The New Sudoku Players' Forum

[MikeF]

I've got this far and and am totally stuck, despite much time looking for a logical next step. Can someone suggest one please?

7*1 239 64*
6*2 145 **7
*49 867 *1*

4** *5* *7*
9** *8* *61
*6* *2* *53

*9* *18 724
*** 47* 5**
*74 59* 1*6

tnx, Mike

[Nick67]

[Edit: Argh, I missed the boat with this post!
My hint did not lead anywhere ... and I realize
now that Simple Sudoku is very well known ...
my bad!]

There is a naked pair in the 1st column.

Let me recommend a program to you called Simple Soduku,
which is available free here:

http://www.angusj.com/sudoku/

In just a few seconds, I pasted your puzzle into the
program, clicked on the Hint button, and
the program reported the hint I wrote above.
It's a great program!

Cheers,
Nick

[emm]

From the naked pair I can solve this by testing candidates 3,5 in r3,c1 and from there through boxes 2 and 3 and back to 1.

From this I deduce r3,c1 can't be 5 otherwise r1,c2 would also be 5. Is this what is called forcing chain(or just T&E)?

Is there another way of doing it eg Xwing of 2s in r8 and r9 that doesn't require T&E?

[Nick67]

I'm sorry, I can't quite see how you were able to
deduce that r3,c1 is not 5. Could you please
explain once more?

Thanks,
Nick

P.S.

For the record, I took this route:
I eliminated 3 as a candidate
from r8,c1 and r9,c1, based on the naked pair.
Next, I eliminated 8 as a candidate from r4,c2 and r8,c2.
This is because 8 appears as a candidate in box 1 only in c2.


Next, I eliminated 2 as a candidate from r8,c2, because
2 appears as a candidate in box 2 only in c2.

Similarly, I then eliminated 3 from r2,c8, because
3 appears as a candidate in box 9 only in c8.

But then ... I'm stuck. Actually, I confess that I
used the Hint Button in Simple Sudoku to find all
of the above. And when I reach this point, and
click the button again, the program reports
"No hint available".

So ... a lot of help I am!

[emm]

Hmmm! Strangely, I can't figure out my own reasoning not even with all the brilliant hieroglyphics in the margin. I expect I made a mistake that resulted in the 3 being placed in r3,c1 which unlocked the puzzle.

Well if SS can't solve it I may as well pick up my pencil and move on.

PS : I can't believe I missed the locked candidates I was so busy looking for something complicated!

[Nick67]

I wonder if there is indeed a good reason for
placing 3 in r3,c1? As you suggested, it
is exactly the right move! But why?
Maybe you were on the right track when
you suggested there might be a forcing
chain somewhere?

Just by the way, there is a nice description of
forcing chains here:

http://www.simes.clara.co.uk/programs/sudokutechnique7.htm

... but I can't figure out how to find the starting point
of a forcing chain in our puzzle.

[stuartn]

A 4 at R6C6 and it all falls apart aswell - might be an easier place to start looking for a chain.

stuartn

[Nick67]

I also wonder if this puzzle can be
solved using one of the
"advanced coloring" techniques.
(I'm guessing that the solution
requires more than simple coloring
techniques, since SS doesn't give any hints.
I also tried simple coloring manually ...)

BTW, apologies to MikeF for not recognizing
earlier that this is a tough puzzle!

[Wolfgang]

A 4 at R6C6 and it all falls apart aswell - might be an easier place to start looking for a chain.
stuartn

I only found a rather long chain for that:
r1c2=8->r2c2=3->r8c2=1->r4c2<>1->r6c1=1->r6c6=4
r1c2=5->r1c9=8->r3c9=5->r3c7=2->r5c7=4->r5c6=3->r6c6=4

[MikeF]

Many thanks for for all the replies. I guess that, apart from forcing chains, there is no other logical approach here that might work. The various naked pairs -- like the 35s in col 1 -- don't seem to help further reduce candidates in a way that solves the puzzle. Personally, I hate forcing chains or any T&E type approach.

[Jeff]

Do you consider xy-chain an T&E approach? If yes, don't read further.

