Sudoku U Papers: Weirder Cages

追加: 2026-05-04

[00:00:15]Hi and welcome to Brimstone Puzzles and welcome back to Sudoku U. Now, you may say, "But you just did a set of Sudoku U." But there's a couple of things that have happened that made me return. The first of all is the next set of five puzzles which is going to be coming out this week uh from a current class which is the Mathematical Reasoning Through Puzzles class by Full Deck and Missing a Few Cards. Um and all the this week that these puzzles are coming out is actually the final week of that class. So, getting puzzles from the class that is about to finish seemed like a really great time to do it and Full Deck and Missing a Few Cards reached out to me and said, "If you could do these puzzles this week, that would be absolutely phenomenal."

[00:00:55]So, of course I'm going to try and do this this puzzle this week. The second thing is I've actually been really dry on submissions. Like in the last month, I think I've got three submissions. So, but I've got a bunch of Sudoku U puzzles that I could do. So, while I'm a bit submissions dry, I'm actually going to just work through Sudoku U. People enjoy the puzzles. They the comments on them are really positive and they're sitting there waiting to be done. So, I'm going to work through those and try and build up some submissions. But on that front, if you've got a puzzle that you would like to submit or recommend, my submission guidelines are available. Mostly it's just sent through an email, but I do need permission from the creator in order to do the puzzle. So, if you do want to recommend a puzzle, try and reach out to the creator and get permission. Um that's really it. I want to have a look at this one. So, this is Weird Occasions by a Jac Wacka.

[00:01:48]Um and yeah, I cage is puzzle. So, yeah, the um I don't know much about the Mathematical Reasoning Through Puzzles class, but um I I love puzzles. So, of course I'm going to do this one. It kind of looks to me when I first opened the grid it's like if they tried to put a QR code into the grid or something. I saw the the boxes in the corners. But this is I'm looking forward to giving this a try. Of course there'll be a link below to where you can try this puzzle for yourself and I don't know if there's an upcoming Signet Sudoku book or anything like that. But as soon as I know anything, I will post that as a free post over on my Patreon. You can sign up to my Patreon for free, but it'll also get posted to Full Deck and Missing a Few Cards as website which I promote heavily on this page as well. But link below to the puzzle. Let's go through the rules which are fairly simple for this one and then give the puzzle a try. So, what do we have? 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. And then we've got cages which is that digits in cages cannot repeat and must sum to the value shown in the upper left corner of the cage.

[00:02:59]So, those three those three digits will sum to 9, those two will sum to 10, those five will sum to 16. Something there.

[00:03:08]And the same is true for all the cages.

[00:03:10]I'm going to restart the puzzle to restart my timer. Let's give this a shot. So, I mean this is obviously something this is obviously something I can see some stuff here, but I'm going to go through this in principle. So, where do I want to start? I'm going to start in box one. So, we know that these have to sum to 9 and these have to sum to 6. But we can actually do a trick with these by adding putting those cages together and then thinking about because those cages are all in the same box, we can't repeat digits between those two cages. And if we add 9 and 6 together, we get 15.

[00:03:44]So, with those summing to 15 without being able to repeat digits, the lowest we could do with five positive integers that cannot repeat is 1 2 3 4 5 and 1 2 3 4 5 sum to 15. So, these must be 1 2 3 4 5. But we cannot put a three into this two-cell six cage. So, if we put a six a three into here, the other digit would need to be a three and we can't put two threes into the cage. So, this is either 1 5 2 4. There is a three in here with the other 1 5 or 2 4. But I don't know which, but I do know there's a three in here.

[00:04:19]So, these digits here are from 6 7 8 9 which means or this is forced. It means the lowest I can put in here is 6 and 7 which sums to 13. Absolute minimum if these were 6 and 7. But this is a five-cell 19 cage with those having a minimum sum of 13. If I subtract 13 from 19, I'm left with six. But the minimum these could be would be 1 2 and 3 which is six. So, 6 + 13 is 19. These have to be 13. So, these are the 6 7 and these are the 8 9.

