## Trying to graduate to hard

Advanced methods and approaches for solving Sudoku puzzles

### Trying to graduate to hard

And this one's driving me nuts. I've gotten this far:

* * * * * * * 2 *
1 3 * 4 * 2 * 8 9
* * 2 6 * 8 3 * *

2 * * 5 * 9 * * 4
9 7 * * 1 * 2 5 *
3 * * 2 * 7 9 * 8

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

I'm not so much interested in a solution as how to attack it.
Loren Pechtel

Posts: 21
Joined: 06 June 2005

Look for "disjoint subsets" in row 8, block 7 and block 8. (The numbers are 1,3,6 and 5,7 and 1,3,6 respectively.)

(If you need to know what these are, here's my attempt at an explanation www.sadmansoftware.com/sudoku/nakedsubset.htm)
Last edited by simes on Sun Dec 11, 2011 2:39 pm, edited 1 time in total.
simes

Posts: 324
Joined: 11 March 2005
Location: UK

Yes, if you look at r8c4, r8c5 and r8c6, you should be able to see that together they must take up the 1, 3 and 6 leaving r8c3 and r8c7 as 5 and 7. You can use pairings in box 7 to work out where the 3 goes in that box.

Hope this helps!!!

George
george-no1

Posts: 150
Joined: 20 May 2005

simes wrote:Look for "disjoint subsets" in row 8, block 7 and block 8. (The numbers are 1,3,6 and 5,7 and 1,3,6 respectively.)

(If you need to know what these are, here's my attempt at an explanation http://www.simes.clara.co.uk/programs/sudokutechnique5.htm)

Simes
http://www.simes.clara.co.uk/programs/sudoku.htm

ARGH!!

I should have seen that one. When I initially pencilled in the 5's I screwed up and had a slew of extra 5's from missing the 5 in block 8. In going over things I caught the extra 5's but apparently only after evaluating that row for disjoint sets.

george-no1 wrote:Yes, if you look at r8c4, r8c5 and r8c6, you should be able to see that together they must take up the 1, 3 and 6 leaving r8c3 and r8c7 as 5 and 7. You can use pairings in box 7 to work out where the 3 goes in that box.

Hope this helps!!!

George

Here I'm puzzled. I found the disjoint set I was overlooking and it was useful but so far it hasn't revealed where the 3 goes. With the 1, 3 and 6 known to be on row 8 that forced r9c6 to be 4 and some other numbers fell into place with that. I don't have time to hunt the whole thing right now, though.
Loren Pechtel

Posts: 21
Joined: 06 June 2005

To me, an easier way of solving this puzzle is to notice the 8,9 pair in the cells (4,9) and (5,9).

I haven't tried the other methods of solving this, but it looks at first glance as though they involve more complexity.

I don't know about other people, but when I am solving Sudoku, one of the things I immediately note in pencil (in the corner of the cell) are those numbers that are restricted to only two cells in any row/column/box. This makes finding pairs (and x-wings) a lot easier. It also immediatlely leads you to another answer if you fill one of the two cells with a different number.

If you find two numbers that are both restricted to two numbers in a row/column/box then you know immediately that there are no other candidates for that cell.

After spotting the 8,9 pair, the puzzle snowballs.
abailes

Posts: 27
Joined: 02 June 2005

Loren Pechtel wrote:Here I'm puzzled. I found the disjoint set I was overlooking and it was useful but so far it hasn't revealed where the 3 goes.

OK well I might be wrong. but because r9c1 and r8c3 can only be 5 and 7, you can assume that the 3 must go in either r7c2, r9c2 or r9c3. However, there is already a 3 in r2 so that only leaves one candidate for a 3 in box 7.

Have fun!

George
george-no1

Posts: 150
Joined: 20 May 2005

george-no1 wrote:
Loren Pechtel wrote:Here I'm puzzled. I found the disjoint set I was overlooking and it was useful but so far it hasn't revealed where the 3 goes.

OK well I might be wrong. but because r9c1 and r8c3 can only be 5 and 7, you can assume that the 3 must go in either r7c2, r9c2 or r9c3. However, there is already a 3 in r2 so that only leaves one candidate for a 3 in box 7.

Have fun!

George

Oh, I understand now--I was looking at the stuff on row 8.
Loren Pechtel

Posts: 21
Joined: 06 June 2005

Have you solved it now?

George
george-no1

Posts: 150
Joined: 20 May 2005

george-no1 wrote:Have you solved it now?

George

Yup.
Loren Pechtel

Posts: 21
Joined: 06 June 2005