Sudoku U Papers: Sgt. 1st class

Added: 2026-05-12

[00:00:16]Hi and welcome to Primes and Puzzles.

[00:00:17]I'm back to Sudoku U which are puzzles created by students of university classes where puzzles are used as educational material and creating puzzles is used for that purpose. And today I'm doing a puzzle called Sergeant First Class by Harder not Smarter and I believe that this called the B A I assume a Sergeant First Class and Chevron. Is that the right thing? It's definitely their insignia.

[00:00:43]So at least I assume it is. I'm not I don't know American military rank classes. I'm assuming it's American.

[00:00:51]So yeah, there'll be a link below to where you can try this puzzle for yourself as well as to the Sudoku U playlist which this puzzle will be added to.

[00:00:59]Let's quickly go through the rules and give the puzzle a try. So we have 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.

[00:01:11]We have entropic lines which is any set of three adjacent cells along an entropic line must contain a low digit, a digit from 1 2 3, a middle digit, a digit from 4 5 6 and a high digit, a digit from 7 8 9. So in those three cells there's a one digit from 1 2 3, one from 4 5 6, one from 7 8 9. Same in those three, same in those three, same in those three. Any three cells that are directly connected. Then we've got cages. Digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage. So for example those four cells sum to 21, those two cells sum to 17. They're the rules of the puzzle. I'm going to restart the puzzle to restart my timer. Let's give this a shot. So there's a few gimmies here. So first of all three different digits that have to sum to six. One, two, and three are the minimum I can do without repeats and they sum to six. So, this is actually a low digit. So, these are a middle and a high um because any set of three must contain a low, a mid, and a high. But well, there's no two here because of the two.

[00:02:16]But um 17, well, the highest digits I can put in are eight and nine and eight and nine sums to 17. So, this must be an eight, nine.

[00:02:27]So, this is the high digit from this run of three as well as from this run of three and this run of three, actually.

[00:02:33]Similarly, I can't put a low digit in any of those because that run of three already has its low and that run of three already has its low. 16, okay, how do I do 16? It's going to resolve this because this has to be seven, nine because I could do nine plus seven, the next option would be eight plus eight and I'd be repeating digits, it doesn't work. So, that's seven, nine, so that's the eight and that's the nine.

[00:02:54]10 in four. Okay, for for a while there I thought this had to be 10 in three, but it's 10 in four and the minimum digits you can do in four are one, two, three, and four. So, these have to be one, two, three, four cuz if you add those together, you get 10. So, we've got one, two, three, four, seven, eight, nine, these are five and six, which means that's a middle digit, which means this has to be a low digit, a one, two, or a three. This has to be a middle digit because that run of three is missing its middle digit, so this is four, five, six. This now this can't be a middle digit or there'd be two middle digits in that run of three. So, that's not a four.

[00:03:27]Okay.

[00:03:31]But there must be a high digit in one of those two, which makes sense cuz where's the seven in the box? And there must be a middle digit in one of those because I've already got the low, so one of those is mid, one of those is high. The only high digit available is the seven, so there must be a four, five, six in here, which is going to match up with the four, five, six there, so that can't be a four. That's a low digit. There's a four in one of those two.

[00:03:53]Okay.

[00:03:57]>> [snorts] >> So, Well, 23 must have a nine in it. Because if it doesn't have a nine in it, the maximum would be 6 7 8, which is only one or 23 is forced actually, because the maximum is 7 8 9. Now, 7 8 9 sums to 24. So, I need to reduce one of need to reduce one of those digits by one to get from 24 down to 23. But, the only digit I can reduce by one without causing a duplication is the seven down to a six.

[00:04:26]If I reduce the nine down, I'd have two eights. And if I reduce the eight down, I'd have two sevens. So, this is actually 6 8 9.

[00:04:34]That's not really helping.

[00:04:37]Cuz if that's seven, that could be 8 9.

[00:04:39]If that's seven, that could be six. So, I'm not sure how that's actually going to reduce.

[00:04:46]Ah, there's another 17 like this one.

[00:04:47]So, this is an 8 9.

[00:04:53]Which puts nine in one of those three.

[00:04:56]Can I put nine in the 16 cage? The other two digits would need to sum to seven, and that doesn't work.

[00:05:02]Well, I can't put nine here, because if I put nine here, then I would be conflicting with that nine. So, nine is in one of those two.

[00:05:11]But, if I was nine here, then these digits would need to sum to 16 minus nine, which is seven. But, the minimum they could be without a 1 2 3 is 4 5, which is nine in this cage would sum to 18 as a minimum. So, that's not the nine. That's the nine. I could have got that by the entropic line.