[00:04:54]Okay.

[00:04:56]What can I do with that? Well, this is forced.

[00:04:59]How do I do 16 in two cells where I can't repeat? Well, I could do 9 + 7.

[00:05:04]The next option would be 8 + 8, but it won't let me do that because I can't put two eights in the I can't repeat eights.

[00:05:11]So, this is 9 + 7.

[00:05:13]And now this becomes forced.

[00:05:17]Well, it does. Maybe.

[00:05:20]It actually does because the the minimum Well, the minimum here Right. Because of the 1 2 3 here, the minimum here is 4 5 and 6 which is 15.

[00:05:33]So, if I put the minimum here, 4 5 and 6, the absolute minimum I can put in here, what can these cells be? Because 15 and two different digits Um so, 18 - 15 is three. And these therefore those two digits there have to sum to three. But the only way I can make those sum to three is to be the two lowest digits. So, these have to be 1 2.

[00:05:57]These have to be 4 5 and 6. This becomes the eight.

[00:06:01]>> [snorts] >> And now there's a whole bunch going on.

[00:06:02]The 1 2 looks up making that the three taking three out of those.

[00:06:08]Um but there's a bunch of other stuff.

[00:06:10]The three can't be here.

[00:06:12]The 6 7 is looking down making that the nine and that the seven.

[00:06:16]Um I can see there's what stuff going on with the 1 2.

[00:06:22]How do I want to proceed with this?

[00:06:27]This is an eight.

[00:06:29]But I could do more than that I think.

[00:06:31]But I can see by Sudoku eight can't be in those because of the 8 9 looking down eight can't be in those. There is an eight here.

[00:06:37]But I think I can do math on this box.

[00:06:39]Well, you could do math on this box. Can I do math on this box? I don't know.

[00:06:44]Because these digits here are 31. And 31 + 3 is 34.

[00:06:53]Now, we know or we don't know, but we can deduce that because all of the digits in this box we know that we know that any box of a Sudoku contains all of the digits 1 through 9. And if we add those digits together, you get 45. So, if we have 45 - 31 is 14 - 3 is 11.

[00:07:12]Those digits have to sum to 11. So, how can we do 11? Well, 9 + 2 isn't possible. 8 + 3 isn't possible. 7 + 4 isn't possible. This has to be 5 + 6.

[00:07:25]Which means that's the four and there's no four there. The 5 6 looks up saying there's no five there.

[00:07:33]The four looks up saying there's no four there. And this is a three now.

[00:07:41]Because 4 5 6 7 8 9 are already placed in the column. So, this has to be a 1 2 or 3 in order to fill the column cuz 4 5 6 7 8 9 are not available. So, this these cells in the column have to be 1 2 and 3. But the 1 2 here makes this the three taking three out of here making that the three.

[00:08:03]But we know what these digits are now. 1 2 3 or 5 6 7 9. And if we add 4 7 9, well 4 7 is 11 + 9 is 20. 20 + 3 is 23 + 8 is 31. And the math works.

[00:08:20]But if these are 4 7 9, I can't put a four in this six cage. Which means I can't make this six sum by using two and four. This has to be one and five meaning that's the two, that's the one.

[00:08:32]The five looks down making that the six and that the five. I could have used the 6 7 to do that. I'll get there eventually. The 1 5 means there's no one or five in here and the four looks up making that the two and that the four.

[00:08:47]Can I take that any further?

[00:08:51]Not yet that I can see, but I loved being able to do all of this in that left-hand stack. That was fun.

[00:09:00]Especially as I know the makeup of this cage, but I can do more before I even get to this because I know I'm actually going to talk about this even though I can resolve some of this stuff. Because this 16 cage um the minimum digits as I discussed over here that you can put into five cells without repeats are 1 2 3 4 5. And those sum to 15. So, in order to get from the 15 that I've got to 16, I need to increase one of those digits by one. But I have to do it without causing repeats.

