The New Sudoku Players' Forum

[puzzleme]

Please help with this puzzle.

______________________________________________________

| 3 178 127 | 6 2478 18 | 5 124 9 |
| 4 1578 127 | 257 3 9 | 128 12 6 |
| 9 1568 126 | 245 2458 158 | 1238 1234 7 |
______________________________________________________

| 7 2 5 | 3 9 4 | 6 8 1 |
| 1 4 3 | 57 68 68 | 79 579 2 |
| 6 9 8 | 1 57 2 | 4 357 35 |
_______________________________________________________

| 2 167 14679 | 459 456 356 | 1379 135679 8 |
| 5 67 4679 | 8 1 36 | 2379 23679 34|
| 8 3 1469 | 2459 2456 7 | 19 1569 45|
_______________________________________________________

[Shazbot]

for starters, if you use code and /code (with the square brackets) around your grid you'll keep the spacing and make it much more readable to those trying to assist.

Using colours on 5s (Simple Sudoku suggests multiple colours but I don't understand the technique, so will explain it "my way"):

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79   -579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   |*2459   2456  7    | 19    1569   -45   |
*----------------------------------------------------------*


r9c4 is the intersection of two opposite signs (at r5c4 and r9c9), eliminating 5 as a candidate from this cell.

That's the last clue available - this puzzle apparently has 79 solutions.

[puzzleme]

Sorry about the presentation. We are new to this Forum. This is a hard level puzzle. Don't quite understand the +. -, and intersection bit, please elaborate. Also, shouldn't there only be one solution per puzzle? Would just like to know the next available move.

[tso]

The puzzle as you have presented it is neither hard nor easy -- it is invalid, as it has multiple solutions. Either you transcribed it incorrectly or it was invalid at the source.

Code: Select all

+-------+-------+-------+
| 3 . . | 6 . . | 5 . 9 |
| 4 . . | . 3 9 | . . 6 |
| 9 . . | . . . | . . 7 |
+-------+-------+-------+
| 7 2 5 | 3 9 4 | 6 8 1 |
| 1 4 3 | . . . | . . 2 |
| 6 9 8 | 1 . 2 | 4 . . |
+-------+-------+-------+
| 2 . . | . . . | . . 8 |
| 5 . . | 8 1 . | . . . |
| 8 3 . | . . 7 | . . . |
+-------+-------+-------+


Shazbot's example of coloring was flawed -- there is no justification for labeling r9c9.

The plus and minus signs are used in ascii diagrams instead of coloring. See these explanations:

Simple Sudoku
[url=http://www.simes.clara.co.uk/programs/sudokutechnique12.htm]
Sadman Sudoku[/url]

Be aware that beyond "simple" coloring there are other other forms of coloring that different sources refer to with different names.

To make legible diagrams, create them using a simple text editor with monospaced fonts, cut and paste the diagram into your post, placing [code] before the diagram and [/code] after it. Selecting the diagram and then clicking the CODE button accomplishes the same thing. You MUST uncheck DISABLE BBCode in this post. Preview before submitting.

[puzzleme]

Thank you for the assistance and the helpful hints. I won't spend any more time on this puzzle since it's invalid. Hope others did not spend a lot of time on trying to help.

[Cec]

"..To make legible diagrams, create them using a simple text editor with monospaced fonts.."

When I joined the forum it took me a while to understand what the above meant. The following format may not "look" right but a suitable grid will result when the appropriate code tags are inserted at the beginning and end of this text.
+-------+-------+-------+
| 3 . . | 6 . . | 5 . 9 |
| 4 . . | . 3 9 | . . 6 |
| 9 . . | . . . | . . 7 |
+-------+-------+-------+
| 7 2 5 | 3 9 4 | 6 8 1 |
| 1 4 3 | . . . | . . 2 |
| 6 9 8 | 1 . 2 | 4 . . |
+-------+-------+-------+
| 2 . . | . . . | . . 8 |
| 5 . . | 8 1 . | . . . |
| 8 3 . | . . 7 | . . . |
+-------+-------+-------+
Cec

[Shazbot]

Shazbot's example of coloring was flawed -- there is no justification for labeling r9c9.

