In Sudoku, a hidden pair occurs when two digits can only fit in two specific cells within a row, column, or box, even though those cells might also be able to contain other digits; this technique eliminates all other possibilities from those cells, leaving only the two digits to be placed.
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NYT Hard Sudoku Walkthrough | May 23, 2026本站添加:
Hello, let's do the New York Times hard Sudoku for May 23rd, 2026. There's a link in the description if you'd like to try the puzzle yourself, and I'm going to get started right now.
All right, this box is all has a lot of givens in it. Let's go through the givens one at a time and then we'll look more closely at the box itself.
So, the one I mean, I am seeing these two ones look in. That's a one in one of these two.
Uh, I'm seeing one in one of these two.
All right.
The two, we only have two twos.
It doesn't quite do enough in this box.
All right, the four, we only have two fours. Doesn't do enough in this box or this box. All right.
Um, I was looking at four in this column, but there's unfortunately still three places for it.
The fives look in here. Five looks up, placing this five. Let's keep going on five since we just placed one.
Five is placed there. These fives look in. Five looks down. Five is in one of these two.
Five is also in one of these two. I think we have six fives. One, two, three, four, five, six. Yeah. So, there's three fives remaining and they're going to be in this L-shape. I mean, the two is occupying one spot, but sort of classic L-shape when you have three left. There is one other option, which is like all in the same stack or all in the same band, but a lot more common is the L-shape.
Um, but those are the only two options when you have three left of a digit.
All right. Uh, seven. Sevens are done horizontally. Not seeing anything vertically.
All righty.
Um, four digits left in this box. Let's just take a look.
We need a 3 6 8 9.
So, I'm seeing we have this three and this eight looking in here.
And that tells us that this is a hidden 3 8 pair.
What does that mean? Well, I got to put a three and an eight in the box. That's Sudoku rules. I got both of them in there. I need two cells for that. These are the only two cells that can be three or eight. So, one of these will be three, the other will be eight, meaning we can't put anything else there. It removes the other digits that could have been there, leaving only the three and the eight. It's an elimination tactic of the cells that you find it in.
In general, if a technique is called hidden, this is a hidden pair, a hidden technique, hidden single, hidden pair, hidden triple, etc. Those will eliminate from the cells you find it in. So, we found a hidden 3 8, it eliminates from those. A naked technique, naked single, naked pair, naked triple will eliminate from other cells in its row, column, or box. Um So, like a naked pair would eliminate those two digits from the whatever row, column, or box that both cells share.
Anyway, that leaves two digits here. We do need a nine. This nine looks up.
That's the nine. The other digit is six.
All right.
So, three digits left in this row. We need 1 2 4.
I only see this one.
Anything else with that? Does the six or the nine do anything?
I am noticing the sixes looking here.
So, six is one of these three, but we can't quite make a hidden triple yet.
It's only two digits in three cells.
Does mean these are slightly more restricted than we might have thought, but removing the five and six from here isn't enough to mark them.
Maybe this cell cuz it's not I mean, it already wasn't five. So, the how many digits is this? 1 2 3 4 5. So, it's already not five digits, and the six is a sixth digit that it's not. That is That does leave three digits that it can be. So, we can mark that.
That's um 3 4 and eight is what's left there.
I mean, this whole column is just four digits though. It's 3 4 6 8.
Um everything sees something.
So, that's not a four. That's not a three, and that's not an eight.
I don't think they do anything yet.
All right.
Um anything else related to this box I move on? I don't think so.
This four doesn't do a crossing, unfortunately.
All right.
This box, we have five, seven, and eight. Fives we basically took care of, right? We have That's the one we have Yeah.
Bunch of the seven.
Seven's not great.
You know, something I want to do is this box here has four givens in kind of a avoiding over an entire row and an entire column. And when you have that pattern, it doesn't have to be like this, it could be like this.
It could be like this. It's just we're avoiding an entire row and entire column. So, in this case, this is the easiest one to see.
We You kind of want to just immediately look at the rest of the row and column that it isn't in to see if there's any givens there that aren't yet in this box. And so, the only thing I'm seeing is the nine. But, that does cause pointing. So, there's a nine in one of these two.
That does point up. This nine looks in.
Nine's one of these two.
