Thanks again for a wonderful solve, Simon! Thrilled to have been featured again for this, and you're right that this was very hard to set :P - I was convinced for a good few days that I would be forced to use an extra constraint or given digits, and I was overjoyed when I discovered this was possible with a clean grid with only cages, and remained fun! *Spoiler Time* 57:37 - You mention this step is really hard, and it's true that it's definitely the hardest point in the puzzle to progress, but figuring out the 25 pair is one of multiple ways to continue at that point. Primarily, the top (pink) cage can be narrowed down through parity, meaning R4C2 must be odd, which means it can only be 3 or 5. If R4C2 is 3, that makes R3C1 9, forcing both the green and pink cages to both be 47, which is impossible, so R4C2 is 5, and can finish from there. :) Also, you could immediately place 6 in R1C3 because 6 could never be used to make up 13 or 19, which you did talk out, but didn't quite follow through with. ;) Glad to see this didn't end up being the marathon I was concerned it might be, and very impressed by your mental arithmetic! Everyone will be pleasantly relieved to know I am not planning on making a 10x10, and I look forward to whomever may create an 8x8, but I have other ideas with similar non-repeating cage totals with stuff other than primes... :P - Mega "Xenonetix" Lamb Logic-Masters Germany ID: 000IGV
Thanks for another great puzzle! In terms of larger grids, if you're ever planning on revisiting it in a far future, I think it would work great as an 11x11 chaos construction :P
Fibonacci numbers, perhaps? The fact that 21 is both Fibonacci and triangular would surely come up. Probably also that 34 has only one representation as 5 distinct digits.
Took me an hour more than simon and had to restart twice due to too-hasty logic (once i forgot 1-3-1 was possible for the 5 cage and put in 2-1-2 which doesn't work, and once I somehow convinced myself that nineteen can't be created without a nine in the bottom right cage, then completely forgot about that logic to proceed with the top left cage), but my final progression was exactly through the 6 at r1c3, then the 3 or 5 in r4c2, then a five because after the 47 in the big cage at the top one can't get to 53 at the big cage at the bottom (didn't even check if you could get to 47 as well). Gotta say, it didn't even occur to me to examine the massive 73 cell to its possible combinations, but it's absolutely brilliant! Firstly i think it's (while still very hard), easier than seeing that the 3 in r4c2 breaks the puzzle, secondly it's astoundingly beautiful you actually know the cumulative sum of all the moving parts in that monstrositiy of a cage, and thirdly i didn't end up using that cage at all - except to check in the end i got a prime number. That way you actually use that part of the puzzle as well. Anyway thank you for a fantastic puzzle @megalamb, and a beautiful way forward i completely missed @Cracking The Cryptic
1:06:45 Simon exclaiming "I am going to actually have to put on my thinking cap" one hour into the puzzle has the same energy as "this isn't even my final form", and I love it.
As of about 25 minutes in I'm sitting at the PC very vocally informing Simon why the "3579" pencil mark in the bottom left of box five cannot have a three in it. This is where my wife comes in and started with "You know that...". I'm fully expecting her to say that he cannot hear me but no! Her full sentence: "You know that he does not understand Afrikaans!" Of course yes.. *That's* the problem!
@@martina.710 At the point I am rn it could be a 5 as well 🤔 gotta see what he comes up with or what I'm missing Edit: Nevermind, I got it 5 seconds after commenting 😂
I was proud to finish this puzzle by myself yesterday in a bit over two hours with extensive note-taking. I then of course tuned in today to watch Simon's solve, in half the time, with nothing but intuition, logic, mental math, and lots of good humor. Simon is truly one of a kind :D
I've been watching CTC for around 4 years. I still smile every time Simon says I'm one of his favourite people and shares the secret. The only difference now is that I can see it coming which means I start smiling even before he says it. Thank you
Simon, your birthday greeting to me was mind-blowing - thank you so much for your kindness. I have had a wonderful birthday visiting my relatives and Mount Rainier and other wonderful sites and sights in Washington State, but your greeting is very special. Now to watch the video - it might be tomorrow or the next day before I get back to it, though, because of travel.