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79    579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   | 2459   2456  7    | 19    1569    45   |
*----------------------------------------------------------*


If r6c5 is 5, then r5c4 cannot be, nor can r6c8 or r6c9. So r5c8 must be - simple colouring.

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79   -579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   | 2459   2456  7    | 19    1569    45   |
*----------------------------------------------------------*


If r5c8 is 5, then the only location for a 5 in box 9 is r9c9.

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79   -579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   | 2459   2456  7    | 19    1569   -45   |
*----------------------------------------------------------*


This leads to the intersection/contradiction at r9c4.

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79   -579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   |*2459   2456  7    | 19    1569   -45   |
*----------------------------------------------------------*


Note the method doesn't lead to an elimination or a placement at r9c9, but it does lead to a correct next step - as useless as it is with this particular puzzle.

Simple Sudoku offers Multiple Coloring as the next step (from the original puzzle) - and eliminates 5 from r9c4 just as I've done. I do not understand that technique but use the above to arrive at the same conclusion - it works every time for me, so it may not be called "simple coloring" (though it begins with that technique) or "multiple coloring" but I certainly don't believe it's "flawed".

And puzzleme, yes there should only be one solution for a VALID puzzle, but it depends on the source - obviously if you've made no typing or placement errors when entering your grid, the source of this puzzle is not a quality one.

[MCC]

Code: Select all

*----------------------------------------------------------*
| 3  178   127    | 6      2478  18   | 5     124     9    |
| 4  1578  127    | 257    3     9    | 128   12      6    |
| 9  1568  126    | 245    2458  158  | 1238  1234    7    |
|-----------------+-------------------+--------------------|
| 7  2     5      | 3      9     4    | 6     8       1    |
| 1  4     3      |+57     68    68   | 79   -579     2    |
| 6  9     8      | 1     -57    2    | 4     357     35   |
|-----------------+-------------------+--------------------|
| 2  167   14679  | 459    456   356  | 1379  135679  8    |
| 5  67    4679   | 8      1     36   | 2379  23679   34   |
| 8  3     1469   | 2459   2456  7    | 19    1569    45   |
*----------------------------------------------------------*


If r5c8 is 5, then the only location for a 5 in box 9 is r9c9.

What if, r5c8<>5 what then?

Shazbot, you're working from a known solution, the elimination of a 5 from r9c4, and trying to fit your colouring to suit the elimination provided by Simple Sudoku.

MCC

[puzzleme]

This is the valid original puzzle and it's solvable.

Code: Select all

*------------------------*
| . . . | 6 . . | . 5 9  |
| . . . | . 3 9 | . . 6  |
| . . . | . . . | . . 7  |
*------------------------*
| . . 5 | 3 . . | 6 8 .  |
| 1 . . | . . . | . . 2  |
| . 9 8 | . . 2 | 4 . .  |
*------------------------*
| 2 . . | . . . | . . .  |
| 5 . . | 8 1 . | . . .  |
| 8 3 . | . . 7 | . . .  |
*------------------------*



I made an error copying it into my worksheet. The error was in row1 col H the number "5". When running into difficulty, I tried verifying the puzzle, of course, using the original valid puzzle. My apology. Interesting that it generated all these intelligent discussions. Thanks to all.

[Shazbot]

What if, r5c8<>5 what then?

Shazbot, you're working from a known solution, the elimination of a 5 from r9c4, and trying to fit your colouring to suit the elimination provided by Simple Sudoku.

MCC

coloring started in box 5, not box 6. If r6c5 is 5 then r8c5 MUST BE 5. If r6c5 is NOT 5, then r5c4 would be and r8c5 would not be and you can't continue from there.

