . | 7 4 . | 5 . .    25    3     4     | 6     9     1     | 8     7     25      2569  19    126   | 4     8     7     |+69    256   3       69    8     7     | 2     3     5     |-1469 +16    149    -------------------+-------------------+-------------------  1     2     9     | 8     5     4     | 7     3     6       68    4     68    | 3     7     2     |+19   -15    159     3     7     5     | 9     1     6     | 2     4     8      -------------------+-------------------+-------------------  4     5     23    | 1     26    8     | 36    9     7       7     19    1238  | 5     26    39    | 1346  1268  124     289   6     1238  | 7     4     39    | 5     128   12    `

-- xy-wing in the three cells marked with a plus sign eliminate 1s from both r3c7 and r5c8, marked with minuses.

More singles, then:

Code: Select all
` 2 3 4 | 6 9 1 | 8 7 5  5 . . | 4 8 7 | . 2 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 9 | 8 5 4 | 7 3 6  . 4 . | 3 7 2 | . 5 .  3 7 5 | 9 1 6 | 2 4 8 -------+-------+------ 4 5 . | 1 . 8 | . 9 7  7 . . | 5 . . | . . .  . 6 . | 7 4 . | 5 . .    2     3     4     | 6     9     1     | 8     7     5       5     19    16    | 4     8     7     | 69    2     3       69    8     7     | 2     3     5     | 469   16    149    -------------------+-------------------+-------------------  1     2     9     | 8     5     4     | 7     3     6       68    4     68    | 3     7     2     | 19    5     19      3     7     5     | 9     1     6     | 2     4     8      -------------------+-------------------+-------------------  4     5     23    | 1     26    8     | 36    9     7       7    +19    1238  | 5     26    39    |-1346 -168  -124    +89    6    -1238  | 7     4     39    | 5    +18    12    `

-- another xy-wing is marked above that excludes 1s from FOUR exclusions.

More singles, then:

Code: Select all
` 2 3 4 | 6 9 1 | 8 7 5  5 . . | 4 8 7 | . 2 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 9 | 8 5 4 | 7 3 6  . 4 . | 3 7 2 | 1 5 9  3 7 5 | 9 1 6 | 2 4 8 -------+-------+------ 4 5 . | 1 . 8 | . 9 7  7 . . | 5 . . | . . .  . 6 . | 7 4 . | 5 . .    2     3     4     | 6     9     1     | 8     7     5       5     19    16    | 4     8     7     | 69    2     3      +69    8     7     | 2     3     5     | 4x69 +16    14     -------------------+-------------------+-------------------  1     2     9     | 8     5     4     | 7     3     6       68    4     68    | 3     7     2     | 1     5     9       3     7     5     | 9     1     6     | 2     4     8      -------------------+-------------------+-------------------  4     5     23    | 1     26    8     | 36    9     7       7     19    1238  | 5     26    39    | 346   68    24     +89    6     23x8  | 7     4     39    | 5    +18    12    `

-- A non-repetitive nice loop is marked with plus signs. It eliminates the candidate 8 from r9c3, as either r9c1 or r9c8 must be 8, and the 6 from r3c7, as either r3c1 or r3c8 must be 6.

-- Now there is a naked pair of [23] in box 7, eliminating 2 and 3 from r8c3, bringing us to here:

Code: Select all
` 2 3 4 | 6 9 1 | 8 7 5  5 . . | 4 8 7 | . 2 3  . 8 7 | 2 3 5 | . . . -------+-------+------ 1 2 9 | 8 5 4 | 7 3 6  . 4 . | 3 7 2 | 1 5 9  3 7 5 | 9 1 6 | 2 4 8 -------+-------+------ 4 5 . | 1 . 8 | . 9 7  7 . . | 5 . . | . . .  . 6 . | 7 4 . | 5 . .    2    3    4    | 6    9    1    | 8    7    5      5    19   16   | 4    8    7    | 69   2    3      69   8    7    | 2    3    5    | 49   16   14    ----------------+----------------+----------------  1    2    9    | 8    5    4    | 7    3    6      68   4    68   | 3    7    2    | 1    5    9      3    7    5    | 9    1    6    | 2    4    8     ----------------+----------------+----------------  4    5    23   | 1    26   8    | 36   9    7      7    19   18   | 5    26   39   |[346] 68   24     89   6    23   | 7    4    39   | 5    18   12   `

Finally, all undecided cells have exactly TWO candidates -- except r8c7 which has THREE. The candidate 6 appears three times in the row, column and box that contains r8c7. Therefore, in order to avoid BUG, a 6 must be placed in this cell. After this placement, the rest is trivial.
tso

Posts: 798
Joined: 22 June 2005

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