Starting r6c3, [78]-[81]-[14]-[43]-[37] => r6c4<>7 => r6c4=9 => r5c4=7 and r6c3=7

Starting r6c1, [18]-[82]-[23]-[34]-[41] non-repetitive => r8c1<>8, r4c6<>3 and r8c6<>3

Starting r8c2, [31]-[12]-[26]-[63] => r7c1<>3 => r7c1=5

There are so many xy-chains, but these 3 are sufficient to solve the puzzle. There is another non-repetitive one after the 9 and 7s are fixed if you would like to find it as an exercise.

[MikeF]

That's pretty impressive Jeff. No way could I spot all that with mere pencil and paper in hand. Thanks very much for outpointing.

Mike

[Jeff]

MikeF

Actually, xy-wing, xy-chain, xyz-wing and xyz-chains are much easier to spot than x-wing, swordfish, turbot fish and colours (some people may disagree), techniques I am sure you would consider logical. This is because the formers don't require any filtering and are therefore most suitable for direct pencil/rubber on newspaper application. It all comes down to practice as to how many of these patterns you could spot in a puzzle.

As to forcing chains, it can be T&E, but then again can be not T&E at all. It hinges on whether you have a system to identify these chains. Forcing chain itself is not T&E, but usually the process of finding these chains can be T&E. Using a bilocation/bivalue combination plot, coupled with a set of proven rules, I can identify forcing chains without T&E. It is a time consuming process, but in return you would enjoy full satisfaction for being able to solve the puzzle logically.

[Nick67]

I found that Nick70's coloring technique is also a
good way to solve this puzzle.
Here is the puzzle after adding candidates and
doing a few standard reductions:

Code: Select all

 
7     58    1    |     2     3     9    |    6     4    58
6     38    2    |     1     4     5    |    389   89   7
35    4     9    |     8     6     7    |    23    1    25
----------------------------------------------------------
4     123  38    |     369   5    136   |    289   7    289
9     235  357   |     37    8    34    |    24    6    1
18    6    78    |     79    2    14    |    489   5    3
----------------------------------------------------------
35    9    356   |     36    1    8     |    7     2    4
128  13    368   |     4     7    236   |    5     389  89
28   7     4     |     5     9    23    |    1     38   6


Next, let's add coloring, starting with cell (6,1).
(I'll place colors directly below candidates.)
There are many conjugate pairs, so many of
the candidates can be colored.

Code: Select all

7     58    1    |     2     3     9    |    6     4    58

6     38    2    |     1     4     5    |    389   89   7

35    4     9    |     8     6     7    |    23    1    25

----------------------------------------------------------
4     123  38    |     369   5    136   |    289   7    289
      BB                          A
9     235  357   |     37    8    34    |    24    6    1
      A                           AB         BA   
18    6    78    |     79    2    14    |    489   5    3
AB                                BA         B
----------------------------------------------------------
35    9    356   |     36    1    8     |    7     2    4

128  13    368   |     4     7    236   |    5     389  89
B    AB
28   7     4     |     5     9    23    |    1     38   6


There are 2 candidates with the B color in cell (4,2),
so B must be false. Therefore A must be true.

So, every candidate with the A color is the correct
candidate for its respective cell, and every candidate
with the B color can be eliminated, leading to
this:

Code: Select all

7     58    1    |     2     3     9    |    6     4    58
6     38    2    |     1     4     5    |    389   89   7
35    4     9    |     8     6     7    |    23    1    25
----------------------------------------------------------
4     3    38    |     369   5    1     |    289   7    289
9     2    357   |     37    8    3     |    4     6    1
1     6    78    |     79    2    4     |    89   5    3
----------------------------------------------------------
35    9    356   |     36    1    8     |    7     2    4
28    1    368   |     4     7    236   |    5     389  89
28   7     4     |     5     9    23    |    1     38   6



From here the solution is straightforward.
[/quote]

Thanks to Nick70 for this coloring technique,
which is described here:

http://www.setbb.com/phpbb/viewtopic.php?t=77&sid=f1a9110279421a8b358d722f515d3729&mforum=sudoku

[Jeff]

post cancelled