Might work through this particular puzzle some more - though if it's an invalid puzzle perhaps the clues available just aren't right. Even though in this case I used the hint, I didn't look at the elimination it made until AFTER I'd done the work myself - saw it used colours on #5, got rid of the hint, started with colours on #5 myself and worked through. Then undid my steps and used the hint to see that I made the same elimination. I've used this method often (without the hint) and it's always given me the correct solution.

Think I'll go and investigate "multiple colouring" and see where it differs to my method, maybe I've stumbled on a new solving technique....

[tso]

coloring started in box 5, not box 6. If r6c5 is 5 then r8c5 MUST BE 5. If r6c5 is NOT 5, then r5c4 would be and r8c5 would not be and you can't continue from there.

I think you mean "If r6c5 is 5 then r5c8 MUST BE 5.


However, the deduction that r9c4<>5 IS valid, but not by coloring.
It is a Nishio.

r9c4=5 -> r5c4<>5 -> r6c5=5 -> r6c89<>5 -> r5c8=5 -> r79c8<>5 r9c9=5 -> r9c4<>5.
This is a contradiction, therefore r9c4<>5

More simply and humanly,
r9c4=5 -> r6c5=5 -> r5c8=5 -> r9c9=5 -> r9c4<>5.

Code: Select all

*--------------------------------------------------------*
| .   .    .    |  .      .     .    |  5     .     .    |
| .   5    .    |  5      .     .    |  .     .     .    |
| .   5    .    |  5      5     5    |  .     .     .    |
|---------------+--------------------+-------------------|
| .   .    5    |  .      .     .    |  .     .     .    |
| .   .    .    |  5      .     .    |  .    +5     .    |
| .   .    .    |  .     +5     .    |  .     5     5    |
|---------------+--------------------+-------------------|
| .   .    .    |  5      5     5    |  .     5     .    |
| 5   .    .    |  .      .     .    |  .     .     .    |
| .   .    .    | +5      5     .    |  .     5    +5    |
*--------------------------------------------------------*

In Nishio, "plus" means "true" and "minus" means "false".
This is NOT the case in coloring! In coloring "plus" and "minus" do NOT represent true and false, they mark which cells have a conjugate relationship.

[Wolfgang]

This again is just a turbot fish (r9c4, r5c4,r5c8,r6c9,r9c9). I really recommend to look for turbot fishes before trying other advanced coloring techniques. I suppose that they cover 95 % of possible coloring eliminations.

[Shazbot]

Isn't Nishio just another word for guessing? I got that impression from a thread I read fairly early on. Nishio and Turbot Fish are techniques I haven't looked at - have seen the names, but not looked at nishio 'cause I thought it was guessing (or maybe more accurately trial and error - which I guess this probably is), or turbot fish 'cause I had my hands full with colouring and swordfish. Maybe I'll go look a little more at those - and again multiple colouring - what I've done here and in many other puzzles seems to give me the same elimination as what angusj calls multiple colouring - I just don't use as many cells to get there as he seems to so figure I'm not using quite the same technique. Thanks for the alternatives to follow up.

[tso]

Some people frown on Nishio as being limited trial and error restricted to a single digit. However, it is a *very* human friendly method that predates most of the tactics discussed here as well as the western world's discovery of Sudoku. It's often an 'eyeball' tactic and can even come into play with few or no pencil marks.

See: http://www.simes.clara.co.uk/programs/sudokutechnique8.htm

[Wolfgang]

Hi Tso,

the link does not say, *how* to make nishio eliminations. I only saw sussers technique, which i think is not very user friendly. The 4 samples in the link can be solved with x-cycle (x-chain, multiple coloring or how you want to call it), but there are nishio eliminations that cant be done with it (have no sample now).
So, do you have a user friendly method that detects *all* possible nishio eliminations ?
[edit:] MJ's filet-o-fish swordfish there
is a sample for nishio that cannot be solved with x-cycle.