The New Sudoku Players' Forum

[Madolite]

Sometimes, when I "solve" a Sudoku puzzle, I end up with interchangeable pairs that can't be definitively resolved (or so it seems). Is this a design flaw, or is there something on my board that I've missed? The puzzle was found in a Sudoku book, it's "Black Belt" difficulty. The issue below is trying to see the definitive location of 9 and 6 on c7, c8 and c9:

As far as I can tell, either placement is fine and will solve the puzzle.

[champagne]

One could say that this is a puzzle with multiple solutions,
on the other side, I see 2 times the digit 9 in column 4 and this is not possible

[999_Springs]

it looks like you messed up the puzzle right at the end, like champagne said there are 2 nines in column 4 and 2 ones in column 6. But this is very easy to fix, all you need to do is erase these 3 cells

Hidden Text: Show

r1c4
r1c8
r3c6

and the puzzle solves itself from there

[Madolite]

Ah yeah I see it now, so after I fix it and put 1 into r3c8 it'll resolve. thanks guys!

[SteveG48]

But to answer your other question, if the puzzle did have multiple solutions, then this would be considered a design flaw in the puzzle.

[Madolite]

Interestingly, I've since learned (through Youtube) that, if you do find a candidate for an unsolvable "double-double", then you can eliminate that as even a possibility, meaning that a number must be in some alternate cell. I mean it makes sense, but I never thought of that until I saw it.

[SpAce]

Interestingly, I've since learned (through Youtube) that, if you do find a candidate for an unsolvable "double-double", then you can eliminate that as even a possibility, meaning that a number must be in some alternate cell. I mean it makes sense, but I never thought of that until I saw it.

Yeah, it makes sense. Like, zero sense to be exact. It seems like you're talking about Unique Rectangles but with some really weird spin. Or maybe you're talking about something else entirely. Impossible to say.

With all due respect and friendliness, how about concentrating on one thing at a time? I'd appreciate if you explained your weird logic here before throwing more of it around.

[Madolite]

How does it make zero sense though? Let me ask you instead, for simplicity. In the below example, where only 12 can be in the three cells where you see 12 - In that fourth cell where you see only a 1 (in a situation where you're just about to find out if a 2 can be there or not), can you have a 2 there and still have a valid puzzle, or can you not? Because if not, and the puzzle is indeed valid (because it's been quality-assured as such), then you must necessarily conclude, by way of elimination, that the 2 must be in come other cell, no?

Because how exactly would you solve the puzzle if 12 are the only valid candidates of all 4 cells? It's hermetically closed. No 1 or 2 could be introduced in any row or column that would resolve it.

As for my other problem elsewhere (assuming we're thinking of the same one) - I already explained how my logic was incorrect, so I shouldn't need to explain that logic because there was no valid logic with that other puzzle.

It seems like you're talking about Unique Rectangles but with some really weird spin.

Yeah, it seems like I did do exactly that, didn't it... But for the record, I'll try to be a little less ambiguous in the future, so that things don't have to seem like anything and you can enjoy some absolute certainty and not have to worry about people using a different way of phrasing things than what you're used to. I am, after all, still learning things and may not be perfectly articulate - or else I wouldn't be here asking about things. So yeah, Unique Rectangles sounds about right. Thanks for teaching me that expression.

Sorry if I seem a little sharp here. But it seemed to me that you were a little passive aggressive in your reply. If not, then I apologize.

[SpAce]

How does it make zero sense though? Let me ask you instead, for simplicity. In the below example, where only 12 can be in the three cells where you see 12 - In that fourth cell where you see only a 1, can you have a 2 there and still have a valid puzzle, or can you not?

No, but you can't have a 1 in there either. If those two are the only candidates left in that cell (as in your first example), you either have an invalid puzzle or you've made a mistake. Either way, there's no way to decide which number goes into which cell in that rectangle. If you only have one of them (and no other digits), as in your second example, then you've definitely made a mistake.

Because if not, and the puzzle is indeed valid (because it's been quality-assured as such), then you must necessarily conclude, by way of elimination, that the 2 must be in some other cell, no?