[00:05:26]High meaning that had to be high, so that was always 7 8 or 9.

[00:05:31]So, these are a low and a medium.

[00:05:35]So, what's the maximum I can put here?

[00:05:38]The maximum I could put here is be a three and a six, which is nine.

[00:05:46]That is a bit restricted.

[00:05:49]Oh, that has to be medium.

[00:05:52]That's four, five, or six because it can't be low because it sees all the one, two, threes and it can't be high because it it's um next to it not uh it would be within three three of that high. So, that's four, five, six. So, this is one, two, or three.

[00:06:04]Now, [snorts] if this was a one, those would have to sum to 15, which would have to be six nine, which I can't do. Five 10, which can't be done, or four 11 doesn't work.

[00:06:13]So, that's not a one. Now, a two would need those to sum to 14, which I could do with six No, I couldn't do it.

[00:06:19]I couldn't do six eight or five nine and four 10 doesn't work. This can't even be a two. That's a three and those have to now sum to 13.

[00:06:28]Now, I can't do four nine, but I could do five I can't do five eight either because that doesn't work. So, this is six seven.

[00:06:35]And now one, two, three, six, seven, eight, nine, these are four and five.

[00:06:38]That's a middle digit.

[00:06:42]But they sum to nine. 21 minus nine is 13.

[00:06:49]12. 21 minus nine is 12. So, those have to sum to 12.

[00:06:53]I could do nine three.

[00:06:56]I can't do eight four. I can't do seven five. I can't do six six. These are nine and three to get the 12. The nine looks down making that the three that the nine.

[00:07:06]And so, now we've got no low in that run of three. So, that's one, two, or three and we've got no high in that run of three. So, this is seven eight nine.

[00:07:17]No nine here because of the nine looking down.

[00:07:23]Okay. This is a low digit cuz there's no low in that run of three. This is one, two, or three.

[00:07:33]Get the feeling I'm looking at this the wrong way.

[00:07:36]But So, those This might be forced, actually, because these sum to 19. 19 + 19 is 38.

[00:07:52]So, an entire row of a Sudoku contains all of the digits from 1 through 9. And 1 through 9, if you add them together, is 45. So, the entire row of the Sudoku sums to 45. But, those digits sum to 19, and those digits sum to 19 because of the cage.

[00:08:10]So, rather than trying to figure out how to make the 19, what I want to look at is the fact that those digits sum to 38.

[00:08:16]And 45 - 38 is 7.

[00:08:20]So, those digits there need to sum to 7.

[00:08:24]And that's going to give me a lot, because the minimum they could be is 1 2 3, which is 6. So, to get from 6 to 7, I need to increase one of those digits by 1. And the only digit I can Well, actually, because of the three, the maximum the minimum they could be is 1 2 4, which is 7.

[00:08:38]So, those are 1 2 4. So, I've got 1 2 3 4 5 6 and 8 going to there. And if I add 5 6 and 8 together, I'm at 19. So, that actually proves out Well, it doesn't prove it, but it that's confirming that what I did over here is probably right. But, I know it's right because of the way the math on the row works. The 1 2 4 means that's not 1 or 2, that's the 3.

[00:09:00]And I can probably do this 12 now.

[00:09:03]Because if this is 3 1, that'd be 4, that would need to be an 8, and it can't be. 3 2 would be 5, and that would have to be 7. 3 4 would be 7. Hang on. And that would have to be Wait. Wait. Wait.

[00:09:14]Wait. Wait. Wait. Wait. Wait. Wait.

[00:09:15]Wait. Wait. Wait. Wait. Wait. 3 Yeah, hang on. 3 2 is 5, and that would have to be 7. 3 4 is 7, and that would have to be 5.

[00:09:34]8 is in one of those two now, cuz 8 can't be in those and the rest of them are filled.

[00:09:42]I wonder if I could do more tricks like that.

[00:09:48]That can't be a two. Where's two in this box?

[00:09:51]It can't be in any of those because of that and there's no two in those. So two is in one of those three. So that's not a two. Two actually because it's in one of those it has to be up here.

[00:10:03]I wonder if it's this 20.

[00:10:10]It probably is, you know, because without a nine the maximum is 8 7 6.

[00:10:16]Um again, that's not me pencil marking this, but 6 7 8 is the maximum they could be. If you add 6 7 8 it's 21. So again, I need to reduce those one of those digits by one to get down to 20.

[00:10:28]And I can't reduce the eight or the seven without causing duplication. So this has to reduce the five down to uh the six down to a five and this becomes 5 7 8. That's forced. So there's no five there.

