## Looking for a LOGICAL next step

Advanced methods and approaches for solving Sudoku puzzles

### Looking for a LOGICAL next step

Hi

I just can't seem to move forward (in a reasoned way) from where I am in the puzzle below.

{3}{68}(5678}{5789}{2}{6789}{69}{4}{1}
{59}{69}{1}{4}{56}{3}{7}{2}{8}
{4}{2}{678}{789}{678}{1}{369}{39}{5}
{7}{468}{3}{28}{468}{5}{428}{1}{9}
{1}{5}{89}{2789}{3478}{789}{2348}{6}{247}
{2}{4689}{689}{1}{34678}{6789}{5}{378}{47}
{8}{3}{259}{6}{1}{47}{249}{579}{247}
{59}{7}{4}{3}{58}{2}{1}{89}{6}
{6}{1}{25}{578}{9}{478}{248}{578}{3}

Thanks for any help

June
Prunie

Posts: 5
Joined: 30 July 2005

r1c2 = 8 is the next step.

There's an XWing at r2c2, r4c2, r2c5, r4c5 for 6. This leaves 8 as the only candidate for r1c2.

Simes
simes

Posts: 324
Joined: 11 March 2005
Location: UK

Yes, just found that one, having spent ages not seeing it!!

But it doesn't really seem to move me forward - or maybe I'm just getting x-eyed
Prunie

Posts: 5
Joined: 30 July 2005

Oh you wanted the next step as well!?

r2c1 = 5

forced from either candidate of r3c3
if r3c3=6 => r2c2=9 => r2c1=5
if r3c3=7 => r3c5=8 => r8c5=5 => r8c1=9 => r2c1=5

Simes
simes

Posts: 324
Joined: 11 March 2005
Location: UK

Yes, OK, very clever (I mean it!!)

I'd got there by another chain but I really don't like having to solve them this way. I was hoping there might be another more calculated (kind of) route.

I know all moves are really hypotheses which you test but somehow chains seem kind of "cheating"
Prunie

Posts: 5
Joined: 30 July 2005

How do you find out which forcing chains to pursue? I've been staring at this one a long time and only came up with a short chain eliminating 6 in r3c5.........
Anette

Posts: 55
Joined: 09 June 2005

Prunie wrote:I know all moves are really hypotheses which you test but somehow chains seem kind of "cheating"

It examines the board and finds a logical conclusion. I can understand if you'd regard it as trial-and-error, but personally, I can't see it as cheating.

Anette wrote:How do you find out which forcing chains to pursue? I've been staring at this one a long time and only came up with a short chain eliminating 6 in r3c5.........
I cheat! I use my solver to tell me there is a chain between two cells... although, after that I have to find the chains myself.

Simes
simes

Posts: 324
Joined: 11 March 2005
Location: UK

Prunie wrote:I know all moves are really hypotheses which you test but somehow chains seem kind of "cheating"

I don't agree with this notion that has been bandied about a few times. Yes, all moves can be rephrased as hypothesis-testing, but the converse isn't true: some moves can be written out explicitly without the need to hypothesise, and others can't. So there is a difference, I say, and you're perfectly justified in your feelings of cheating (Not that I'm saying this is the only position that can be taken on the issue, or even the only justifiable one, just that it is a logical one to take).
PaulIQ164

Posts: 533
Joined: 16 July 2005

PaulIQn - people will always use chains - some will even give names to the shapes they form. If that's OK with them then so be it. They're with us and we live with it. If our own particular 'take' on reality is at odds with this then it's our own value problem- nobody elses.

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

simes wrote:forced from either candidate of r3c3
if r3c3=6 => r2c2=9 => r2c1=5
if r3c3=7 => r3c5=8 => r8c5=5 => r8c1=9 => r2c1=5

There's also a simpler one:

r3c5=7 => r3c3<>7 => r3c3=6 => r2c2<>6 => r2c5=6
r3c5=8 => r8c5<>8 => r8c5=5 => r2c5<>5 => r2c5=6
Nick70

Posts: 156
Joined: 16 June 2005

stuartn wrote:PaulIQn - people will always use chains - some will even give names to the shapes they form. If that's OK with them then so be it. They're with us and we live with it. If our own particular 'take' on reality is at odds with this then it's our own value problem- nobody elses.

stuartn

Oh, I agree. I just thought Prunie was seeming a little to aplologetic for not liking using those methods. I just wanted to back up that it was a perfectly valid opinion to hold, if not the only one or the 'best' one.
PaulIQ164

Posts: 533
Joined: 16 July 2005

I'd also like to add that the xy-chain in cells r2c1-r2c2-r3c3-r3c5-r8c5-r8c1-r2c1 is quite apparent, especially if you look at the puzzle with Simple Sudoku filtering for pairs.
Nick70

Posts: 156
Joined: 16 June 2005

Nick70 wrote:I'd also like to add that the xy-chain in cells r2c1-r2c2-r3c3-r3c5-r8c5-r8c1-r2c1 is quite apparent, especially if you look at the puzzle with Simple Sudoku filtering for pairs.

Also, r2c2-r2c5-r8c5-r3c5-r3c3-r2c2 is a shorter xy-chain that excludes 6 from r2c2.
Scott H

Posts: 73
Joined: 28 July 2005

These xy-chains are shown as follows:

Jeff

Posts: 708
Joined: 01 August 2005

It might be helpful -- though it will make for longer posts -- to give at least some explanation of how you went about finding any specific forcing chain in response to a "can't find the next logical step" request. This might help to some degree bring some of the factions in the T&E debate somewhat closer.

It seems to me that COLORING is a METHOD that is used to find a particular type of pattern, but X-WINGS, SWORDFISH ... FORCING CHAINS are the end result, not the method. We often say things like: "There's an x-wing in 4's in rows 2 and 3" -- that doesn't explain HOW it is found.

Personally, finding swordfish -- even if I KNOW one is there, even if I KNOW what DIGIT, is still a short brute force search for me, and I wouldn't know what to tell someone in order to help them find one other than "look for it." On the other hand, whenever I find a forcing chain, I always feel as if I'm following a nearly inevitable course of action to construct it, eliminating possibilites in the same way one eliminates candidates until the path is obvious. So far, I haven't come up with a general method that works in all cases. I'll try to follow my own suggestion in the future, at least for forcing chains. I'm also interested in how others find them.
tso

Posts: 798
Joined: 22 June 2005

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