This grid has me chuckling and smirking. We found all the primes where they're lurking. When victory we've tasted, Much time I have wasted When I know that I should have been working.
Usually Simon will do ANYTHING to avoid doing Sudoku, over obsessing on the variant rules. Today we see the exact opposite, as he desperately looks for anything to avoid having to face the fact that, sooner or later, he'll have to balance massive square relationships.
I am constantly in awe of how Simon can keep track of all the maths needed to solve puzzles like this in his head. Had I attempted this puzzle, I definitely would have written down the list of primes on a sheet of paper and checked them off as I used them. In this case, that likely would have helped him work out the sums of the last three cages a bit quicker.
"Do have a go." Sure. *five minutes later* The only thing I know is r6c4 is odd, the four cages in box 5 are all odd/even pairs. Those 4 pairs plus the leftover odd in r6c4 sum to to 45. Also its lunch time in the American Southwest. So I'm just gonna let Simon do it while I eat.
that still puts you ahead of Simon who, at 28 minutes in, is wondering if he can put a "3" into r6c4 when he already has a 3-4 cage in box 5. Simon's logic and break-in skills are unmatched, but his sudoku and pencilmarking have me pulling my hair out every time.
40:36 - "Fascinating" is so the right word to use. Absolutely fascinating how, after just putting in the two nines and the 8-9 pair (40:18), he ignores the 9 that would disambiguate it! That's why we all love you Simon.
One bit of logic I found that eliminated some of the math from the final two cage disambiguations was that r4c2 had to be odd, because the purple cage's total would otherwise be even, since it picks up 24 from boxes 2 and 3, plus two always-even digits and two always-odd digits in box 1. But if it has to be odd, by the time you're disambiguating the final cages the only option by sudoku is 5, which then locks all the other totals in, no math required.
At around 35:00 in the solve, I think it's a little easier to look at the maximums for the two cages occupying the middle of row 7 together. The three cells in row 6 are a max 789, the five cells in row 7 are a max 56789 and the one cell in row 8 is a max 9. Sum these together and you have 24+35+9=68, which just happens to be the sum of the next two lowest primes (31+37). The square 2x2 therefore had to be 31, the Z pentomino 37, and the rows use the maximal digits available. But other than small point, I thought that was a masterful solve!
This is a sudoku discovery to me! When I first solved it few days ago, I just stunned by the fact that this exists. Just a small point, without doing complicated calculation, because a 2-cell cage or a 3-cell cage can never add up to 29 or more, and there are 8 such small cages, we can instantly say that they must add up to the lowest 8 prime number (except 2). Then the 4-cell cage in box 3 can only add up to at most 30, so it must be 29.
I finished in 79 minutes. I have no idea how you can construct something so simple looking with a minimal ruleset and have it be this beautiful. The break-in was really fun and I was so excited to find that the 5 cage was in a 3 cell cage. This series was so fun and one felt fresh. Great Puzzle!
Finished in 39:55. What lovely logic for the break-in. I particularly like how 1 of my assumptions was immediately upended from how the center box had to be filled out. Fun puzzle!
It took me 3 hours to solve... but I was a bit distracted by the kids doing kid things at times. This one was fun. I loved every minute of it. I was having a hard time getting started, but I watched your first 2 minutes just to hear how you were going to break this down. The big trick I pulled from you was that the total of all the cages had to add up to 405. Once I knew that, I was able to isolate all of the Prime Number values that would be used. I had mapped out all of the possible sets of usable primes. After some time, I had determined that the 2, 3 & 4-cages had to use all of the primes from 3 to 31 (10 Prime Values for each of the 10 cages). For any of the 4 cages to get to 37 was impossible, and any of the 2 cages using 2 was impossible. I then worked out what the possible values could be for the 5-cage, 7-cage, 10-cage and 11-cage. I then started working on the middle and made a few mistakes which caused me to restart... that's where most of the time went. However, after resetting, it was all downhill. Once the middle was basically solved, and I had assigned Primes to each of the 3-cages & 4-cages, the 5-cage was a given, and then the 7-cage only had one option. Between the 10, 11 & 20-cages I had figured out by process of elimination what their values ought to be (43, 53 & 73). After that, the puzzle just resolved itself. [I had to use a spreadsheet to keep track of all of this]
Solved in 82:56. I rarely take on these hour plus challenges, but this one seemed like the kind I could handle. I made a little math mistake at one point near the end. When counting the digits in the 53 cage, I missed the 1 in box 3. I immediately noticed something was wrong, as the 13 cage no longer added up, but I had to check the video to see what the mistake was. Other than that, I solved it on my own without guessing.