[00:10:45]So this is 5 7 8.

[00:10:50]Actually don't know what to do with that.

[00:10:59]Weird, but I don't.

[00:11:11]Huh.

[00:11:12]>> [sighs] >> Okay, exploring these. If this was a one, those would have to sum to 17. This can't be a one. If this is a one, those digits would have to sum to 17 in two.

[00:11:23]And we know those are that would The only way to do that is 8 9. So these would be 8 9 and I'd have three digits in the column that would have to be from two digits, 8 and 9. That's not a one.

[00:11:33]So, those [snorts] Oh, and the two looks up making that the four. So, there's no four in those. That means this is the two, this is the one. Now, with that being a four, those have to sum to 14.

[00:11:43]Nine five is possible, eight six is possible.

[00:11:47]If it's nine five, it's nine here and five here. If it's eight six, I think it's either order.

[00:11:58]Oh, but the eight nine means that's the six.

[00:12:01]So, four and six is 10, so that's the eight.

[00:12:04]Which means there's no eight there.

[00:12:06]The eight looks up making that the nine and that the eight. The nine looks down making that the seven and that the nine.

[00:12:11]That was where I had to look. The only cage I haven't resolved now is this 14 cage.

[00:12:17]I'm wondering if I can force something about it.

[00:12:21]>> [snorts] >> Or if there's something else I should be looking at.

[00:12:24]This is a five or a seven.

[00:12:33]>> [snorts] >> The three is looking down saying no three there.

[00:12:37]Oh, the three is saying no three in any of those. So, that's the one, that's the two, that's the three. Which means no three there. That doesn't do anything by the entropic line because I've already got those as low digits, those as middle, that is high. The only entropic [snorts] line that's doing anything at this point is this one and I'm not sure which way that digit goes.

[00:12:59]Like I know none of these are low, but I'm not seeing how to force high or medium out of any of them yet.

[00:13:13]It might be possible, but I'm not seeing it. So, this 14 cage is the thing that's looking the most restricted.

[00:13:20]Nine [snorts] Okay, nine because of the six eight nine isn't in any of those.

[00:13:23]It's not in any of those and it's not there. So, nine is in one of those two. Oh, and that nine looks up saying not there. That's the nine.

[00:13:32]Which doesn't do anything for the line because I already had those as high digits. What's this triple? 1 3 5.

[00:13:43]There's no five there because of the 5 7 8.

[00:13:46]There's no three there.

[00:13:50]Mhm.

[00:13:54]Is it the 14 cage?

[00:13:56]Cuz there's no six, eight, or nine.

[00:14:01]If I don't put a seven in it, the maximum would be 5 4 3.

[00:14:06]Because if I don't put a seven in the cage, because there's no 9 8, there'd be no seven, there'd be no six. The maximum would be 3 4 5, and 3 4 5, if you add them together, is only 12. So, there must be a seven in the cage.

[00:14:21]And then I need two more digits that sum to seven.

[00:14:25]Now, 1 6 is not possible, 2 5 is possible, 3 4 is possible.

[00:14:32]If it's 2 5, the two would be up here, and the five would be somewhere.

[00:14:38]And if it's 3 4, the three would be here, and this would be 4 7. I'm not seeing how to restrict that. All I know is there's a seven in the cage somewhere.

[00:14:49]Nine is in one of those two.

[00:15:11]Am I being completely blind?

[00:15:18]I've got to be being blind somewhere.

[00:15:23]Six is in here somewhere, but I'm not seeing Ah, where's eight in this box?

[00:15:32]Eight can't be in any of those. Eight can't be in any of those. Eight can't be there, and because of the 5 7 8, it can't be there. That's an eight.

[00:15:40]Which hasn't done much.

[00:15:44]Two in this box is in one of those two cuz of the two looking down.

[00:15:49]Four in this box.

[00:15:56]I don't see it.

[00:16:02]Is it this line? Because those are the same high low.

[00:16:08]This can't be eight or nine. It would have to be seven if that's eight.

[00:16:17]We'd put [snorts] seven in one of those two and eight in one of those two.

[00:16:22]That does us Well, I know eight is in one of those two actually cuz eight can't be in any of those or any of those. Eight is in one of those two.

[00:16:32]But if this is six, that would be a middle digit, which could be any of them. That would be seven and that would be seven.

[00:16:44]Which also seems okay.

[00:16:54]Huh.

[00:17:02]Unless I've made a mistake with one of these sums.

[00:17:10]Oh, there's a 12 cage here and they sum to five. If they sum to five, if that was a five, I'd only even to 10. That's a seven. That's a five. How did I miss that for so long?

