A Perfectly Folded X-SUMS Sudoku (with no given digits 🤪)

Added: 2026-05-15

[00:00:16]Hi and welcome to Brain Teaser Puzzles, a channel where I showcase the fun that could be had in the world of variant Sudoku. And today I'm doing a puzzle by Nicholas du Hayle called Fivefold.

[00:00:26]Um and this is an X sums puzzle that I have been told will be one I enjoy. We did an X sums pack um last year called the X sums files, um which was a lot of fun. So, but I haven't done any X sums puzzles since I did that pack. So, it will be kind of interesting to see how this one goes. Um there'll be a link below to where you can try this puzzle for yourself as well as to its page on Logic Masters Germany, um which is where this was originally posted. Um I am going to say go check out Puzzle Patzer and Timber Tab for the current Sudoku Chutes set. Um I am releasing that as a pay what you want. Um I fixed my Ko-fi page so you can just generate a couple of bucks. Um or the best way to support that pack is to go and subscribe to Timber Tab and Puzzle Patzer. But, let's have a look at Fivefold by Nicholas du Hayle. So, we've got normal Sudoku rules apply, which means in every box, in every row, and in every column, the digits 1 to 9 must be placed without repetition. And then clues outside the grid um indicate the sum of the first X digits, where X is the first seen digit.

[00:01:31]So, for example, if this was a five, that would mean those five digits have to sum to 20. If this was a four, that would mean those four digits have to sum to 20. Um and it's the same for all of the clues. If this was a two, those two digits would sum to 10. If this is a three, those three digits would sum to 10. That's the way it works. I'm going to restart the puzzle to restart my timer. Let's give this a shot. Now, there's a A of big digits here.

[00:01:57]So, okay. One of the There's a couple of concepts with X-Sums that you want to appreciate, which is, for example, no uh you can never put a one in any of uh these clues. No X-Sum clue can be a one without um the act or no X-Sum can have a one next to it unless the clue is a one, because you'd be summing one digit, which is a one, and therefore the clue would have to be a one.

[00:02:22]Now, the maximum digit you can put in here is the minimum that four digits could be.

[00:02:29]Like, if I made this a five, I've got a problem. Um and the reason for that is five If I was to add five digits, the minimum that five digits could be would be 1 2 3 4 5, which is 15. So, because the minimum five digits can be is 15, I can never put a five here. The minimum four digits could be is 1 2 3 4, which is 1 + 2 + 3 + 4, which is 10. So, this could be a four. So, this has to be 2 3 or four. It can't be a one, and it can't be any higher than four. So, [snorts] all of the 10s are 2 3 and 4. So, I can just go around and put 2 3 and 4 next to all of the 10s.

[00:03:05]Now, the next most constrained one to my mind is 40. And I'm going to think about this a different way.

[00:03:11]Uh I've got a few 40s, but an entire column of a Sudoku, this entire column here, and it's true for all of them, but an entire column of a Sudoku contains all the digits 1 to 9. And if you add all the digits 1 to 9, you get 45. So, the entire column sums to 45. But, I know that if the um if the X-Sum has to sum to 40, it means the digits after the X-Sum finishes have to sum to 45 minus 40, which is five. Now, I can do five in one digit. I can do five in two digits by using 1 4 or 2 3. I can't do five in three digits, because five in three digits doesn't work cuz the minimum three digits can be is 1 + 2 + 3 which is six. So this has to be a seven or an eight because the X sum can take seven digits leaving two digits summing to five or eight digits leaving one digit sum to five. So every 40 clue has to be a seven or an eight. So that is a 78 pair.

[00:04:13]Because that is a seven or an eight and that is a seven or an eight.

[00:04:17]And that one can't be an eight. If that was an eight, then this digit here would need to be a five and I can't do 10 in five. So that's the seven, that's the eight, that's a five.

[00:04:27]Beautiful.

[00:04:29]And this clue here is done.

[00:04:32]>> [snorts] >> Now that means these two digits here have to sum to five.

[00:04:37]Which means if those two digits sum to five, this can't be a two. Because if this is a four, this is a one. If this is a three, this is a two. And if this is a two, this is a three. Because this X sum clue must end there.

[00:04:53]Um that's the seven.

[00:04:55]Uh the actually the way to mark that might be this seven clue is the is those digits.

[00:05:04]Now, so these two digits here have to sum to five.