[00:09:33]So, if I was to increase the one by one, I'd have two twos. If I was to increase the two by one, I'd have two threes. So, the 1 2 3 and 4, if I was to increase those digits by one, I'd end up with repeats in the cage. It doesn't work. I have to increase the five to a six. And this becomes 1 2 3 4 6 and that's forced for this cage.

[00:09:53]But the other important thing I I do, and this is probably more powerful, is there must be a one in this eight cage because we know if there's no one, the minimum digits are two, three, and four.

[00:10:03]And we've already proven here that two, three, and four added together sums to nine. And this is lower than nine, so there must be a one in the eight cage, meaning that's the five and that's the one.

[00:10:13]Which means there's no one here, there's no one here. The two, three, four come out of here. This is only one or six.

[00:10:19]The one, two, three come out of those, which means this is a four, six, which means this has to be the one because four and six come out of those. There's no six there and there's no four there.

[00:10:29]So, this is the one, this has to be the two, three, and this is the four, six.

[00:10:34]And now, that digit is under a lot of pressure.

[00:10:38]But not as much as I might think.

[00:10:45]Hmm.

[00:10:47]Now, I definitely know there's a one in this eight cage for the same reason.

[00:10:51]But what could this be?

[00:10:53]One, two, well, hang on, there's no five in here. So, if I did one, two in here, that would sum to three and in order to get to eight, I'd need another five, which I don't have. So, I can't put a two in this cage. The next option is one, three and then I need another four and then after that I run out of options because the next option is one, four, three and I'm repeating. So, this is one, three, four. This is the two, this is the three.

[00:11:21]Okay. And now, this 10 cage becomes forced because in order to do a 10 sum, I need a digit below 10 and a digit above 10 um to make the 10 sum. I could do 1 + 9, 2 + 8, 3 + 7, or 4 + 6. 5 + 5 doesn't work cuz I can't use two fives and I can't use two digits above five or two digits below five. I don't hit the correct sum.

[00:11:43]And one, three, and four are not available. So, because I need either a one, a two, a three, or a four, I must use a two in the cage um with an eight.

[00:11:51]I can't put the two there, so this is the two, this is the eight. I'm trying to talk about some first principles here to lock it in.

[00:11:58]Um that's interesting. So, where do I go from here?

[00:12:04]Um is it this six cage now?

[00:12:08]Maybe.

[00:12:13]Oh, this eight cage is another one that must have a one in it. So, that becomes the two and that becomes the one. And for the exactly the same reason, this is now a one, three, four cage and the one and the three look down making that the four, meaning this is a one, three pair.

[00:12:27]The four looks across saying that there's no four there.

[00:12:31]And this 10 cage has the same properties of this. It must have a low digit, a one, two, three, four, and a high digit, a six, seven, eight, nine. But this can neither be one, two, three, or four. So, this is one, two, three, four. This is six, seven, eight, nine. But the three says that's not the three, so that's not the seven.

[00:12:48]Not sure that that's helped me that much.

[00:12:51]And this is where it's like, I need to do some more math and I I hate doing the math. Okay, so what have we got in this row maybe?

[00:12:59]Or is it this row?

[00:13:03]Well, actually, I might be able to do it by I'm not sure the best way to do this.

[00:13:19]If this was one, three, four, we'd have four, one, three. That seems okay for this.

[00:13:25]One, two, oh, this either has to be one, two, five or one, three, four. We've already discussed this because um if these were have one and two in them, we need a five. If it's one, three, it needs a four.

[00:13:38]But I can't So, there must be a four or a five in this eight cage.

[00:13:42]But it can't be in those cells. So, this can't be the one, this has to be the four, five, and these are from one, two, three. And the one must be down here, which means the one must be over here and the one can't be here. So, the question is, can that be the one?