I think this is the most I've ever been faster than him, got it in 55 min 42 sec, I've only ever been faster than him a couple of times. Amazing puzzle
OK, coming back to this after watching it in a few parts over the past few days, between travel and sightseeing and the like. This was an amazing puzzle. Although it is far, far longer a video than I would ordinarily think I could solve the puzzle myself, I actually think I might be able to do this one because of the great foundational work in the earlier puzzles of this type. Thanks for working your way through this (and so many others), Simon, with such thoroughness. It truly teaches the way to do these. And thank you again for the birthday greetings. (I confess to having listened to them more than once - is that too much hubris? I hope not - it gives me such pleasure to be part of this CtC community!)
I ran an exhaustive search for 15-tuples of prime numbers that sum to 405: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 79 = 405 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 53 + 73 = 405 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 59 + 67 = 405 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 43 + 47 + 53 + 67 = 405 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 43 + 47 + 59 + 61 = 405 Kids, whatever you do, *do not* try nesting fifteen for loops. Just as the top rated industrial safety boots are only good for 200 Joules, which is equivalent (at least on Earth, where a mass of 1kg. has a weight as near to 10 Newtons as damn it is to swearing) to 20kg. falling from a height of 1m. and so you might just as well lift weights in your bare feet for all the good any fancy shoes are going to do you, this is one of those rare occasions where a little gentle recursion might actually be slightly less insane than the "proper" way.
I think I'd break a metatarsal if I dropped that extended analogy on my foot, but I sure appreciated the work you put into it and finding the possible solutions.
At 50-00 it seemed that whether its 13 or 19, 6 cannot go into the cage. Thinking more about it, if 6 goes into the cage and you sum to 13 you need 16, 25, 34. Neither works. if you then try to sum to 19, you ned 6 + 13 and thats 49, 58, 67, which also doesnt work
57:10 If the grey cage is 66 or 72, it needs to reach an odd number for it to be prime so the part of grey in box 7 needs an odd digit so 5 is always in that domino.
while watching i was guesstimating the sum of the larger cages just going by an average value per space of 5, so for the green cage for example there are 10 spaces so the estimated value of the cage should be around 50 so i was quite happy to see how close i was
57:28 Simon not knowing the secret of two adjacent cells with the same three candidates each: their sum can only have three values. In this case the values are 2+4, 2+5 and 4+5. Given the context this was in it must be odd (since if added to either 66 or 72 must give a prime), and not a multiple of three, so it must be a (2,5) pair.
This was hard ... 298:30 for me (spread over two nights), solve counter 1876. I figured out relatively quickly roughly which prime numbers are needed (with some wiggle room at the upper end), and which cage-sizes fit to which prime (thanks to the pidgeon hole principle 3, 5, 7, 19, 23, 29, 31 had just one option, 11, 13, 17 had two options for a while, and the larger primes had to share the larger cages). Though I mis-counted the 7-cage as a 6-cage 😕, and also otherwise did some wrong calculations. Finally I took my command line calculator to help me out. Then I spent most of the time on the Sudoku part ... and got stuck. Remembered to re-count the cages and use some parity (the primes here are all odd!), which helped.
Now watching Simon do it: He managed to get it much more straightforward, going by size of cages and primes. (I had to use the Phistomefel ring at the end to make sure which digits go where exactly, but I see Simon managed it without it.)