[00:05:09]Now, that means for this 10 clue, if this was a two, that would need to be an eight and it can't be. Now if this is a three, yeah, I could do that. If this is a If this was a three, this would have to be a one because I couldn't go 33 and I couldn't go 32 because if these sum to five. So if this is a three and that was a two, that would also have to be a three and it doesn't work. So if that's a three, that's a one and that would have to be a six. But that seems okay.

[00:05:39]But what about this one?

[00:05:41]There is an overlap here. This can't be a two because then that would need to be an eight.

[00:05:45]So that's a 34 pair and there's no three there.

[00:05:52]Okay.

[00:05:53]Can there be a four now? I think it can.

[00:05:59]So, the question now is maybe the 35s.

[00:06:07]I think there's something going on with those tens, but I'm not sure how to do it.

[00:06:13]Or there's something going on with these tens.

[00:06:17]Like, if that was a three, 10 in three, 10 in three can only be done one way.

[00:06:29]Is that true? No.

[00:06:31]If this was a three, those would need to sum to seven.

[00:06:35]They could be 1-6. They couldn't be 2-5.

[00:06:38]They couldn't be 3-4.

[00:06:40]So, if this was a three, this would be 1-6.

[00:06:51]If [snorts] this was an eight, that would be a five. If that was a seven, those two digits would sum to five.

[00:06:59]How do I Mm.

[00:07:06]Those digits must sum to six.

[00:07:09]No.

[00:07:10]If this is 3-2, that's a four, and that sums to six. If this is 4-1, that's a three, and that sums to four.

[00:07:18]So, This sums to four or six.

[00:07:27]Hang on. That's either Well, this is from 1-2-3-4-5, but I kind of And it can't be one. This is 2-3-4-5.

[00:07:37]Because these two di- It's either Is being a five, if that's an eight or these have to sum to five. Now, this can't be a two cuz if this is a two for the 20, this would have to be a two followed by an 18.

[00:07:55]20 in three would need those to be eight nine because 20 minus three is 17 and those two digits would need to sum to 17, which would be eight nine. That's not a three.

[00:08:09]20 in four would need those to sum to 16.

[00:08:18]And it would be four one. So, those would need to sum to 15.

[00:08:24]Which would be six nine because if this is four one, that's a seven and the only way to do 15 in two digits is with six nine.

[00:08:33]But I don't see why that's a problem.

[00:08:40]I'm a little bit confused by this.

[00:08:43]Now, maybe I need to mark all these others.

[00:08:46]The minimum 20 can be done in is three with three eight nine.

[00:08:52]The maximum 20 can be done in is five because the minimum six digits is is one plus two plus three plus four plus five plus six, which is 21. So, these are three four five. All the 20s are three four and five.

[00:09:07]So, those are three four five. This one can't be a five.

[00:09:11]So, this is three or four. So, that's a three four pair.

[00:09:16]So, this can't be a four anymore. If this was a four, that would have to be one two three four and break that.

[00:09:21]That's the three, that's the four, that's the one cuz they had to sum to five. Now, this is three digits sum to 10, but I already have This is now a four, by the way, but I already have um by Sudoku and that's not a four and that's not a four, but this is four at um So, this has to be the six to make the three digits sum to 10. And this 10 clue is now done. The seven clue is now fully marked.

[00:09:50]And this is a four 10 clue, so those have to be two three because the only way to do 10 in four digits is 1 2 3 4.

[00:09:57]That's the two, that's the three. That's very cool. And the 10 clue is now done.

[00:10:11]Okay.

[00:10:16]Now.

[00:10:23]25 can't be done in three because if it was three, those two digits would need to sum to 22, which is not possible. The maximum is 17. It can be done in four because if this is a four, those digits would have to sum to 21, and there are ways of doing that.

[00:10:39]So, 4 5 6, it can't be seven because seven, the minimum is 1 through 7, and that is 1 + 2 + 3 + 4 + 5 + 6 + 7 is 28. So, this can't be a seven. So, it's 4 5 or 6, and it can't be a five because there's already a five in the box. Those digits sum to 20.

[00:11:03]So, if those sum to 25, and that's an eight, those sum to 33. So, those three digits sum to 12. I'm not sure how that's helping me. Although, that's at least a five.

[00:11:16]Actually, that's at least a six. That's a six or a nine only cuz it sees 1 2 3 4 5 7 and 8.