[00:13:57]If this is the one, these would need to sum to 13. They couldn't be nine, four.

[00:14:02]Like Yeah, I don't think this could be the one. If this is the one, those two digits there would need to sum to 13.

[00:14:08]How do you sum to 13? Nine, four is an option, but I can't use it. There's already a four in the box and in the row. Eight, five is an option, but I can't use it. There's already a five in the row. Seven, six is an option, but I can't use it. There's already a six in the row. And after that, I'm repeating when I hit six, seven. It's the same as seven, six. So, this can't be the one.

[00:14:26]This is the one, making that the three and that the one.

[00:14:32]And now, three must be in this 14 cage.

[00:14:36]But by Sudoku, three can't be in those, three can't be in those, and three can't be there. So, there is a three in here with two digits that sum to 11 because 14 - 3 is 11. I could use nine, two. I can't use eight, three cuz I can't repeat three in the box. I can't use seven, four. I can't use five, six.

[00:14:54]This is nine, two, three to get to 14 and we know there's no three or two there. That's the nine.

[00:15:02]This is the two, three. So, take the nine out.

[00:15:05]And that is now a one, two, three triple.

[00:15:08]So, I've got one, two, three, four, five, six. These are a seven, eight pair.

[00:15:18]Okay.

[00:15:19]Oh, the four looks up making that the six and that the four. So, one, two, three, four, five, six, five, seven, eight. So, these are five, seven, eight.

[00:15:28]And there's no seven or eight there because of those. That's the five.

[00:15:32]That's not a five. This is a seven, eight. But the five looks across making that the four, so these have to sum to four, which means these are one, three, which means that's the two, that's the three.

[00:15:44]Now, this nine has to be forced surely because nine is similar to 10. How do I make nine? One, eight, not possible.

[00:15:50]Two, seven is possible. Three, six is not possible. Four, five is not possible. So, this has to be two, seven, meaning that's the eight, that's the seven, that's the eight.

[00:16:02]And the seven looks across making that the two and that the seven. Am I solving this the most efficient way? Probably not, but I'm having fun. One, two, three, four, five, six, seven, eight, nine. That's a six and then one, two, three, four, five, six, seven, eight, nine. These are five and nine.

[00:16:20]Okay. I can now probably do some math on this box.

[00:16:25]Is that what I want to be doing? Yeah.

[00:16:27]Well, I can tell that eight has to be in one of those two because this digit has to appear in this box. It's not one, two, or three and it can't repeat in its cage, so it has to be in one of those two.

[00:16:40]Seven is up here somewhere.

[00:16:46]Can I do more with Sudoku? Well, I can tell four is in one of those two.

[00:16:52]I know what these two digits are. One, two, three, four, five, six. These are seven and eight and the eight looks across making that the seven and that the eight.

[00:17:00]Two therefore is in one of those two.

[00:17:05]And the rest are a little bit more ambiguous.

[00:17:10]How is this not resolved yet?

[00:17:18]The eight looks down saying that's not eight. Whoops, I didn't mean to remove both digits here. So, this isn't two.

[00:17:30]Oh, one, three, four says that's not the four, that's the four.

[00:17:36]There's a couple of ways of looking at this and I'm not sure what the best way is.

[00:17:40]I can see seven is in one of those two because seven can't be in those and the rest are filled. So, one, two, three, four, I need to put five up here, not sure. Six, not sure. Seven and nine, not sure. Well, I've got the seven there.

[00:17:54]But I can do some math over here because these sum to 12 and 12 minus um 34 minus 12 is 22. So, I know those digits there sum to 22.

[00:18:08]In fact, I shouldn't have actually bothered removing the um removing all of that. What I should have done is 34 minus eight is 26.

[00:18:19]Yeah, 26.

[00:18:21]So, these digits here sum to 26. 26 + 6 which is what those sum to. 26 + 6 is 32.

