## Hard Puzzle : can it be solved without assuming a number?

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

### Hard Puzzle : can it be solved without assuming a number?

Hi,

I would like to know if it is possible to solve the following puzzle without having to "try a solution":
Code: Select all
2..|8..|.61
.1.|.5.|...
74.|..6|.5.
---|---|---
3.4|.81|...
...|...|...
...|67.|9.4
---|---|---
.8.|3..|.19
...|.2.|.4.
16.|..8|..5

If I don't use the method consisting in assuming a number and finding that it doesn't work, I am stuck here:
Code: Select all
2..|8..|.61
.1.|.5.|.9.
74.|.16|.5.
---|---|---
3.4|.81|5.6
...|5..|1..
..1|67.|9.4
---|---|---
48.|36.|.19
...|12.|648
16.|..8|..5

Marjorie
Marjorie

Posts: 3
Joined: 07 February 2006

Hi Marjorie,

I'm not sure what techniques you're familiar with, as your post doesn't have the pencilmarks.

The puzzle up until this point (& possibly yor posted solutions) can be solved using only naked singles:

then:
Code: Select all
*-----------------------------------------------------------------*
| 2      359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 247    5      2347  | 23478  9      237   |
| 7      4      389   | 29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3      279    4     | 29     8      1     | 5      27     6     |
| 689    279    26789 | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      2379  | 479    49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 2 From r5c3 (Column 2 & Box 4 Box-line interaction)
*-----------------------------------------------------------------*
| 2      359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 247    5      2347  | 23478  9      237   |
| 7      4      389   | 29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3      279    4     | 29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      2379  | 479    49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 3 From r9c3 (Row 8 & Box 7 Box-line interaction)
*-----------------------------------------------------------------*
| 2      359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 247    5      2347  | 23478  9      237   |
| 7      4      389   | 29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3      279    4     | 29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      279   | 479    49     8     | 237    237    5     |
*-----------------------------------------------------------------*
r2c4 Must only have 47 as valid Candidates (29 is a Naked Double in Column 4)
r9c4 Must only have 47 as valid Candidates (29 is a Naked Double in Column 4)
*-----------------------------------------------------------------*
| 2     -359    359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 47     5      2347  | 23478  9      237   |
| 7     *4     #389   |*29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3     *279    4     |*29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      279   | 47     49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 9 From r1c2 (Finned XWing in rows 3 & 4) ---- or SASHIMI Xwing
*-----------------------------------------------------------------*
| 2      35     359   | 8      349    3479  | 347    6      1     |
| 68     1      368   | 47     5      2347  | 23478  9      237   |
| 7      4      389   | 29     1      6     | 238    5      23    |
|---------------------+---------------------+---------------------|
| 3      279    4     | 29     8      1     | 5      27     6     |
| 689    279    6789  | 5      349    2349  | 1      2378   237   |
| 58     25     1     | 6      7      23    | 9      238    4     |
|---------------------+---------------------+---------------------|
| 4      8      257   | 3      6      57    | 27     1      9     |
| 59     3579   3579  | 1      2      579   | 6      4      8     |
| 1      6      279   | 47     49     8     | 237    237    5     |
*-----------------------------------------------------------------*
Eliminating 9 From r5c3 (Box 1 & Column 3 Box-Line interaction)
Eliminating 9 From r8c3 (Box 1 & Column 3 Box-Line interaction)
Eliminating 9 From r9c3 (Box 1 & Column 3 Box-Line interaction)

Then it should be easy from here

Tarek

tarek

Posts: 2699
Joined: 05 January 2006

Hi Tarek.

Tarek wrote:Eliminating 9 From r1c2 (Finned XWing in rows 3 & 4) ---- or SASHIMI Xwing

That elimination can also be regarded as a simple Turbot Fish.

Regards, Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Carcul wrote:That elimination can also be regarded as a simple Turbot Fish.

I agree, the same goes for the other puzzle that required assitance in another thread.

it seems that with every turbot fish there is a Finned or an Almost finned X-wing that reaches the same conclusion

tarek

tarek

Posts: 2699
Joined: 05 January 2006

Interesting one - I'm not up to speed on turbot fishes or finned x-wings (which are undoubtedly quicker if you can see them) so used colouring to solve:

Basic eliminations (locked candidates and naked pairs) from the puzzle as posted give:
Code: Select all

{2}     {359}   {359}   {8}     {349}   {3479}  {347}   {6}     {1}
{68}    {1}     {368}   {47}    {5}     {2347}  {23478} {9}     {237}
{7}     {4}     {389}   {29}    {1}     {6}     {238}   {5}     {23}
{3}     {279}   {4}     {29}    {8}     {1}     {5}     {27}    {6}
{689}   {279}   {6789}  {5}     {349}   {2349}  {1}     {2378}  {237}
{58}    {25}    {1}     {6}     {7}     {23}    {9}     {238}   {4}
{4}     {8}     {257}   {3}     {6}     {57}    {27}    {1}     {9}
{59}    {3579}  {3579}  {1}     {2}     {579}   {6}     {4}     {8}
{1}     {6}     {279}   {47}    {49}    {8}     {237}   {237}   {5}

Very sorry - my colouring efforts were misguided. Please ignore this.
Last edited by CathyW on Fri Feb 10, 2006 7:12 pm, edited 1 time in total.
CathyW

Posts: 316
Joined: 20 June 2005

I'm beginning to sound like a broken record but, coloring on 9's with two conjugate chains (r4c2,r4c4,r3c4,43c3 make one & r5c1,r8c1 the other)eliminates 9 in r8c3 & r9c3 which eliminates 9 in r8c6 (box line interaction, locked candidates, whatever one chooses to call it), which leads to singles the rest of the way.

