A Sudoku With Only 6 Given Digits?!

追加: 2026-05-10

[00:00:14]Hello and welcome to Sunday's edition of Cracking the Cryptic on a very special day because it's an Ard van de Eiter in day here on the channel. Ard is of course probably the most famous Sudoku constructor in the world.

[00:00:31]Um and this puzzle is called In Between Taken and if you've never tried an Ard van de Eiter in puzzle, please give yourself a treat and click the link under the video. It'll take you to a page that looks exactly like this one where you can play the puzzle on whichever device takes your fancy. Um but one thing you can basically be assured of is that you will have uh well, the puzzle will give you a lot of joy joy. Um Ard is responsible for many of our very biggest videos on the channel including the Sudoku with only four given digits which has now had 10.19 million views.

[00:01:15]It's just staggering, isn't it?

[00:01:17]Absolutely incredible. Loads of Ard's puzzles have had more than a million views.

[00:01:23]He has this ability to really just I don't know. I think I think solvers just fall in love with the simplicity, the elegance, the the look of the puzzles.

[00:01:37]He always gives you a few given digits.

[00:01:39]Ard does as well. Look at how many we've got today. We've got six. And um yeah, and and the and the logic that tends to exist in his puzzles is never normally monstrously hard to find, but when you do find it, you feel you feel you've done something clever.

[00:01:56]Um so that is what I hope I'll be able to do today. And the other thing about Arts Puzzles is that the rule sets are very short. Um, and this one I think is just between lines. So, don't worry if you don't know what they are. I will explain them properly in a moment or two's time when we go through the rules together.

[00:02:11]Um, but this is what we're going to attempt in today's video. Now, what can I tell you about before that? Um, not very much news today. Uh, we should be back in the Blueprints Mansion tomorrow for those of you who've been following our our progress through that incredible game. We've been visiting the Blueprints Mansion about once a week for over a year. So, um, hopefully it won't be too much of a surprise that we're back there tomorrow evening. I'll try and remember to put a link to that on the screen in case you're interested. Uh, it the stream will start at 10:00 p.m. And um, what else? Over on Patreon, we have got uh, it's been running for a while now, um, since the 1st of May, we've we've had our Newsudoku competition running. Themed this month on the legendary Spider-Man. Um, and uh, yeah, features eight puzzles. Lots of you have been having a go at that and enjoying it, which is lovely to see. So, do do get involved. The closing date's the 20th. And um, the prize, as usual recently, is the chance to come onto the channel and to solve a puzzle that will appear in a video. So, uh, those of you who enjoy such things may remember Merel from um, last month. Um, absolute you know, it's just a a real it's a treat for me actually to to make those videos. So, um, if you if you fancy if you fancy coming on, then do get involved in that.

[00:03:36]So, we're on Patreon right now. And I've got one birthday to do today, too, which is for Jaya.

[00:03:43]Jaya, your boyfriend, Grayson, wrote to me uh, and told me that you've started to I think only watching the channel this academic year, but you you watch to wind down um while you've been finishing your first year of at college doing neuroscience. So, best of luck with your remaining studies. I hope you have an absolutely brilliant birthday today. And of course, I hope Grayson has sorted you out some very heavily iced chocolate cake.

[00:04:11]That's all the news. Shall we have a go at In Between taken by Ardo and Debaterin. The rules, which are not going to take long to read, are as follows. We have got normal Sudoku rules applying. So, we've got to put the digits 1 to 9 once each in every row, every column, and every 3 by 3 box.

[00:04:29]Um then the values of the digits along a line must lie between the two values of the circles at either end of that line.

[00:04:39]So, let's pick this line.

[00:04:41]If we were to put two here and seven there, then the digits on this line, let me just highlight the line. Those cells would have to have a value between two and seven. So, they couldn't include ones, twos, sevens, eights, or nines.

[00:04:59]They'd have to be threes, fours, fives, and sixes.

[00:05:04]That's That's how between lines work.

[00:05:08]Do you have a go. The way to play is to click the link under the video as usual.

[00:05:11]But now, I get to play. Let's get cracking. Now, I'm going to start off by mentioning I I know very, very few secrets about between lines, um but one secret is is Well, it's worth repeating probably.

[00:05:30]Um you can never on a between line put an extreme digit like a one or a nine. Because imagine this was a one.

[00:05:37]What would you put into the circles now?

[00:05:39]Because the circles have to One of those circles has to be lower than the value one, and there are no such Sudoku digits. Similarly, if you put nine on on a line, you've got the same problem.

[00:05:48]You'd have to put 10 in a circle or or a higher number in a circle, which we can't do.

