## Solved by guessing.

Advanced methods and approaches for solving Sudoku puzzles

### Solved by guessing.

I became stuck on this puzzle I found in a newspaper and assumed it was do-able but didn't know by which logic an expert would use to solve it. Can someone explain where I should have gone from this point:

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

9 * 5 1 7 8 4 * 2
8 * 7 4 2 6 9 * *
* * 2 5 9 3 8 * 7

7 * * 2 * 4 * * *
5 2 * * * * * * 4
3 8 4 6 * * * 2 9

I knew column 1 still needed a 4 & 6 so I put a 4 in r3c1 and solved. What technique should I have used to prove that this was right?
krazyarde

Posts: 6
Joined: 30 September 2005

To begin with you've got a couple of locked candidate set-ups, involving Box 4. Then you've got the same set-up using Box 6, and again with Box 8.

Now, you've got a Hidden Pair in Row 3, this reveals a Quad in Column 5 and from this point on it pretty much opens up. You can place a few in the top row of boxes and shortly after it becomes apparent why you need a 4 in r3c1.
Karyobin

Posts: 396
Joined: 18 June 2005

What technique should I have used to prove that this was right?

Well, start over and put a 6. You should be able to find the puzzle unsolvable. That will prove 4 was right.

This is how one solves by guessing.

If you use pencilmarks, you should not have to resort to guessing for this puzzle.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

You seem to have missed an important point implicit in krazyarde's question there Mac.

Many moons ago when I first joined this site I remember a comment being made along the lines of "Sudoku can be solved with a gun to your head; you should be able to bet your life on any individual entry, because you should always know precisely why you are filling a certain cell".

I utterly agree with this sentiment and as such I don't think that your offering, which was essentially 'it doesn't matter why you know what's right, so long as you get there in the end' helps to answer krazyarde's question, which was basically 'how should I prove that 4 is the correct entry without guessing?' A trial-and-error method, whilst applicable in situations requiring the likes of Forcing chains, is really unnecessary for this particular puzzle.
Karyobin

Posts: 396
Joined: 18 June 2005

I took Mac's advise and put in pencilmarks but still don't see. I see the locked candidate 3 in box 4 and 6 but don't see one in 8 Kary. What don't I understand?

2 7 (369) (39) (1356) (159) (156) 4 8
1 (4569) (689) (89) (4568) (59) 2 7 3
(46) (456) (368) 7 (134568) 2 (156) 9 (156)

9 (36) 5 1 7 8 4 (36) 2
8 (13) 7 4 2 6 9 (135) (15)
(46) (146) 2 5 9 3 8 (16) 7

7 (69) (169) 2 (1358) 4 (1356) (158) (156)
5 2 (169) (389) (138) (179) (1367) (18) 4
3 8 4 6 (15) (157) (157) 2 9
krazyarde

Posts: 6
Joined: 30 September 2005

Okedoke:

1's and 3's are locked in Box 4, 3's and 6's are locked in Box 6 and 9's are locked in Box 8. Then go for the Hidden Pair in Row 3 and the Quad reveals itself nicely.
Karyobin

Posts: 396
Joined: 18 June 2005

I see the light. Thank you Karyobin for your expertise. I am amazed at your skills!!!
krazyarde

Posts: 6
Joined: 30 September 2005

Oooohh, stop it! You'll make me blush.
Karyobin

Posts: 396
Joined: 18 June 2005

### Solved by guessing

Karyobin wrote:To begin with you've got a couple of locked candidate set-ups, involving Box 4. Then you've got the same set-up using Box 6, and again with Box 8.

Now, you've got a Hidden Pair in Row 3, this reveals a Quad in Column 5 and from this point on it pretty much opens up. You can place a few in the top row of boxes and shortly after it becomes apparent why you need a 4 in r3c1.

Interesting thread this. After Kary's above eliminations I was left with candidates [46] [456] and [38] in Box1(row3). Still couldn't see why 4 must go in r3c1 until I eventually spotted the candidate 6's locked in Box 3 which enabled the other candidate 6's to be removed from r3c1 leaving 4 to occupy this cell. Was this a necessary further clue to fill cell r3c1 (other than for me) or is there a simpler explanation? Help appreciated.

Bonsai Cec
Cec

Posts: 1039
Joined: 16 June 2005

[quote]What technique should I have used to prove that this was right?[/quote]

Heh, I am a programmer, not a SuDoku person, so I tend to be literal.

To the exact question asked, I provided an exact answer. Then I added that such an approach would be "guessing" and is not necessary.

I left to the gurus the task of providing hints. You did that. Good. You trashed me. Bad, but feel free to keep it up. I won't protest next time.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

cecbevwr wrote:Still couldn't see why 4 must go in r3c1 until I eventually spotted the candidate 6's locked in Box 3 which enabled the other candidate 6's to be removed from r3c1 leaving 4 to occupy this cell. Was this a necessary further clue to fill cell r3c1 (other than for me) or is there a simpler explanation?

Well to be honest yours is as good as any. Personally, I found that there was a triple in Box 2 {3,9}, {8,9}, {3,8}. That allowed me to place the 1 and 5 in Box 2 and the growing lack of clutter then helped me to spot the locked 6's in Row 2. Same thing either way really.

Mac - sorry for taking your literal response as a pithy quip, unfortunately they crop up with alarming frequency.
Karyobin

Posts: 396
Joined: 18 June 2005

QBMac you're a programmer how come you have trouble with the quote box. It's a very nice little arrangement and it bothers me when it doesn't come out right. You need to use the brackets and quotes correctly so that you have
blah, blah, blah

and then the whole piece will sit nicely, like so.

Oh and also preview before you shoot.

Right, anyone else.....!
emm

Posts: 987
Joined: 02 July 2005

Is misuse of the
quote

function your Theme for the Day then em?
Karyobin

Posts: 396
Joined: 18 June 2005

Yes. It's like a housekeeping job I've had in mind for quite some time. I'm on the rampage now and everybody's going to keep doing it until they get it right!
emm

Posts: 987
Joined: 02 July 2005

I properly enter the quote and code without any error of any kind. I use the little boxes under "Subject", which gives the same result as typing.

My problem seems to be that "Disable BBCode in this post" is always ticked when I come to this site. I unclick it, and the quote works. I sure would like to know how to make unticked the default.

Oh and also preview before you shoot.

That's the key! I keep forgetting to preview. Will try harder. Thanks, em. And OK, Karyobin,

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

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