[00:11:23]And those digits sum to 25, and that's an eight. So, these digits So, those digits there sum to 33.

[00:11:34]Those there sum to 33. So, those digits there have to sum to 12. If that's a nine, they would sum to three and be one and two. If that's a six, those would have to sum to six, which would be two and four. So, these are only from one, two, four because the only way I could do If this is a nine, the only way I could make these sum to three is one plus two. This is a six, these would have to sum to six.

[00:11:59]And the only way to make those sum to six is either be one five, which is not possible, or two four.

[00:12:12]That's very strange.

[00:12:15]Eight is now in one of those two, and eight is in one of those two.

[00:12:22]Four Uh, that could still be either if that's a five.

[00:12:27]If that's a four, that's a one, and that's a seven.

[00:12:34]But I need to remember that green sums to 12.

[00:12:40]Is it this now?

[00:12:43]Five digits summing to 20.

[00:12:46]No, you can't do five digits summing to 20.

[00:12:49]It's not possible.

[00:12:51]Because Oh, no, you can. You absolutely can.

[00:12:54]For some reason Yes, you can.

[00:13:02]You can't do five digits summing to 16.

[00:13:04]I don't know why I was I was thinking of that.

[00:13:06]So, how do I do 35?

[00:13:09]So, the minimum 35 could be four digits summing to 35.

[00:13:17]Well, you can't do three digits summing to 35, or those two digits would need to sum to 20 something. So, this is 6 7 It can't be eight because if I did eight, then that would need to be 45 minus 45 minus 35, that would need to be a 10.

[00:13:30]So, six and seven works. Can you do 35 in five? Yes, you can.

[00:13:34]You can't here, but you can do 35 in five, and that's the minimum cuz five six five plus six plus seven plus eight plus nine is 35. Cuz six seven eight nine, if you add them together, is 30. Six plus nine is 15, seven plus eight is 15. You add five, you get to 35. So, the minimum is five, and the maximum is seven. So, this is five is five six seven.

[00:13:59]This is five six seven, and can't be a seven.

[00:14:03]So, that's a four five six, so this is not a four anymore.

[00:14:06]Oh, and this can't be a two, cuz if this is a two, that would need to be an eight, and it can't be. That's a three, and those two digits sum to seven.

[00:14:15]They could be one six. They can't be two five. They can't be three four. This is a one six.

[00:14:22]So, that's a four.

[00:14:23]That's a five. That's a six.

[00:14:27]This is cool.

[00:14:29]And I've broken the puzzle.

[00:14:33]Because that was supposed to be a six all the way back here.

[00:14:38]I'm going to go up and do it cuz I haven't used it, but all the way back here, when I said that these had to sum to 10, that had to be a six. So, I'm going to roll all the way back forward.

[00:14:53]This is three Those digits have to sum to 10, but I've only made them sum to nine. That's supposed to be a six. Everyone's been yelling at the screen, but I found it eventually.

[00:15:03]Sorry, that was a mistake.

[00:15:05]At least I didn't use it to resolve the four five six. At least I don't think I did.

[00:15:11]No, I didn't.

[00:15:14]Okay.

[00:15:15]In fact, I think I removed the right digit for the eight, whatever.

[00:15:18]So, the three means this is a two, which means this is an eight, and these are 1 2 3 4 5 6 7 and 9. But these digits need to sum to 25. So I can get something about that digit, because those sum to 12, so those need to sum to 13, which would be 9 + 4, which doesn't work. So it has to be 7 + 6.

[00:15:41]And that means that's the nine.

[00:15:43]This is a triple, 1 2 8. Well, there's no eight there.

[00:15:49]So the eight is in one of those two.

[00:15:56]Now, remember, these have to sum to 12.

[00:16:02]Well, those sum to 12, so these have to sum to 13. I'm not sure that's resolving it yet.

[00:16:09]Those have to sum to 20.

[00:16:13]I don't think that's resolving it yet, either.

[00:16:18]If this was five digits summing to 20, those would need to Oh, yeah, this has to be a five, because those four digits sum to 25. And if I take the entire column, which is 45, and I remove those four digits, which sum to 25, what's left? Those digits are going to sum to 20, cuz 45 - 25 is 20. So that is a five. So there's no five there. And that's going to resolve it with these being 1 2 3 9. And if I add those, 6 + 9 is 15 + 5 is 20.