[00:05:53]So, ones and nines, I mean, actually, it looks like this line might be where we stop, but ones and nines can never go on, you know, on the line cells themselves.

[00:06:09]Yeah, I mean, it's a it is a bit interesting in box two, actually, isn't it?

[00:06:14]Because these two cells can't be ones.

[00:06:16]That These can't be ones by the home.

[00:06:18]No, it's actually very interesting this box. We can We actually just get to place a one. That's That's completely trivial. Now, ooh, nearly. We almost get a one in box one. Can't go on the lines. Can't go in its own row, so it's in one of two places.

[00:06:34]Can't one of two places in box four.

[00:06:38]Nearly. One of two places in box seven.

[00:06:42]Should we try box eight?

[00:06:44]Yes. Okay, look at box eight. It's It's a bit weird to look at, but it does work. Where's one in box eight? Not in these cells. Not on lines.

[00:06:54]And uh oh, hang on. Ooh, I I missed this Ah, Bob Bobbins. I very nearly made a mistake then.

[00:07:01]I I I didn't realize that the one could go there.

[00:07:06]Which is a circle, obviously, but that's fine.

[00:07:11]Okay. Okay, but what we can do is note that one in box eight can't go on a line or in this this central cell because of the one in row five, column five. So, we can ask where does one go in row eight?

[00:07:25]And there's actually only one cell that's that's going to work.

[00:07:29]And now, where does one go in box six?

[00:07:32]One of two places.

[00:07:34]And that's good. Where does one go in box three? So, we're chasing these ones around the grid. Can't go on a line, so it's going to have to go here.

[00:07:44]And therefore, one is not in a circle over on this side of the grid.

[00:07:53]So, now okay, hmm.

[00:08:00]I don't know whether I should I'm going to try the same with nines and then we Oh.

[00:08:07]Yeah, no, let's try the same with nines first. Let's just see if we can do any with those.

[00:08:13]What about one in box eight? Nine in box eight even.

[00:08:19]One of two cells, I think, given it can't go on a line. So, one of two cells in box five.

[00:08:29]Box Hmm, no, box three, I think I think it very much could go in this cell. We probably need to investigate this cell in a moment or two.

[00:08:43]The the other thought I was having though is is if there are lines in the puzzle now that can't have ones in their circles, then you can't put two on those lines.

[00:08:53]It sort of becomes iterative because if you put two on a line that can't have a one in a circle, what did you are you going to put on the circle? What What value could you put into the circles that's less than the two?

[00:09:04]So, there would be no value value available.

[00:09:07]So, for example, I it's not a very good example, but this line, that none of those cells can be a two. Anyway, let's let's look at this cell. And the reason to look at this cell is we've got a five on one end of the line and a seven on this end of the line. So, we need a digit that's higher than seven to go in here. So, that has to be eight or nine.

[00:09:32]And in fact, this line therefore, in fact, that digit's naked.

[00:09:37]Um because what we need to do is to populate this line now with digits that lie in value terms between five and a maximum of nine. So, we can only put six, sevens, and eights into these cells. So, if even I'm prepared to pencil mark that, and you can see this one by Sudoku using our using the given digits, therefore, must be a six.

[00:10:02]Um now, okay, that didn't do as much as I was hoping.

[00:10:08]Um Yeah, so these digits are now two, three, four, and five.

[00:10:21]Nine in a circle is really not an interesting creature, is it? That's not going to be where we have to look, I don't think.

[00:10:31]Ooh, okay.

[00:10:33]Well, I'm suddenly stuck. I don't know where to look. What about two, three, four, five, six into row three? Is that in any way helpful?

[00:10:51]Oh, I'll tell you what we could do.

[00:10:53]Where's nine in box one?

[00:10:56]It can't go on a line, so I really don't know where it goes, but I do know it's in one of three cells, and that's going to that's going to be good cuz now I've knocked it out of two of the three cells it could have been in in box three. So, I'm going to have to put the nine here, but that's given me eight in the circle now.

[00:11:13]Which means eight now can't go on this long line anymore.

[00:11:17]So, we're only looking at sixes and sevens.

[00:11:23]Where's nine in column eight? Again, let's not put it on a line, so we can get another Where's nine in box five?

[00:11:30]Suddenly, we're actually doing a lot better. What Oh, nearly.

[00:11:35]Where's nine in box four? Now, we've got to be careful here because nine could go in the circle. It wouldn't put very much pressure on this line, but it actually I mean, that doesn't matter. It could still go there.

[00:11:50]Now.

[00:11:54]So, can we do anything better? Where's nine in box I think nine can go in five different places in box seven.

