help in solving a difficult sudoku

Advanced methods and approaches for solving Sudoku puzzles

help in solving a difficult sudoku

Postby hana somekh » Sat Jul 30, 2005 2:37 pm

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

Postby Animator » Sat Jul 30, 2005 4:16 pm

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

Postby SteveF » Sat Jul 30, 2005 4:35 pm

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

Postby hana somekh » Sat Jul 30, 2005 7:27 pm

Steve,

Thank you for your reply.

Could you kindly point out to me where the
swordfish and colour combination is at ?
hana somekh
 
Posts: 28
Joined: 30 July 2005

Postby hana somekh » Sun Jul 31, 2005 3:34 am

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

Postby supertorpe » Sun Jul 31, 2005 4:17 am

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).

Start with the former: (1,1).

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

Postby hana somekh » Mon Aug 01, 2005 12:05 pm

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

Postby emalvick » Mon Aug 01, 2005 5:18 pm

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

Postby hana somekh » Tue Aug 02, 2005 7:25 pm

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

Postby Jeff » Wed Aug 03, 2005 4:02 am

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

Postby Bunnybuck » Wed Aug 03, 2005 4:29 am

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

Postby Nick70 » Wed Aug 03, 2005 5:31 am

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

Postby Bunnybuck » Wed Aug 03, 2005 5:58 am

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

Postby Jeff » Wed Aug 03, 2005 7:32 am

Bunnybuck

That's not just colouring, rather a mixture of forcing chains and colours. It works but.
Jeff
 
Posts: 708
Joined: 01 August 2005

Postby hana somekh » Wed Aug 03, 2005 3:24 pm

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

Next

Return to Advanced solving techniques

cron