[00:17:20]I know how I missed that for so long so long. My name is Brimstone.

[00:17:25]And that's going to restrict this 14k journey even further.

[00:17:29]Because if it's 7 3 4 So it's either 7 2 5 or 7 3 4. If it's 7 2 5, the five is there and this is 2 7.

[00:17:40]And if it's 7 3 4, the three is there and this is 2 4. So that is fully restricted like that.

[00:17:48]That can only be three or five and that is a 1 3 5 triple.

[00:17:56]So 1 2 3 4 is in one of those.

[00:18:00]4 6 7 and 8 are what those are.

[00:18:05]I don't see how to use that.

[00:18:12]This is either 2 7 or 4 7.

[00:18:22]Have I missed more Sudoku like I missed up here with that cage?

[00:18:32]Five is in one of those two by Sudoku.

[00:18:36]So these are from 1 2 5. These are from 1 2 8.

[00:18:41]In here I need to put four almost anywhere. A six. Ah, this is a 6 8 pair. Six and eight can't go in any of those and those are filled. This is a 6 8 pair.

[00:18:53]So 1 2 3 4 5 6 4 and 7. These are 4 and 7.

[00:19:03]And that is now a 2 4 7 triple. So now with that being a 2 4 7 triple, the two must be in here. So two and seven are in here and that must be the five.

[00:19:13]So, we And this is a two-seven. That's insane. That's the four. That's the seven. And this is a one or a three.

[00:19:22]Looking down making that the two, that the one, and taking one-two out of those, the four looks down making that the three, that the four. That's a really nice twist.

[00:19:31]I like that. The five looks down saying that's not the five.

[00:19:36]So, Oh, the three looks across saying that's the one, that's the three. So, one, two, three, four, five, six, seven, eight, nine. These are four and six.

[00:19:48]Where's one in this box now? That one says it's not there, so that's the one, meaning that's the five, that's the three. One, two, three, four, five, six, seven, eight, nine. These are three and five, with the three looking down making that the five, that the three. Now, that um can't be a um uh a a high digit because it's two away from that. Well, basically, this has to be a high digit because I've got a low and a mid. This is seven, eight, or nine, and it can't be eight or nine.

[00:20:14]That's the seven, and now that can't be the seven. This is missing a middle digit, so this is four, five, or six.

[00:20:20]This is now missing a high digit, so that's the eight, and there's no eight there.

[00:20:25]Four is in one of those two by that, but the one here means that's the two.

[00:20:30]Meaning that's not the two, that's the two. The five is looking down making that the six, that the five. Six makes that four and that six. These are one and four, with the four looking down making that one and that four, looking across making that six, and that is the four, but to complete the four-five-six triple. Six looks up making that eight and that six, and these are four and seven, and the four-seven here resolve it as seven and four. Very nice.

[00:20:56]The eight says that's not the eight, so that's the eight. The five looks up saying that's not the five, that's the five. These are a one-two pair. The one looks up making that the two and that the one. Very cool. These are one I've got two three four five six one and seven. So those are one and seven. And that's going to do a lot for down here in that cage. Because where is seven in this column? The one seven means I can't put seven in any of those or both of those it have to be one. Can't put seven in any of those. So seven has to be in one of those two. That seven says not there. That's the seven making that the eight that the five.

[00:21:33]The eight looks up saying no eight there.

[00:21:38]Um The eight looks up saying no eight there. So that's the eight. The five looks up making that the six that the five. The six looks down making that the nine that the six.

[00:21:49]So this column one two three four five six seven eight nine. So these are four and six. That six means that's the four that's the six. This box is missing one nine now.

[00:22:01]And this box one two three four five six seven eight nine. And these are two and three. The three looks up making that the two that the three. The two looks down making seven and two. The seven means one and seven and the one looks down making nine and one. That is an amazingly fun puzzle.

[00:22:20]And it's only had four solves and I know this puzzle is like a year old.

[00:22:25]So I mean I don't know how long it's been in Sudoku Pad but this puzzle was from a class last year. So it's maybe only a few months but it's still older than it looks and deserves a lot better.

[00:22:39]What an amazing puzzle.

[00:22:42]First sergeant first class. Definitely puzzle first class.

[00:22:47]Again proving that puzzles don't need to be diabolically different difficult to be elegant.

[00:22:52]It's what I love. People send me puzzles like this. Great stuff.

[00:22:56]Thank you everyone for watching. I hope you enjoyed this as much as I did. And as always good luck with your solving.

[00:23:03]>> [music] [music]