[00:12:08]So, I'm not sure we can do anything terribly clever with that.

[00:12:12]Um and we've got an eight here now.

[00:12:21]So, this digit is six or lower.

[00:12:27]This digit Well, this digit can't be six.

[00:12:34]So, that Okay, so this digit can't be five either because between five and eight, there's no valid number that we could put in. So, that's got to be two, three, or four. And this has got to be higher than that. So, this is three, four, or five.

[00:12:51]But Okay, don't know what we do there.

[00:12:59]So, what's odd hidden in this grid?

[00:13:06]Is it this five? Is there something going on there or eight?

[00:13:17]Yeah, okay, I see.

[00:13:19]Eight Oh, I don't actually see, but eight has to be in one of these two cells now.

[00:13:24]In box one.

[00:13:26]On a line, which means Well, what does it mean? If the eight is here, you can see this is the position that nine would have to go to frame this line. And if the eight is here, this would have to be a nine. So, one of those two cells is a nine. Which does mean Yeah, that's that does it actually, doesn't it? So, because because one of these green cells is a nine, how could this be a nine in box four?

[00:13:58]If this was a nine, neither of these could be a nine and this eight couldn't exist on a line wherein we know it must be. So, this is not nine and now I seem to only have one place left for nine.

[00:14:11]Now, that's weird though because that doesn't mean that this isn't a nine as well.

[00:14:19]It could still be a nine.

[00:14:22]It just means that corner digit isn't a nine. Oh, we're getting a fly past from Maverick. How lucky for us.

[00:14:28]So, nine in box seven is more restricted than it used to be. Only one of three places now.

[00:14:36]And this line is totally hopeless. I mean, literally, we can put in any values on this on this line in box one now cuz it's got one and nine on its outskirts.

[00:14:53]Right.

[00:14:57]So, where should we look next?

[00:15:07]I don't know.

[00:15:11]Gosh. Um Is there If that was a nine, this would have to be six, seven, or eight, but it looks very much like it could be that.

[00:15:28]Have ones been pushed around somehow as a result of what we've just done?

[00:15:38]Don't think so.

[00:15:42]I put a one here, so that this can't be a one anymore.

[00:15:46]I don't know how long I thought that could be a one, but one ones are in this congregation of cells. We've got a sort of two two X-wings of ones left.

[00:16:00]And well, some of if this was a one, it would be really quite useful.

[00:16:07]So, maybe it's something to do with Is it something to do with twos or Thing is, I know so little about twos.

[00:16:20]Is it possible that this We might be able to work out whether this is a high digit or not. Ah, in fact, hang on. I've just noticed something. This cell This cell is either quite little or it's eight because it can't be 5, 6, 7, or 9.

[00:16:41]Now, if it's eight, there's no pressure on this line at all.

[00:16:49]If it's eight, I wonder.

[00:16:58]If it's Yeah, maybe I'm I'm not sure I'm not quite sure where we're meant to look here.

[00:17:06]Maybe I'm going to check eight in box six.

[00:17:09]Now, for eight to be on a line, you'd have to be able to put nine in a circle, but actually you can, can't you? Nines could go in these positions down here.

[00:17:22]All right, so I don't actually think that is it then. It might be this cell.

[00:17:27]Although if it's eight, this line's under no pressure. If it's not eight, what would we be doing with it then?

[00:17:34]These would be terribly close together, which would be quite interesting because this could only be two, three or so that would be this would have to be two or four.

[00:17:45]Ah, that this might be disprovable.

[00:17:48]Right, let's just think this through. So this cell here is really low.

[00:17:54]And this cell here, if it's not eight, is going to have to be by Sudoku two, three or four. But we have to allow a gap, don't we? We can't make this two and this two, then we couldn't fill anything onto the line. And the only way of making this work would be to have two and four into these two cells and threes in all of those. Now that probably won't work. We're just going to have to work out quickly why.

[00:18:23]Three threes there. Is that really possible?

[00:18:31]I don't know, maybe it is. Okay, well that's two, three, four or eight.

[00:18:36]Maybe this can't be eight for some reason.

[00:18:42]I think it can be. Oh, oh no, it can't.

[00:18:45]Oh, that's very ah, ah, you got me. You got me. Well done.

[00:18:50]Ah, why can't this be eight?

[00:18:53]Because what would I fill into this cell?

[00:18:55]It would have to be six or seven and it can't be either. Oh, that this is gorgeous then. So these are these do have to be two and four and I have to fill three onto that line three times.

[00:19:06]And now this isn't a three.

[00:19:10]So, I know that could be still or five and this digit is therefore two, four or five.