[00:16:52]That is absolutely fine. There's no one or three there.

[00:17:01]Oh, the six means that's a seven.

[00:17:05]And if that's a seven, those digits sum to 35, so those digits need to sum to 10. They could [snorts] be 1 9, with one there and nine there. They could be 2 8, with two there and eight there. They can't be 37 or 46. So, they're the only possibilities giving me a 1 2 pair in the column.

[00:17:29]>> [snorts] >> Five is in Oh, five is right there. Five can't be in any of those. Five can't be there and the others are filled. That's a five.

[00:17:38]Oh, I didn't mark this 20.

[00:17:41]That could have been important.

[00:17:42]So, what can 20 be? 3 4 5 It can't be six. So, this is 3 4 or 5 and it can't be a five. If this is a three, those would have to be 8 9 and they can't be.

[00:17:51]That is a four.

[00:17:53]And those digits have to sum to 16.

[00:17:59]But that four means that's not a four.

[00:18:04]If that's a seven, those digits have to sum to 10.

[00:18:08]If that's a six, those digits have to sum to 10. That actually all looks okay.

[00:18:18]These are 7 8 9. There's no eight there.

[00:18:23]Okay, what clues are done? This five clue is done.

[00:18:27]The 35 isn't. The 10 is. The 25 isn't quite. This 25 is.

[00:18:34]The 10 is. This 35 isn't.

[00:18:38]Interestingly enough, those digits there need to sum to 10 because those sum to 35. So, those are 45 minus 35. Those digits sum to 10.

[00:18:49]There's only one way of doing 10 without a one, which is 2 3 5.

[00:18:54]Which would make this a five and those a 2 3 pair. I don't see why that's not possible.

[00:19:00]But I could use a one.

[00:19:08]Oh, that's a five now. So, that has to be an eight. If that was a seven, those two digits would need to sum to five and they can't. That's the eight.

[00:19:16]And that clue is now done. Because I've now got the the total.

[00:19:21]>> [snorts] >> Okay.

[00:19:28]So 1 2 3 4 5 6 7 and 9. These are 6 7 and 9 must include a 6.

[00:19:41]And I haven't put a five That's a five.

[00:19:44]Where do I put the five in this column?

[00:19:47]Five and five means five is in one of those two, but eight is also in one of those two. So this is a five-eight pair.

[00:19:54]But that can't be.

[00:19:56]I've got an eight-nine there for some reason.

[00:20:00]This is a five-eight pair, but why do I have an eight-nine there?

[00:20:10]Because those two digits had to sum to 10.

[00:20:13]So if that was a five, this is a five-eight pair. Absolutely, this is a five-eight pair by Sudoku. Five-eight five-eight, these are five-eight. But because of this 35 clue, those sum to 35, those have to sum to 10. If that was a five, that would also have to be a five. That's the eight, that's the five, that's the two, that's the one, that's the two.

[00:20:35]And this is a six or a nine to complete the column.

[00:20:38]These still need to sum to 12. Nine one, that's not or six four. I don't know which way.

[00:20:45]But that is now a If that's nine one, that's a six. If that's six four, that That's a one. So one and six are are fully placed in that row.

[00:21:02]Well, I know what this digit is. That's a three.

[00:21:06]>> [snorts] >> And those four digits have to sum to 20.

[00:21:09]So those two digits have to sum to 13 because those are seven. So it's either 9 + 4 which it can't be. That's the six and that is a seven to get to 13 to make the 20 work.

[00:21:21]And if that's a six, that's the nine and remember these have to sum to 12, so that's the one. Oh, I could have got that from the one here.

[00:21:29]I'm getting there eventually.

[00:21:32]We all solve in different ways. Some of us solve well and then there's me. 1 2 3 4 5 and 9 go into those. 1 2 3 4 5 6 7 8 9. These are 3 and 4. Great.

[00:21:48]The 35 clue is now done.

[00:21:54]The 25 clue is now done because we've got 12 18 + 7 is 25. That's done.

[00:22:05]A very nice little puzzle.

[00:22:11]Still Oh, this can't be a nine because if this was a nine, all of those would have to sum to 35, but an entire row of a Sudoku is 45. We've already discussed this. So if those are 35, that sums to 10 without a three.

[00:22:28]Maybe if that's a seven, those sum to 10 which would be 9 1 3 7 is not possible.

[00:22:34]2 8 is and 1 9 isn't. There's possibilities there.