[00:18:32]So, what I've got here is 32. 45 minus 32 is 13. So, those digits have to sum to 13 and contain an eight. So, those are five, eight. And the five looks across making that the eight and that the five. The eight looks back making that the nine and that the eight. And now, I know exactly what these digits are. One, two, three, four, five, six, seven, and nine. And if I add all of those together and that In fact, this was probably forced at the beginning. I may have not needed to do any of this math. I may have just forgotten my my totals because the maximum five digits could be are five, six, seven, eight, nine. Six, seven, eight, nine is 30.

[00:19:10]Five, six, seven, eight, nine is 35. I had to reduce one of those digits by one and exactly the same concept of increasing one of those digits by one meant that the only digit I could have reduced is five to four and those digits have been forced from the beginning.

[00:19:24]I got there a different way and everyone can laugh at me in three, two, one. See, I can count.

[00:19:30]Um Okay, the nine looks across saying that's not the nine. So, we have a six, seven pair. There must be a nine in one of those two, which means there's a nine in one of those two.

[00:19:40]Um Okay. Oh, the seven looks up taking seven out of both of those. So, that's the six, that's the nine, that's the seven. The six looks across making that the seven and that the six. I made this way harder than I needed to. But I had fun. 1 2 3 4 5 6 7 8 9. So the Well, the seven looks across saying that's not the seven, so that's the seven, that's the nine, and these are a five six pair.

[00:20:05]And I don't know. But the nine looks down making that the six and that the four, and now the six looks up making that the five and that the six.

[00:20:14]The four looks up saying that's not the four. This four looks up saying that's not the four, so that's the four.

[00:20:20]Excellent.

[00:20:21]So this column I still haven't resolved it Ah, I can resolve this now. Because the only way of doing six is either 1 5 or 2 4, and I can't put a four in this cage anymore. So this is 1 5.

[00:20:33]Cool.

[00:20:34]The four and the seven look across making that the nine, which makes that the seven and that the four. The six looks across making that the five and that the six.

[00:20:43]Let's do stuff in these columns. 1 2 3 4 5 6 7 8 9. So these are 2 and 5, and 1 5 looks across making that the two and that the five. 1 2 3 4 5 6 and 9 go into those, and the nine looks across making that the six and that the nine.

[00:21:01]This column is missing its one and its three, and the one looks across making that the three, that the one, that the three. Looking down making that the one and that the three. The one looks down making that five and that one. The five looks up making that nine and that five.

[00:21:15]And I need to put a two in this box.

[00:21:17]That two says not there and that two says not there. So that's a two. Let's put in the triple 7 8 9. We'll use the eight to remove eight from those and put the eight in, and then we'll use that seven to make that the nine, that the seven. And that was a lot of fun. Um I really enjoyed that one. Thank you, Jack O'Wacka, for that puzzle weirder cages.

[00:21:38]Um I got a little bit messed up in this cage. I could have done a lot more there a lot faster, but I very much enjoyed the concept. A really nice introductory killer puzzle um is a tricky thing to come across and very, very tricky to do well that is also interesting. Now, I was a lot slower than I would have been if I'd done this as something like a Brimster without Brimster. But um when I'm slowing down to figure out how do I explain the logic I'm seeing, it always is a different experience. As I said, try it sometime. Even if all you do is you record your your solve so that you can watch it back and see for yourself what you're doing. It's a very, very interesting experience, and I highly recommend people do it just to try and solidify your thought processes. Because if all you're doing is you're doing things by rote, then um you're not actually reinforcing the concepts. It's It's a very, very interesting learning um technique. Um it's uh the same thing that they do when they get people to document their their um their thought processes. It's um the same sort of thing.

[00:22:43]Thank you, everyone, for watching. I hope you enjoyed this series of Sudoku U, and as always, good luck with your solving.

[00:22:52]>> [music] [music]