CathyW--I'm trying to use and understand coloring on a single digit (sometimes with more than one chain) but I could not see how any of the eliminations stated in your post were made. I may not understand like I think I do.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

Marjorie,

You may want to check out the sites below for some of the basic techniques to help you understand the colouring / Turbot Fish being talked about.

Simple Sudoku
Crazy Girl

Posts: 189
Joined: 08 November 2005

TKiel wrote:CathyW--I'm trying to use and understand coloring on a single digit (sometimes with more than one chain) but I could not see how any of the eliminations stated in your post were made. I may not understand like I think I do.

It could well be me who does not understand like I thought!

And so it turned out! Apologies all round.
Last edited by CathyW on Fri Feb 10, 2006 7:13 pm, edited 1 time in total.
CathyW

Posts: 316
Joined: 20 June 2005

### Coloring for the win!

Greetings all. It seems once again the agrument between coloring and fishy cycles (including turbot fishes and finned x-wings) has come up. I'd just like to say that fishy cycles are not always faster (easier to spot and execute) than coloring. Personally I find coloring to be much easier to spot, because all you have to look for are conjugate pairs. You should check out the post I made a while back where I try to explain the more advanced aspects of coloring, and how to use it easily:
http://forum.enjoysudoku.com/viewtopic.php?p=14558#p14558
as well as
http://forum.enjoysudoku.com/viewtopic.php?p=14695#p14695
Hanyou Hottie

Posts: 8
Joined: 15 October 2005

Thank you HH for the pointers to your other posts.
Last edited by CathyW on Fri Feb 10, 2006 7:14 pm, edited 1 time in total.
CathyW

Posts: 316
Joined: 20 June 2005

CathyW,

After reading HH's posts, I'm not sure that your exclusion are valid. Each of her conjugate chains is marked with two different colors, indicating opposite states (one being true, the other false but not assigning one as true and the other as false). Her chains also relate to each other by having one color from each chain share a group. Since both those colors can't be true, then at least one of the opposite colors in each chain is true. Any cell that intersects with both those 'opposite' colors can be excluded, since one of those colors must be true. In looking at your grid for conjugate 2's, the seperate chains don't share a group so which is true and which is false can't be determined. Plus you don't indicate in your individual chains any sort of oppositeness between the conjugate links. They are all marked with A in the case of one chain and B in the case of the other. In that case, an A cell intersecting with a B cell could make an exclusion even though both really have to be false.

Having said that I will also say that even though your concept of colouring does not mesh with my understanding of colouring it is entirely possible that there may be some logic behind it, as the odds seems very remote that, without some kind of logic, all of your exclusions were mere 'happy coincidences'. It would seem likely that some of them would not have been 'allowed' by the program you use and that has not been the case. (Unless you have that feature turned off.) So it does seem to have some merit that I just haven't been able to follow.

Tracy
Last edited by TKiel on Thu Feb 09, 2006 8:44 am, edited 1 time in total.
TKiel

Posts: 209
Joined: 05 January 2006

### Re: Hard Puzzle : can it be solved without assuming a number

Marjorie wrote:"...If I don't use the method consisting in assuming a number and finding that it doesn't work, I am stuck here:

Hi marjorie,
If you haven't seen these then you may find the following links (just click on them) are helpful in explaining various solving techniques:
http://www.angusj.com/sudoku/hints.php
http://www.simes.clara.co.uk/programs/sudokutechniques.htm
Cec
Cec

Posts: 1039
Joined: 16 June 2005

TKiel wrote:After reading HH's posts, I'm not sure that your exclusion are valid.

I think what I've been trying to do is called multi-colouring which is explained a bit more on the Sadman Sudoku site: http://www.simes.clara.co.uk/programs/sudokutechnique12.htm
You may be right about the 2s in the puzzle above, or is the exclusion cell at the intersection 'weakly linked' to both sets of conjugates even though they don't share a unit? I would really appreciate some further guidance on this multi-colouring technique.

It was in response to another post about colouring which I can't now find that another player suggested colouring conjugates in one colour rather than alternating colours to help with identifying them in situations where there are more than two separate sets of conjugates.
CathyW

Posts: 316
Joined: 20 June 2005

Hi everybody,

Thank you very much for your replies!

Eliminating 9 From r1c2 (Finned XWing in rows 3 & 4) ---- or SASHIMI Xwing

Tarek, I was actually stuck there.

This helped me to solve the Sudoku without trial and error. Thanks! However, I find these special patterns hard to find.
About colouring, I find this technique very similar to trial and error except that you use a "tool" (the colours) to help you do the job.

Thanks again.

Cheers,
Marjorie
Marjorie

Posts: 3
Joined: 07 February 2006

Marjorie,

The colours only help you identify the conjugate links and the relationship between cells in the chain. They neither state nor imply that one colour is true and the other false. If the chain was short enough to follow in your head and there was no need to actually color the cells, would that still be quessing? Colouring allows one to say: If either this cell or that cell is true, then this one can't possibly be. It's really not much different that a naked pair: Either this cell contains the value or that cell contains the value, but no other cells can. I don't think you'll get much agreement for your contention that it is trial & error.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

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