[00:22:40]Now, if this was a seven, those would be 35 and those would need to sum to 10, but I can't do that. That is a six.

[00:22:50]And now those sum to 35, so those have to sum to 10 which is 8 + 2.

[00:22:57]And the 35 clue is now done.

[00:23:03]I put six here. Six and six can't be in any of those. That can't be a six and that can't be a six. That is a six.

[00:23:09]Let's mark this triple. 1 3 8.

[00:23:15]Well, there's no 8 there. There's no 3 there.

[00:23:25]Okay.

[00:23:29]So, >> [sighs and gasps] >> there's a few I haven't done. If this is a seven, those need to sum to 10.

[00:23:39]There are ways of doing that. If this is a six, those need to sum to 10.

[00:23:44]There are ways of doing that.

[00:23:46]1 2 7 1 3 1 3 6 doesn't work, but the 1 2 7 would work.

[00:23:54]If that's a six.

[00:24:01]Four is in one of those No, I've got four. What am I talking about? Four is over here.

[00:24:08]Is it this day Oh, hang on. It This is six digits summing to 35. So, those have to sum to 10. I've already got that. How do I make that work?

[00:24:20]>> [snorts] >> 2 3 5 does still seem to be possible.

[00:24:23]That would be the three.

[00:24:26]That would be the five. That would be the two.

[00:24:38]Um am I looking at Sudoku here? Six is in one of those two.

[00:24:46]One is in one of those two, but I'm not sure how that's helping me.

[00:24:52]Oh, that's a 1 3 pair.

[00:24:54]One and three can't go in any of those or any of those. This is a 1 3 pair.

[00:24:58]There's no two or nine there. That's a 1 3 pair.

[00:25:04]Does that do anything?

[00:25:14]I uh um uh One and four are in here.

[00:25:32]Eight is definitely in one of those, too.

[00:25:47]There's no three there.

[00:25:52]So, three is in one of those, too.

[00:25:58]Five is in one of those, too.

[00:26:05]But, none of that seems to be Okay, so these digits here have to sum to 16.

[00:26:12]Actually, that could be it, couldn't it?

[00:26:14]It's this 20 clue because I've got four digits summing to 20. That digit is a four. So, those sum to 16. If that's a nine, I've already at 13 and those would need to sum to seven.

[00:26:26]How would I make those sum to seven? I couldn't use 1 6.

[00:26:30]I could use 2 5.

[00:26:33]So, if this is a nine, these would be 2 + 5.

[00:26:37]It'd be two here and five here.

[00:26:42]That seems okay. If this is a six, though, those would need to sum to 14.

[00:26:48]Which would be 9 5.

[00:26:52]I couldn't use 8 6.

[00:26:58]And 7 7 there's always a five.

[00:27:01]Hang on, that's crazy.

[00:27:04]If this is 4 9, these that is 13 these need to sum to seven.

[00:27:13]I can't use 1 6.

[00:27:15]I can't use 3 4, so it'll be 2 5. If this is a nine, it'll be 2 5. It'll be two here and five here.

[00:27:22]If this is a two, these sum to six, these need to sum to 14.

[00:27:27]>> [snorts] >> I could use 9 5. I can't use 8 6 and 7 7 doesn't work. That's always a 2 9 pair and that's a five.

[00:27:35]That is tricky.

[00:27:38]The five looks down making that the nine, that the five.

[00:27:43]And remember those sum to 35.

[00:27:46]So these have to sum to 10.

[00:27:49]So those two digits there have to sum to five.

[00:27:55]Which is either 1 4 or 2 3.

[00:28:04]1 2 3 4 5 6 These are seven and eight and the eight makes that the seven, that the eight. The seven makes that the nine and that the seven.

[00:28:16]Meaning that's not the nine.

[00:28:18]These are 1 4 9.

[00:28:29]This is 1 2 or 3, but those have to sum to five.

[00:28:36]There's a 3 4 pair there.

[00:28:42]Seven is right here because of the two sevens looking across and the seven looking up.

[00:28:48]Eight is right here.

[00:28:51]And nine is in one of those two.

[00:28:57]The 20 is now done.

[00:28:59]Cuz that's 11 + 9. The 20 is now done.

[00:29:07]What clues aren't done?

[00:29:11]Ah, no, I missed this 20, didn't I?