It also means these aren't nine. This nine looks in. This nine looks in.
Nine's one of these two.
All right.
Um five, seven, eight. Does the eight do anything? We do have these two eights.
Eight's one of these three.
All right. How about this row? We need a one, three, six, eight.
This can't be three or eight. So, this is one, six.
This can't be three or six. This is one, eight.
I think this could be any of them. Oh, no, can't be eight. This is one, three, six.
All right.
Nothing super special there.
Anything vertical with this three, five, seven, nine?
Just the seven.
Seven's one of these three.
Anything else I want to do in this top band? It doesn't look like it.
Let's just move on to the next band here. I don't think this band's going to do much, though.
The nine, the four, and the five.
Um, and the two and the six.
There's no crossings.
There's really nothing to see here, is there?
No no bodies, no good geometry.
Yeah, okay. Let's just move on.
The five and the nine here. I already looked it for this four to be a crossing and it's not.
The fives we took care of. The nine we took care of here.
Okay.
What 1 3 5 8? So The ones we got, the three doesn't seem helpful.
The eight also unhelpful. All right, what this 1 7?
Sorry, I was just double checking that this against this row. Unfortunately, one one and five already here. So it's the three and the eight that go here.
I'm seeing this three, but unfortunately we don't have like the eight eliminated from there either.
Or in addition. Uh this column is down to four digits. We could look at that.
We need a 2 3 6 9.
Um this can't be three or nine. So this is 2 6.
This is 3 6 cuz it's not two or nine.
2 3 6 9.
I think these can be any of 2 3 Oh no, this can't be six. This is 2 3 9.
2 3 6 9. Okay.
Nothing nothing amazing there.
Then the 1 7 uh doesn't do anything.
Huh. Okay. Well, that's very little from our full initial pass. I'm going to go row by row, see if there's anything worth marking, if I missed any pairs or triples, that sort of thing.
Um don't really want to touch that row yet.
None of these rows look interesting.
Maybe columns will be more interesting.
Yeah, I'm not really see like a lot of the most of these rows or all of these rows that remain are are very open. So, let's look at the columns.
You know, there's not >> [sighs] >> Maybe this column.
Wow, it it's really rare to have this this sort of sparseness.
Anyway, we need a 1 4 5 8 9.
This is not 1 5 or 9.
This is 4 8 only.
I'm going to look carefully to see if that does anything.
This is 1 5 8 9. Oh, this can't be 1 5 or 9. So, 1 4 5 So, this is also 4 8.
Oh. So, we So, this is 1 5 9's not here.
And 1 5 and 9 aren't here.
And that leaves three places for 1 5 9.
Or if you prefer, we have a naked 4 8 pair. They are two sides of the same coin. Either way, we're removing 4 and 8 from these three cells.
So, this can only be one. It can't be the 5 or 9. So, really what we have is a 5 9 hidden pair in this column, which may have been spottable from this box.
Cuz 5 9's not here.
These aren't 5 9, and this cell sees a 5 9. So, right from the start, we have a 5 9 hidden pair here, which I didn't notice.
So, we can put that 5 9 hidden pair, and then notice that that can't be 1, and that can't be 1. So, we have a hidden 1 in the column.
And then we're left with a 4 8 pair here. All right. Now, this 1 does resolve the 6 3 and 8 here and this 3.
This can't be 1 anymore. That places the 1 for the row.
This is now a triple.
2 Is it 4? Yeah, 2 4 9. That's not 4.
That's not 9 cuz we have the pointing 9's.
Watermark's reminding us of that. 2 4 9 triple means that's not 4. In In the 2 4 pair also means that's not four. So, that's eight and that's four. And this box, the final digit is an is a six, it looks like.
Six is in one of these three.
Okay, I got this four. Four looks in here, none of these are four. So, four is in one of these two, giving us a hidden 4-9 pair. The overlapping corner marks just immediately tell us that that one of these is four, the other is nine.
Meaning this can't be four, so that's a two, nine and four. So, that places the nine here.
Places our five and our nine there. That gives us four and nine. That's not five, placing this five.
That's not four. I think fives are done Oh, fives aren't done, but they should be, right? Yeah, that's the final five, okay.
