## help in solving a difficult sudoku

Advanced methods and approaches for solving Sudoku puzzles
A turbot fish pattern consists of 5 cells only. You have to select 5 relevant cells from all the cells that contain candidate 3. Then apply logic to deduce which candidate can be removed. Take a look at Nick's thread on Turbot fish - case 4.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff,

I have looked at Nick's thread on Turbot fish case 4, however, when I apply it to this specific puzzle, I cannot come to the conclusion of excluding 3 in r5c2.

The 3's in the first turbot fish which you mention in the first option have two strong sides.

The 3's surrounding the turbot fish that are possibilities in my puzzle are : R1C2, R2C1, R2C5, R2C6, R1C4, R5C2, R5C4, R5C6. Therefore, in both rows 2 and 4 , there are three options for the digit 3 making these lines weak lines , right ?

Are these options of the digit 3 also located in the same place on your possibilities left ?

hana somekh

Posts: 28
Joined: 30 July 2005

Unfortunately the problems last weekend led to the elimination of my previous post and I havn't been able to login since then. Here goes again.

Following on from emalvick's post, after step 3 (ie before looking for a turbot fish) it is possible to eliminate some 6's from box 1 because of where 6's must go in column 3.

It is then possible to eliminate 6 from r3c5 based on colours, using the chain r6c5, r6c9, r4c7, r3c7).

You now have a naked pair in row 3 allowing further eliminations, some eliminations from box 8 because of where candidates must go in column 4, and ditto for box 9.

There is now a swordfish which allows the elimination of 6 from r1c4 (rows 1,2,6, columns 3,5,9).

This allows eliminations from column 4.

Now use colouring on the 3's, eg starting with the r1c2, r2c1 pair and colouring all the possible pairs. It becomes obvious that the colour assigned to r2c1 must be the false colour as it gives two cells in column 5 with the same colour (and other inconsistencies).

Thus you can eliminate 3 from r1c4, r2c1, r2c6, r4c8, r5c2, r6c5 and r7c5.

Things get easier from then on.

I now need to look into this turbot fish possibility as it looks to be a lot quicker than the above.
SteveF

Posts: 86
Joined: 26 March 2005

hana somekh wrote:I cannot come to the conclusion of excluding 3 in r5c2.

From the turbot fish in r1c2,r5c2,r5c6,r2c6,r1c4 with strong sides r1c2-r5c2, r1c2-r1c4 and r5c6,r2c6 it follows that r1c2 must be 3.
emalvick pointed out that with r5c2, r4c1, r2c1, r2c6, r5c6 the 3 must be in r4c1.
So you have 2 possibilities for that.
Last edited by Wolfgang on Thu Aug 04, 2005 4:10 am, edited 1 time in total.
Wolfgang

Posts: 208
Joined: 22 June 2005

I select this one to show you because it looks like a fish.

Jeff

Posts: 708
Joined: 01 August 2005

Hi Steve,

Thank you for the explanation. I follow your explanation up until the swordfish section, where you write :T

here is now a swordfish which allows the elimination of 6 from r1c4 (rows 1,2,6, columns 3,5,9).

This allows eliminations from column 4.

I cannot see a swordfish here !

The 6's in a swordfish must all share the same columns and rows, and r1c4 is part of the swordfish I presume ?

Appreciate a reply as I would really like to finish this sudoku logically and move on to other puzzles
hana somekh

Posts: 28
Joined: 30 July 2005

Jeff wrote:I select this one to show you because it looks like a fish.

Jeff : That's exactly the turbot fish I am looking at, however, this is where I am stuck !! Basically, from the explanation, it seems that r1c2 and r2c1 form a strong line in the turbot fish as do r2c6 and r5c6. In the explanation page attached earlier on to Nick70's explanation of the turbot fish, I cannot see how 2 cells in the same box for a strong line. However, if it is possible, I still cannot conclude this puzzle .... just a bit more help really really appreciated !!!
hana somekh

Posts: 28
Joined: 30 July 2005

if 3 in r2c6, then not in r2c1, then in r1c2
if 3 not in r2c6, then in r5c6, then not in r5c2 then in r1c2
Wolfgang

Posts: 208
Joined: 22 June 2005

No, r1c4 is not part of the swordfish which is why you can eliminate it.

The swordfish I can identify has the following cells which define its shape:

r1c3, r1c9
r2c3, r2c5
r6c5, r6c9

In the original definition of swordfish columns 3,5 and 9 could only contain two candidates, But I believe a later update (as posted on this forum) found that the 'extra' candidate at r2c9 is not a problem.

Thus a 6 in one of the above rows (1) but not in the above columns (4) can be eliminated, ie 6 can be eliminated from r1c4.
SteveF

Posts: 86
Joined: 26 March 2005

Wolfgang - Thank you very much for sorting out the last final part of the puzzle for me !!! That's just great !! I fully understand it now !
Jeff - thank you very much ! + drawing out the problem in coloured format really helped !
hana somekh

Posts: 28
Joined: 30 July 2005

SteveF wrote:No, r1c4 is not part of the swordfish which is why you can eliminate it.

The swordfish I can identify has the following cells which define its shape:

r1c3, r1c9
r2c3, r2c5
r6c5, r6c9

In the original definition of swordfish columns 3,5 and 9 could only contain two candidates, But I believe a later update (as posted on this forum) found that the 'extra' candidate at r2c9 is not a problem.

Thus a 6 in one of the above rows (1) but not in the above columns (4) can be eliminated, ie 6 can be eliminated from r1c4.

Steve : I still had a digit six at r1c9 - ie the 6 had not yet been eliminated out of my possibilities and therefore, I could not see a swordfish. The possibilities at r1c9 just before I solved it via turbot fish, were 2,6,1.
How did you eliminate the digit six at r1c9 ?
hana somekh

Posts: 28
Joined: 30 July 2005

hana somekh wrote:Jeff : That's exactly the turbot fish I am looking at, however, this is where I am stuck !! Basically, from the explanation, it seems that r1c2 and r2c1 form a strong line in the turbot fish as do r2c6 and r5c6. In the explanation page attached earlier on to Nick70's explanation of the turbot fish, I cannot see how 2 cells in the same box for a strong line.

The figures in my explanation are just examples. You can swap row, column and box sides at will provided you keep their relative positions (so if you only have 2 strong sides, they can be any two sides provided they are not consecutive).
Nick70

Posts: 156
Joined: 16 June 2005

The 6 is still a candidate for r1c9, and indeed must be as it is one of the 'corners' of the swordfish.

. . 6 | 6 . . | . . 6
. . 6 | . 6 . | . . .
. . . | . . . | . . .
______________
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . 6 . | . . 6
______________
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .

(Sorry, I'm having no joy cutting & pasting a a template.)

Thus the 6 in r1c4 is the one that can be removed, the others give the swordfish.
SteveF

Posts: 86
Joined: 26 March 2005

Or dont you have a 6 in r3c5 ?
Wolfgang

Posts: 208
Joined: 22 June 2005

The 6 was eliminated from r3c5 by the first application of colours - see my previous post.

What does RTFM stand for?
SteveF

Posts: 86
Joined: 26 March 2005

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