## help in solving a difficult sudoku

Advanced methods and approaches for solving Sudoku puzzles

### help in solving a difficult sudoku

I would really appreciate help in solving the following sudoku,
this is where I got so far :

4 * * * 9 8 7 5 *

* 8 * 7 * * 9 * *

* 9 7 * * * * 8 3

* * 1 8 7 5 * * 9

9 * 8 * 2 * 5 1 7

7 * * 9 * 1 8 * *

2 7 * * * 9 * 6 *

* * 3 * * 7 * 9 *

8 1 9 2 4 6 3 7 5

I need to find the next logical step !
The solution to this sudoku puzzle is :

432198756
586734921
197652483
321875649
968423517
754961832
275389164
643517298
819246375

Thanks !
hana somekh

Posts: 28
Joined: 30 July 2005

The next logical step depends on what you consider to be logic.

You can use the Nishio technique (r1c4) to solve this puzzle but it is (in my opinion) really close to trial and error.

Trial and error is another possibility and I'm pretty sure you can use the Forcing chains technique aswell.
Animator

Posts: 469
Joined: 08 April 2005

Using angusj's simple sudoku program it does get to solving a cell, but it is via a swordfish and 2 separate applications of 'colours'.
- not for the faint hearted!
SteveF

Posts: 86
Joined: 26 March 2005

Steve,

Could you kindly point out to me where the
swordfish and colour combination is at ?
hana somekh

Posts: 28
Joined: 30 July 2005

I have been sitting for hours this morning trying to figure out how to so solve this puzzle - I would really really appreciate help on it as I have absolutely no idea how to take it further logically .....
hana somekh

Posts: 28
Joined: 30 July 2005

### try hypothesis in the square with less gaps

The squares:

(0,0) (1,0) (2,0)
(0,1) (1,1) (2,1)
(0,2) (1,2) (2,2)

The squares with less gaps (3 gaps) are : (1,1) and (0,2).

It is necessary to put numbers 3, 4 and 6. ¡ start with the former !

We can try :

a) 875 b) 875 c) 875
32* *23 *2*
9*1 9*1 931

a) It is trivial to get:

43* 698 75*
*8* 7*3 9**
*97 4*2 *83

3*1 875 6*9
968 324 517
7** 961 83*

27* *39 *68
6*3 *87 *9*
819 246 375

As we can see the number 6 can not be located in squares (0,0) and (2,0)

Try b) and get directly the solution
supertorpe

Posts: 2
Joined: 30 July 2005

Supertorpe : I just cannot follow the logic in your description. What technique are you using ? I would really appreciate a bit more of an explanation )
hana somekh

Posts: 28
Joined: 30 July 2005

### Method

Read as much as you want... I pasted what you originally posted into Simple Sudoku. You may have already eliminated some of the candidates I am elminating at the beginning, but I'm not certain on what you have, so I am making it as straight forward as possible:

1. Eliminate a 4 in r5c2 (The center box only has 4's in r5)
2. This leaves 2 cells with 3 and 6 as candidates in the box in the left-center section
3. Eliminate 3's and 6's from r4c2, r6c2, and r6c3
4. Use a Turbot Fish in 3's with r5c2, r4c1, r2c1, r2c6, r5c6 to find that one of those cells is definitely a 3. That will lead you to another 3 on the right side of the board.

That should get you a bit further along too. I was actually able to finish from that point without any other special moves just a lot of naked and hidden pairs work.

Note: after the work on the 3's mentioned, a swordfish is possible, but I didn't need it. It's just a matter of choice I suppose. It may be possible to not use the Turbot fish, but I find it to be a relatively easy pattern to look for (at least a bit easier than the Swordfish).

Erik
emalvick

Posts: 13
Joined: 01 August 2005

emalvick : Thank you for your reply, however, I still cannot understand how you got there ! Is there any way of using the colouring method instead of turbo ?
Just to clarify , are the 3's options at your turbo situated at :
r2c1, r2c5, r2c6, r5c6, r5c4, r5c2 and r1c4 ?

Would much appreciate some further help ![/img]
hana somekh

Posts: 28
Joined: 30 July 2005

### Turbot Fish

If I may offer some help.

4 cases of turbot fish are available and only 2 fish can be substituted by the colouring method. The other 2 fish cannot be substituted because the colouring method considers continuous strong links only. I consider the latter 2 fish more powerful than colouring as weak links are more commonly found than strong links. 2 of these fish ring patterns, unfortunately a bit hard to identify, are in the cells of 3s. They are:

r1c2, r2c1, r2c6, r5c6, r5c2 and
r5c2, r4c1, r2c1, r2c6, r5c6.

They both lead to the exclusion of 3 in r5c2.
Jeff

Posts: 708
Joined: 01 August 2005

hana somekh
As requested, here's a method which uses colouring.

possible 3s:

Code: Select all
` . 3 . | 3 . . | . . .  3 . . | . 3 3 | . . .  . . . | . . . | . . . -------+-------+------  3 3 . | . . . | . 3 . . 3 . | 3 . 3 | . . .  . 3 . | . 3 . | . 3 . -------+-------+------  . . . | 3 3 . | . . .  . . . | . . . | . . .  . . . | . . . | . . . `

From there,
Code: Select all
` . . . | +3. . | . . . +3 . . | . . . | . . .  . . . | . . . | . . . -------+-------+------  . . . | . . . | .+3 . . . . | . . . | . . .  . . . | .[3]. | .-3 . -------+-------+------  . . . | .+3 . | . . .  . . . | . . . | . . .  . . . | . . . | . . . `

Thus you can eliminate the possibility of a 3 in r6c5, leaving only 6 as the a candidate for the cell.
Bunnybuck

Posts: 15
Joined: 13 June 2005

Bunnybuck wrote:
Code: Select all
` . . . | +3. . | . . . +3 . . | . . . | . . .  . . . | . . . | . . . -------+-------+------  . . . | . . . | .+3 . . . . | . . . | . . .  . . . | .[3]. | .-3 . -------+-------+------  . . . | .+3 . | . . .  . . . | . . . | . . .  . . . | . . . | . . . `

That doesn't make sense to me at all.
Nick70

Posts: 156
Joined: 16 June 2005

There are only two possible cell for 3 in box(2,3)

Case 1: 3 at r4c8
1) only possible location for 3 in box(2,1) is at column 2
2) 3 at r2c1
3) 3 at r1c4
4) 3 at r7c5

Case 2: 3 at r6c8

Either case will eliminate the possibility of a 3 in r6c5.
Bunnybuck

Posts: 15
Joined: 13 June 2005

Bunnybuck

That's not just colouring, rather a mixture of forcing chains and colours. It works but.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff, the turbot fish which leads you to the exclusion of 3 in r5c2 is something which I am still trying to figure out!

The 3's in the first turbot fish which you mention that I have on the puzzle have two strong sides.
The 3's 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 ? I would really appreciate for some further guidance from here !
Thanks !
hana somekh

Posts: 28
Joined: 30 July 2005

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