[00:19:17]Threes are in one of these two positions.

[00:19:21]Threes are in one of the We've got a very good chance of a three in the corner today.

[00:19:27]So, four, five, two.

[00:19:33]And oh oh, this can't be four because again, this little this little line here is crucial.

[00:19:40]It's crucial whether this is eight or in this situation, if this is four, four and five have no digits between them so there'd be nothing to put on the line.

[00:19:47]So, that's two, that's four, that's five because we need a digit between four and eight now. This is two.

[00:19:56]This is three. Oh, it's not three.

[00:19:58]That's four now.

[00:20:01]Okay.

[00:20:02]And suddenly, I feel like we've made quite a bit of progress there.

[00:20:08]And the rest of this box is what then?

[00:20:11]158.

[00:20:13]Let's pop that in as pencil marks. This can't be one.

[00:20:19]So, where's eight in column one? It's got to be in the same two cells that a three is, which means these top cells are six and seven now.

[00:20:31]And we know the order if we if we if we let ourselves use Sudoku, which we Now, we've got a three-six pair over on the right-hand side so these digits are two and nine.

[00:20:45]Right. So, if this was nine, this would have to be eight.

[00:20:50]And if this is two, this has to be three, which it can't be four or five.

[00:20:59]Okay, that that does look possible, doesn't it?

[00:21:04]God, it's really windy today outside. I think that might be keeping Maverick quiet 245 into these cells by Sudoku.

[00:21:14]So, if this was five, this would have to be seven.

[00:21:19]So, it couldn't be six.

[00:21:24]Um Okay.

[00:21:30]And now what about this digit then? Do we know whether this is higher or lower than five?

[00:21:37]Higher than five? We said uh That was Bruce Forsyth, wasn't it? Play your cards right.

[00:21:42]Um You can't get anything for a pair, not in this game.

[00:21:47]Um Hm.

[00:21:51]So, if that if this is higher, this is six or seven cuz it can't be eight.

[00:21:58]And that will put a 6-7 pair in column two.

[00:22:03]It looks plausible, doesn't it? Oh, hang on. We've got a two in those cells. So, this This is a 458 triple.

[00:22:16]Seven has to be over here, but not necessarily on the line.

[00:22:24]Two is definitely in one of those two cells by that fair-weathered friend Sudoku.

[00:22:34]And this congregation of threes that we earned for ourselves, has that done something beyond actually just the digits going into the puzzle?

[00:22:45]36245s Two is in one of these, so these are from 457 on this side of the grid.

[00:22:56]So, I know there's I was wondering if there was some value here that we couldn't have in row two, column eight, but it doesn't look like there is.

[00:23:08]And this line Well, if that's five, maybe that's under pressure.

[00:23:21]But again, it sort of feels like at this point that we need a cleverness, don't we? We need something smart.

[00:23:32]Now, where?

[00:23:34]Where is the smart deduction?

[00:23:37]This digit is 3 5 6 8 9.

[00:23:43]It's got too many options. It just does.

[00:23:47]Five is in one of those four cells.

[00:23:50]That's not it either, I don't think.

[00:23:56]Have we learned any more about nines or ones that we could use to our advantage?

[00:24:04]Or twos even. I have now got a two in the grid. I've got to actually I've got two twos in the grid.

[00:24:09]Ah, yeah, all right. Where's two in box five?

[00:24:12]That's Ah, can I put two here, please?

[00:24:15]Yes, that's it. There we go. Where's two Look at two in the middle box.

[00:24:20]Can it go here?

[00:24:22]No, cuz we need to put one in one of the circles, and we can't, apparently, according to my pencil marks at least, put two in a in those circles. So, two A, it's in one of these cells. Well, is it on this line?

[00:24:37]No, cuz one can't go into either of those circles. It does seem to be true.

[00:24:42]Can it be on this line?

[00:24:44]No, same reason it couldn't be there.

[00:24:46]So, I get two in box eight. Ah, it's just classic hard, this. It's sort of quite surprising where you end up having to look. Now, what about twos over here?

[00:24:56]One of three places.

[00:24:58]This line is impossible because one would have to be in one of those.

[00:25:05]This uh it can almost certainly be in a circle. Two in a circle is not very restricted. But where's two in column eight now then? Cuz I've got twos in these, twos in these. So two has to be in one of those three cells now. It definitely can't be on the line.

[00:25:22]Cuz this can't be a one.

[00:25:25]And it can't be there by Sudoku. So two is here.

[00:25:31]Yeah, this is great. It's twos that are twos that unlock this. Because two is now in these cells, can it go on this line? This would have to be a one. It can't be. So this is two.