Because how exactly would you solve the puzzle if 12 are the only valid candidates of all 4 cells? It's hermetically closed.

Exactly. You can't solve it then, but that's precisely the situation you show in both of your examples. That's why they make zero sense. It's an impossible situation in a valid puzzle if those four corners are in just two boxes, unless you've made a mistake. You seem to understand that at some level, but apparently not the full consequences. There must be at least one other digit besides 1 and 2 there, or if not, then at least one of the 1s and 2s must be a given. It's basic Unique Rectangle logic.

As for my other problem elsewhere (assuming we're thinking of the same one) - I already explained how my logic was incorrect, so I shouldn't need to explain that logic because there was no valid logic with that other puzzle.

Thanks. Glad we're on the same page on that.

[SpAce]

(This stuff was added to Madolite's post while I was typing the previous reply, hence the separate response.)

It seems like you're talking about Unique Rectangles but with some really weird spin.

Yeah, it seems like I did do exactly that, didn't it... But for the record, I'll try to be a little less ambiguous in the future, so that things don't have to seem like anything and you can enjoy some absolute certainty and not have to worry about people using a different way of phrasing things than what you're used to. I am, after all, still learning things and may not be perfectly articulate - or else I wouldn't be here asking about things. So yeah, Unique Rectangles sounds about right. Thanks for teaching me that expression.

That's good, and no problem at all. We're all learning here.

Sorry if I seem a little sharp here. But it seemed to me that you were a little passive aggressive in your reply. If not, then I apologize.

No need to apologize. I was Sorry about that.

[Madolite]

No, but you can't have a 1 in there either. If those two are the only candidates left in that cell (as in your first example), you either have an invalid puzzle or you've made a mistake.

Yeah I kinda fixated on the 2 to spot that even just the placement of the 1s make it an invalid puzzle. Thanks for the headsup.

Also, I woke up on a really bad side of the bed today, so I blew your initial reply completely out of proportion and got really defensive. Just wanted you to know that, cause I can imagine you might've wondered why I reacted the way I did. I just have a bad tendency to think the worst of people's intentions when they reply. Anyways, bygones and cheers. I appreciate all help/tips I get, if it gets me somewhere new and improved.

[SpAce]

Also, I woke up on a really bad side of the bed today, so I blew your initial reply completely out of proportion and got really defensive. Just wanted you to know that, cause I can imagine you might've wondered why I reacted the way I did.

Well, I only wonder about unexpected reactions. I kind of incited yours so there was not much to wonder about. That's not my normal style of communication so why did I? In case you're wondering about that, here's the explanation.

Earlier the same day you had asked some questions about a puzzle and some techniques you had problems with. I spent considerable time replying to your concerns in detail. While I was typing that response, you posted again and declared you had found a solution yourself. I replied to that also, telling you that it didn't seem correct to me. All this in a perfectly friendly manner, because I was happy to help as usual. You said nothing.

Of course I don't normally expect immediate or even timely responses, but in this case you remained online and made several other posts while ignoring my detailed attempt to help. It felt a bit like you were blowing me off. If someone suspects that I've made a mistake, it usually becomes a high priority for me to either refute it, or to acknowledge and to fix it, before getting busy to make fresh ones. You, however, made this post next. Even though it made little sense to me, my response would have been just as friendly as before had you acknowledged my earlier help and the other mistake I'd pointed out. But you hadn't. You see, things like that have a tendency to affect people's attitudes and patience. I didn't much bother to hide that in my response.

[Madolite]

Fair enough, although I'll probably seem always online. I stay logged in at all times and I rarely turn off my computer. But yeah, I rarely blow anyone off (at least not people who're likely to know something that I don't), it'd probably be the other way around and I'm too quick to post a faulty comment and then revise it left and right because my mind and writing tends to be a little disconnected from each other.

Either way, I appreciate your candid reply and clarification.

[SpAce]

Either way, I appreciate your candid reply and clarification.

Likewise! All is cool as far as I'm concerned.