## Avoid guessing.

Advanced methods and approaches for solving Sudoku puzzles

### Avoid guessing.

All,

Is there any way to find another number on this puzzle without guessing? I made a few guesses and got it to work, but I can't seem to apply any technique or make up my own to avoid guessing.

Here is the original puzzle:

Code: Select all
+---+---+---+
|..8|.9.|...|
|.5.|82.|7..|
|...|..1|.6.|
+---+---+---+
|3..|...|.7.|
|7.2|3.4|8.1|
|.1.|...|..5|
+---+---+---+
|.7.|4..|...|
|..4|.62|.8.|
|...|.8.|6..|
+---+---+---+

I've 'solved' it up to this point:
Code: Select all
+---+---+---+
|.48|79.|...|
|.5.|82.|7..|
|..7|541|.68|
+---+---+---+
|385|219|476|
|762|354|891|
|419|678|..5|
+---+---+---+
|876|435|...|
|..4|.62|.87|
|...|.87|6..|
+---+---+---+

With the following options table:

Code: Select all
+--------------------------------------------------+
| 126. 4... 8... | 7... 9... 36.. | 1235 1235 23.. |
| 169. .... 13.. | 8... 2... 36.. | 7... 134. 349. |
| 29.. 239. .... | 5... 4... 1... | 239. 6... 8... |
+--------------------------------------------------+
| 3... 8... 5... | 2... 1... 9... | 4... 7... 6... |
| 7... 6... 2... | 3... 5... 4... | 8... 9... 1... |
| 4... 1... 9... | 6... 7... 8... | 23.. 23.. 5... |
+--------------------------------------------------+
| 8... 7... 6... | 4... 3... 5... | 129. 129. 129. |
| 159. 39.. 4... | 19.. 6... 2... | 35.. 8... 7... |
| 1259 239. 13.. | 19.. 8... 7... | 6... 345. 34.. |
+--------------------------------------------------+

Can anyone explain how I can get a bit further without guessing?

It seems like there is something to the 239's in col 2 and row 3, but can't seem to figure it out.

Thank you!!!

-John
Last edited by jgraves on Mon Oct 24, 2005 7:21 pm, edited 2 times in total.
jgraves

Posts: 10
Joined: 24 October 2005

John,

Your puzzle has four acceptable solutions, which means you'll be forced to guess at some point.
Sue De Coq

Posts: 93
Joined: 01 April 2005

Oh. I guess that's what a 5 star (plus) means.

Is there a good rule-of-thumb for making 'good' guesses?

-John
jgraves

Posts: 10
Joined: 24 October 2005

John,

According to my solver, the original puzzle has four solutions but the partially-completed puzzle has just the one, which means that there's a bug in my solver or you've already guessed somewhere along the line. How did you put the 4 at r6c1 and the 9 at r6c3?
Sue De Coq

Posts: 93
Joined: 01 April 2005

Oops! I seem to have missed a number from the original puzzle. I am very sorry. I corrected the previous post. R8C3 is a 4. Very sorry.

So, now is there anyway to avoid the guess!?!?!?!

-John
jgraves

Posts: 10
Joined: 24 October 2005

That's better! The next three moves are quite subtle. You have to have to spot an X-Wing in the 3s, then a forced chain that emanates from r7c7. Here's what my solver had to say about it:

Code: Select all
1. The value 1 in Box 9 must lie in Row 7.
- The moves r8c7:=1 and r9c8:=1 have been eliminated.
The value 2 in Box 9 must lie in Row 7.
- The moves r9c8:=2 and r9c9:=2 have been eliminated.
The value 9 in Box 9 must lie in Row 7.
- The moves r8c7:=9 and r9c9:=9 have been eliminated.
Consider the chain r3c7-3-r3c2~3~r8c2-3-r8c7.
The cell r8c7 must contain the value 3 if the cell r3c7 doesn't.
Therefore, these two cells are the only candidates for the value 3 in Column 7.
- The moves r1c7:=3 and r6c7:=3 have been eliminated.
The value 2 is the only candidate for the cell r6c7.
2. The value 3 is the only candidate for the cell r6c8.
3. The value 2 in Box 1 must lie in Row 3.
- The move r1c1:=2 has been eliminated.
Consider the chain r3c2-3-r3c7-3-r8c7-3-r8c2.
The cell r8c2 must contain the value 3 if the cell r3c2 doesn't.
Therefore, these two cells are the only candidates for the value 3 in Column 2.
- The move r9c2:=3 has been eliminated.
Consider the chain r7c7-1-r7c8-2-r1c8-5-r1c7-1-r7c7.
When the cell r7c7 doesn't contain the value 1, the chain is self-contradicting.
Therefore, the cell r7c7 must contain the value 1.
- The move r7c7:=9 has been eliminated.
The value 1 is the only candidate for the cell r7c7.
Sue De Coq

Posts: 93
Joined: 01 April 2005

First, there is already a 9 in column 8 so 9 is not a candidate for r7c8.

Next you need to look for an X-Wing in 3's, which will allow you to make the next placement.
SteveF

Posts: 86
Joined: 26 March 2005

So there are two Wombles at work!
Sue De Coq

Posts: 93
Joined: 01 April 2005

Sue De Coq wrote:You have to have to spot an X-Wing in the 3s, then a forced chain that emanates from r7c7.

After the X-wing on 3's, and the subsequent basic steps tidy up, it can also be solved with an XY-wing (in boxes 1 & 2) instead of a forced chain.
angusj

Posts: 306
Joined: 12 June 2005

Looks like you beat me to the draw, Sue.

However I was able to proceed after the X-Wing by eliminating 2 from r1c1, which then leaves an XY-Wing (r1c1, r1c6, r2c3) allowing a placement of 6 in r2c6.

After that it's a case of filling in.
SteveF

Posts: 86
Joined: 26 March 2005

Certainly are Sue, although this one isn't as up to speed on forcing chains as yourself.

Angus, 'fraid it looks as if I was beaten to the punch for the second time in this thread!
SteveF

Posts: 86
Joined: 26 March 2005

Wow.

I thought I was pretty good at these things but....

I've read about X-Wing, but this was my first use. I understand how the forced chain works in this puzzle, but I don't think I'd have seen it without some help. (more practice). The XY-Wing is great.

Thanks!!!!

-John
jgraves

Posts: 10
Joined: 24 October 2005