[00:25:44]So this is two. This is nine. Now we need a digit that's higher than six here. So that's going to have to be eight.

[00:25:52]So that gives us a five in this cell.

[00:25:58]Uh that five is very nice. Five, four.

[00:26:02]We get a four seven pair over on the right of the grid. Let's tidy up our pencil marking.

[00:26:10]One eight here. Six seven.

[00:26:13]So it's six seven and four, isn't it? Uh so this Oh, where's nine?

[00:26:18]Nine can't be there anymore by Sudoku.

[00:26:21]So nine goes here, which is going to unlock the ones, look.

[00:26:25]And the nines.

[00:26:28]So how many nines have we got?

[00:26:31]All all of them. How many ones have we got?

[00:26:35]Not all of them, but nearly all of them.

[00:26:38]We've just got this sort of arrangement left. Twos.

[00:26:46]Nearly all of them. Not quite all of them, but nearly all of them.

[00:26:52]Uh oh yes, and this column needed 4 6 7.

[00:26:55]So, we can place the four because I Oh, no, we can't. Well, no, we can. We can't write four in here because there's nothing between four and five. So, that's the four. That's six or seven, and now this can't be six because six and five have no digits between them.

[00:27:09]So, that's seven. That's seven. That's six. This is six to go between the 5 6 7 here. Now, that cell obviously it can't be eight because there would be nothing between the seven and the eight.

[00:27:28]So, maybe So, it's got to be lower. It's got to be five or lower.

[00:27:34]Now, it can be five. It can be three.

[00:27:37]Those are the only two options. If it was five, this would be six.

[00:27:42]If it was three, this could be four, five, or six.

[00:27:47]Unfortunately, all those options seem to be available. Aha, but what we can't do on this long line is write five in there because then we'd have to fill that entire line with the digit six and we get lots of repeated sixes. So, that is two. That is five.

[00:28:04]That is two. That is one. That is one.

[00:28:06]That is eight.

[00:28:10]And hopefully now we'll be able to do some more sensible things. So, this line is made up of the digit 3 4 5 and 6.

[00:28:21]This isn't three.

[00:28:23]This isn't four.

[00:28:26]This isn't four. This isn't five or six actually.

[00:28:30]That isn't three.

[00:28:36]Okay.

[00:28:38]Oh, where is seven and eight in box eight then? They've got to be there.

[00:28:47]Now, I don't know if that's resolvable, but one thing we can see is that this is an ascending line now, can't we? This This three or five is definitely lower than the seven or the eight on the line. So, that digit has to be higher than a minimum of seven. So, this is eight or nine. It can't be nine. So, that's eight. That's seven on the line. That's eight.

[00:29:11]Now, does that help us?

[00:29:16]Um maybe. This is eight by Sudoku.

[00:29:21]How many eights have we got? Several.

[00:29:25]Yeah, what we can do now is we can look at eight in box nine. And where is it?

[00:29:31]It's only got one place to go, and that's on this line.

[00:29:35]That puts uh no three in the corner, I'm afraid.

[00:29:39]This is not six anymore.

[00:29:41]So, this is a four-five pair. It's not It's not five. So, that's four. That's five. That's three.

[00:29:48]This is six. This is four.

[00:29:53]And okay, what do we need in row seven?

[00:29:55]Three seven.

[00:29:58]We can't put three on the line. So, that's got to be a seven and a three.

[00:30:03]We need six and five into these cells.

[00:30:06]This Sudoku seems to be helping us.

[00:30:09]Six eight nine is lovely. That works very nicely. This is now a three by Sudoku.

[00:30:15]So, this line here, this has to be more than four, and it can't be five. So, this is six or It's not seven. This has got to be six.

[00:30:25]That's That's Oh, yeah, there we go.

[00:30:28]That's three in the corner. That's three in the spotlight losing its religion.

[00:30:33]So, this digit is four seven. So, this should be four five or seven.

[00:30:39]Uh it's not four or seven by Sudoku. So, that's five four seven seven four.

[00:30:45]6 now comes onto this line. 3 here. I think we're there actually. We've just got to tidy up the Sudoku and we should be uh should be golden. So, 4 and 7 go into those cells and that is how to solve a very Well, I'm the first solver and it was a very enjoyable indeed as all odds puzzles are. Just a treat. Um little refresher on between lines. Um if you've never seen them before, there are loads more like this out there.

[00:31:17]Do let me know in the comments how you got on with the puzzle. I enjoy the comments, especially when they're kind and we'll be back later with another edition of Cracking the Cryptic.