[00:29:14]Those So, those sum to 10. So, those have to sum to 10. So, those are 1 9.

[00:29:19]That's a four.

[00:29:21]And now that 20 is done.

[00:29:23]So, it's just this 35 and this 35.

[00:29:31]Can I make that still sum to 10?

[00:29:34]Can I If this is a six, those would sum to 10.

[00:29:37]It would be one here cuz if this is an eight, those would have to sum to two uh two. It doesn't work. So, it'd be one here. If this was a nine, I'm broken.

[00:29:45]So, it'd be one two and that would need to be a seven and it can't be. That's a seven. Making that a six. And now those two need to sum to 10, which is either 1 9 or 8 2. That can't be a one anymore.

[00:29:59]That's now a 2 9 pair. Taking 2 9 out of there, that's a 1 3 pair.

[00:30:04]So, those two digits there have to sum to 10.

[00:30:18]Right.

[00:30:33]That's a 1 3 8 triple.

[00:30:37]Is that doing anything?

[00:30:47]>> Those five digits already sum to the right total. They have done all of that.

[00:30:51]So, it's and as long as those sum to five, four, one, or three, two, those will sum to the right total. If this is four, one, that's a two or a three.

[00:31:04]Two is in one of those two, but that's not a big deal.

[00:31:07]If this is four, one, that's two.

[00:31:09]And this is three, nine.

[00:31:13]If this is three, two, that's one, and that's four, nine.

[00:31:20]I'm not seeing it. That's a seven though. Seven, seven, seven, and seven looking into the box.

[00:31:29]Eight and eight puts eight right there.

[00:31:32]That's it.

[00:31:33]It's the eights.

[00:31:35]Eight not in any of those. Eight not there. Once I got that seven, that eight makes that the one, which makes that the nine. So, that those digits sum to 10 to complete that X sum clue. And now I can do this X sum clue.

[00:31:49]Cuz this is one or two Well, actually no, cuz 15, 20, 35. This is done. The 35 clue will be done as soon as I do this one. So, those sum to five, and those sum to five, whichever way it works.

[00:32:02]That's That's a bit mean. Okay, so, I need something to kick this over.

[00:32:10]It will be Sudoku at this point.

[00:32:14]The two looks across making that the one and that the four looking up making that the two and that the three. There's no That makes this the one, this the three, this the one. I'm going to mark the X sum clue as done. The 40 has been done forever. I just forgot to mark it. The one means that's the nine, that's the one.

[00:32:32]That's very cool. This is now a four, nine, which I recognized earlier.

[00:32:37]Um the one looks across taking one out of both of those, so we get three and eight. So, 1 2 4 5 go into those.

[00:32:47]There's no four there, there's no five there, there's no two there. I'm not sure how to resolve that, but that looks up making that the nine and that the two.

[00:32:55]Um Okay, so this row, 1 2 3 4 5. So, these are 3 4 and 5. There's no five there.

[00:33:05]Oh dear.

[00:33:06]So, I need to put a two in this box in This is a 2 6 pair. 2 6 2 6, and that can't be two or six either. This is a 2 6 pair.

[00:33:17]So, the nine has to go there.

[00:33:20]Nine can't go in any of the others.

[00:33:21]That's the nine, so this is 3 4 5 and it can't be three or four. That's the five making that the two, that the four, that the five. Taking five out of there, that's a 3 4 pair.

[00:33:32]But, the two means this is the six and the two. The 3 4 looks up making that the nine and that the four. Looking down making that the three, that the four, that the three. That congrats. I hope you enjoyed. I very much enjoyed. 447 solves. We want to at least double that, possibly even more. What a great puzzle.

[00:33:52]That's a brilliant X Sums puzzle. You had to think about it in multiple different ways. I love the use of outies in X Sums. I think it's one of my favorite things to do in X Sums, and I loved the way that things like the 7 8 pairs and everything's and the the possible options were whittled down by what the other options were. A pure X Sums puzzle. This is stunning. Great stuff. Um getting pure puzzles of a a bit of a challenge, um which just really caused you to think. Very, very tricky to do, and I love how good this one was.

[00:34:27]Thank you, Nicolas du Hayl, for a wonderful puzzle.

[00:34:30]Thanks, everyone, for watching. I hope you enjoyed the I enjoyed these puzzles.

[00:34:35]I hope you're enjoying Sudoku to set 11 and as always good luck with your solving.

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