Um All right. Let's do this triple. It involves the six, so we can remove that six, but anyway. Um 2-6-7 All right, that's not six, that's not two. And so, that's a pair here.
What two digits is it?
Uh 1 2 3 and 5, it looks like. This three looks down, so that's five Well, not five, but anyway, that is the three.
What's the other actual other digit?
Eight, okay.
That's not an eight. Uh it goes in one of these two.
Um these three 2-6-8 That's not eight, that's not six.
Uh Four digits left in this column. We need a 1-2-6-7.
They all see something, so maybe not this one.
Yeah, not this one, but this sees six, this sees seven, this sees one.
What are we doing to wrap this up?
2-6-8 The eight's in one of these two, but that doesn't really matter.
You also don't really need these sixes marked.
2 3 6 7. This isn't six, so 2 3 7.
Is there like a corner mark I've ignored?
How about this 2 7? Oh, yeah, it's not two. So, that's seven. That's two, six, and seven. That's a three and a two.
That's not a two.
Okay, I think I need to be much more careful about scanning here. Four digits left in this row. We need a 1 4 6 8.
This isn't 6 8, so it's 1 4 only.
Oh, this is a triple. I suppose it's 1 6 8.
It's not six.
1 4 6 8. So, this is 4 8. It's not one or six one or six. 1 4 6 8.
1 2 6 7. We already looked at that.
What's our Uh it's hanging on. This puzzle is hanging on.
Um We know the eight's here, yeah.
Uh I don't really have any interesting markings to look at. What about columns?
Maybe this column, I guess.
Uh We need a 2 3 4.
So, it can't be two. So, we need 3 4 7 8.
This can't be four, so this is 3 7 8.
3 4 7 8. This could be any of them.
Okay, that's unhelpful.
2 4 Anything in the rows?
Okay, what does this row need besides what we already have center marked? 1 3 4 7 8.
There should be one more digit.
It's the nine. We haven't penciled the nine. So, nine does not go here.
Nine does not go here. So, nine in this row has to go here. Oh, that's a sneaky hidden single.
All right, yeah, this nine not here.
Nine not here. Oh, yeah, we just It's not actually that sneaky. These two nines looking at this nine looking down.
It's just I I didn't follow up on all the buddies as I placed cuz I thought we were just cascading.
Um so, maybe I should look more for buddies especially with blue digits.
Um That actually was the last nine.
>> [snorts] >> Um The five. I'm just going to get every digit it's due. Well, fives and nines are done, but these twos look back putting a two in one of these two.
I feel like I should be able to just finish my penciling, but 3 7 9 The five and the nine are done.
What is eight?
No.
Anything?
Three?
So, three's in one of these two. Oh, whoa.
Sorry, I clicked something.
Uh three's in one of these two. The four is in one of these two.
Is this worth marking?
Maybe we should just look at this whole column.
Just mark the rest of it. Uh we need a 1 2 3 4 7.
1 2 3 4 7.
This isn't three or seven, so this is 1 2 4.
>> [sighs] >> 1 2 3 4 7.
1 2 3 7 1 3 4 7 not hopeful.
4 6 1 2 You know the one and the four here.
Yeah, it's cuz we have the 2 6 8 here.
2 4 8 Oh, we have a 2 4 8 naked triple here. The three and the seven go here.
So, that's not eight. This is 3 7.
All right. So, what's left in this box then?
Um the one 1 4 8 Yeah.
It's not a four.
Okay. So, in this box the four is on one of these two. And what unlocked that was this either the 2 4 8 triple or the hidden 3 7. Take your pick.
Either way, this can't be four anymore.
That puts four on one of these two.
That's going to point telling us this has to be a one cuz it can't be four.
That gives us the seven and the three.
That's a seven.
This one had one one last uh sneaky step there.
That's not a one. That puts the one here. That's not a seven.
Um this is two or six.
4 8 pairs, so that's a six.
1 8 pairs, so that's not an eight.
That's an eight. That's one and eight.
That's one.
Um That's a four. That's two and four.
I think yeah.
Uh that's six. That's two. That's three and seven. We get the 2 8 6 4 8 4 2.
That's a six. That's a three. And we're done. All right.
Some sneaky steps in that one. All righty. Well, how'd you do?
>> Mhm.
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