## Sample very hard.sud

Advanced methods and approaches for solving Sudoku puzzles

### Sample very hard.sud

I tried to solve the Sample Very Hard that comes with the program.

Code: Select all
`8**|**1|*3***1|8**|**4***|9**|*7*-----------*5*|**9|6***4*|***|*5***9|7**|*4*-----------*8*|**2|***3**|**5|9***2*|1**|**5`

I can get to the following after which i'm stuck.

Code: Select all
`89*|5*1|236**1|8**|594***|9**|*7*-----------*5*|**9|6***4*|***|*59**9|75*|*4*-----------*8*|**2|***3**|**5|9***2*|1**|**5`

I cheated and tried a solver. It came to the same point as i did before reporting it couldn't be solved by logic. It could solve it by guessing though.

Can this one be solved with logic?
smh

Posts: 4
Joined: 13 June 2005

It sure can be solved by logic... So I guess it's time you start using a better solver

The key to solving it is column 1.

There are two group of numbers. One group has the numbers 4, 5, 6, and the other one has the numbers 1, 2, 6, 7.

If you figure out what that means then you will see that the only place for the number 1 in column 1 is in box 4. This leaves only one place for the number 1 in box 9.
Animator

Posts: 469
Joined: 08 April 2005

Animator wrote:It sure can be solved by logic... So I guess it's time you start using a better solver

It was just an online one. I liked it coz it showed me step by step.

Animator wrote:The key to solving it is column 1.

There are two group of numbers. One group has the numbers 4, 5, 6, and the other one has the numbers 1, 2, 6, 7.

If you figure out what that means then you will see that the only place for the number 1 in column 1 is in box 4. This leaves only one place for the number 1 in box 9.

Thanks.

I've been trying for the last 45 minutes but i can't seem to find what you mean with the two groups. A small hint is greatly appreciated.
smh

Posts: 4
Joined: 13 June 2005

Hmm... I see that I made a mistake...

The first group is 4, 5, 9, and the second group is 1, 2, 6, 7.

The candidates for column 1:

r2c1: 2, 6, 7
r3c1: 2, 4, 5, 6
r4c1: 1, 2, 7
r5c1: 1, 2, 6, 7
r6c1: 1, 2, 6
r7c1: 1, 4, 5, 6, 7, 9
r9c1: 4, 6, 7, 9

I know it might be difficult to see the groups in there, so I'll add some candidates:

r2c1: 1, 2, 6, 7
r3c1: 2, 4, 5, 9, 6
r4c1: 1, 2, 6, 7
r5c1: 1, 2, 6, 7
r6c1: 1, 2, 6, 7
r7c1: 1, 4, 5, 6, 7, 9
r9c1: 4, 5, 6, 7, 9

Do you see the groups now? Where can the numbers 4, 5, 9 go? You have three numbers and the only candidate cells for them are the same three cells...

This basiclly means that they have to have that number, as in, try to fill in another number in r9c1 and see what happens...
Animator

Posts: 469
Joined: 08 April 2005

I think a slightly easier way to tackle this is:

First: col3 where 467 must be in rows 1,8&9
Then: col1 where 7 must be in the middle block
angusj

Posts: 306
Joined: 12 June 2005

angusj is correct that there is also a group in column 3, which allows you to fill in the number 5 in that column.

As soon as I saw column 3 I reliased this question was already asked (and answered). Here is the other thread about this puzzle: http://forum.enjoysudoku.com/viewtopic.php?p=2295
Animator

Posts: 469
Joined: 08 April 2005