7:52 - Simon, the channel is 'Cracking the Cryptic'... you are allowed to be cryptic, especially when it's a long way outside the Sabbath lacking one from Paris. (7,3)
Way too hard for me at this stage but I totally loved the solve path, just a beautiful idea, those Prime Cage Puzzles. Hoping to see a 2+ hour 10x10 video some time soon 😁
I somehow got the 6 Box 1 far earlier than you and as all the digits in the pink cage were fixed apart from 4, I busted out the calculator. Turns out every single option pared it down to either a 3 or 5 due to evenness. I then worked out the grey box like you did and finding the top right cage could have both 4 and 8 just unravelled the whole rest of the puzzle. I don't even know what the grey cage actually adds to!
At around 1:07:00 Simon starts musing about figuring out the value of the remaining cages, but he already had the value of the big cage because all of the digits in all of the boxes it enters are known! You can just count.
Am I missing why he spent so long deciding whether a 2 cage was possible. The smallest cages are two cells large and are dominos so could never be 1-1. Amazing solve, especially without pen and paper tho!
at 21:23 you say you almost wish you can tick them off. You can use open source software like OpenBoard" to draw on your screen to mark off the prime numbers you've used. Might also be nice for the viewer.
Thank you Simon you make me smile and you explain so well that then make me feel smart sometimes when you solve it before Simon, do it only because he explains it so well and double/triple check it is right :)
Amazing puzzle! If you leave out the list of primes under 100 from the rule set, this got to be sudoku with the shortest rule set and no given digits or other info in the grid. Only the cages and the primes constriction. Really amazing!
Any time round 51 minutes, with only the three biggest primes unknown, it makes sense to add up the 12 known primes, which amount to 169. This drastically reduces the possibilities for the last three, especially after finding that the biggest is 73, leaving 96 to be apportioned between the other two.
I gave this a shot and ran into an issue on my first and second goes - I assumed, completely incorrectly mind you, that there was only one possible configuration for that 5 cage, and then subsequently could not add to 8, haha. What I adored about this puzzle was the 31 and 37 cages - after figuring out that the 31 cage must have that sum from the 2, 3 and other 4 cell cage, then taking both it and the 5 cell cage and taking the maximums (24, 35 and 9) you get the 68 sum. It's so beautiful and incredibly clever setting!! I'm astonished at the solve and really enjoyed the challenge. On my last reset it took me an hour and 40 minutes, but the logic to get there took me far longer to fully tease out. Incredibly glad to have given the whole series a shot though! Thank you to all the fantastic setters c:
I want to see Simon playing Starcraft II. It may be fun, it may be not. But I am curious what this brilliant mind would create. Maybe in another channel...
One thing at 1:06:10 The way I solved it was that you knew the contents of the purple cage with the exception of the 59 and the cell below by knowing all of the other digits in box 2. To add to a prime it had to either be a 5 over a 3 or a 9 over a 5 but the three in green cage sees it so it has to be a 9 over a 5
"That is ridiculous! If that's what I'm meant to do it's ridiculous!" (59:00) Is suspect so! I ended up following the exact same path (2-5 pair in box seven, then restrict the 19-cage in box one), though I was stuck for over an hour before I found it!
23:08 Absolutely magnificent feat of construction. As with the previous iterations of this genre the maths breaks down the solution pretty simply, but just building this is incredible in itself.
Crazy. Me seeing the puzzle and writing a script how many combinations of 15 unique primes add up to 405 and beeing really surprised that in 5 possible combinations all numbers up to 37 are required. Me thinking "wow, how should you conclude that?". Going back to Video and then 3 minutes later ... 😅
Simon adds like a calculator but feels substituting one prime with a prime 26 larger, like, just saying here, 47 with 73 is not forced... xd can't substitute 43 with 69, can't you?
In my attempt to solve this, I first proved that both 3 and 5 had to be cage totals, and then I proved that 3 and 5 both can't be totals. So I'm stuck, and very curious how this one can be solved. I guess I'll have to watch the video to find out. *Edit*: never mind, I figured it out: you _can_ have both a 3 and a 5. (The 5 doesn't have to be in a domino.)
When you found that the 3 cage is a 5.. .I was thinking... uhhh I have seen a video with mephisto ring... when is he gonna tell us about it? I have yet to watch the whole video, but it was clear to me, that those numbers must be beside those 3 3-number cages. And yet you did not use it 😥
