I love it when Simon talks about The Secret because he typically also uses the word 'avail', which I always associate with Gandalf's speech before he battles the Balrog ("The dark fire will not avail you"). It makes solving sudokus seem much more epic: "You shall be filled," Simon declared, his voice echoing across the grid. The puzzle paused, and a silent tension filled the air. "I am an envoy of the sacred patterns, wielder of triangular numbers. You shall be filled. The power of The Secret will not avail you, nori nori. Go back to your constructor! You shall be filled!"
One way to see the endpoints are 9: A, B = endpoints R = regional sum T = total sum 0.) Without loss of generality, A= B (B is contained within R) 4.) T >= 9*B (equations 2 & 3) 5.) A*B >= 9*B (1 & 4) 6.) A >= 9 (cancel B) 7.) A
I'm satisfied with just figuring out the 9 in each end of the snake within 1 minute of looking at the possible, and knowing full well the rest of the puzzle would still take me well over an hour. 9s were obvious because the moment you put a digit on the end of a line (say 6 for an example), the region sum for the snake is at least that number, so the total sum of the snake is at least that number times 9 (so in this case 6x9, 9 on the other end), and the moment you place the 9 on the other end, which again forces the same logic the other way, by making the region sum at least 9 and therefore the total sum at least 9x9. Great solve as usual, Simon. Well done!
That's exactly what I did :) Just explained in words rather than equations. My version: (lower end digit) × (higher end digit) = 9 × (region sum) (region sum) ≥ (highest digit on line) ≥ (higher end digit) combining these: (lower end digit) × (higher end digit) ≥ 9 × (lower end digit) and cancel: (lower end digit) ≥ 9 Pretty sure that's the same logic expressed differently
this was also obvious to me and i have been on the edge of yelling at the screen for so long waiting for simon to catch up. you need to enter 9 boxes your max is 9x9. but there is no way to have less than 9 on the ends of the snake if you have 1+8 and a 9 on the end boxes you will always be 9 short. 8x8 on the ends 64 cant be divided into 9 boxes. almost frustrating to watch
@@aj_cheeze7263 haha did he use too much time on that? Simon is a genius, but sometimes I get very annoyed with him. Hahahahahaha. Your logic is the best.
Yep I followed pretty much the same logic as you and @AngelWedge to determine not only that both end digits had to be 9, but that those digits would also be the only snake digit in the end boxes.
the inner machinations of simon's mind truly on full display today! loved that today simon actually said "good brain" and hope those two can keep on solving these wonderful puzzles for us.
I love Small Ant's content and knowing that Tanner watches CtC makes me love him even more. It's always a treat discovering people who also watch this channel. Like the other day, I was working on a tool for Zelda speedrunning and someone name-dropped WooferZFG and I was like, "Hang on, I know that name from sudoku!"
The irony of apologising for long videos only at the point where those of us who DO watch the whole long video would see :) It's a tough balance, finding puzzles that are interesting but don't take too long! I don't envy you, and if I'm too busy to watch a long video on the day, I often come back to it later at least.
Almost three hours for me, but I must confirm they were definitely _"brim full of gorgeous, innovative logic."_ Incredible construction. Thank you CTC for selecting and featuring so many mind-blowing puzzles.
Finished in 47:42. I had 2 lovely Ah-ha! moments. One was the break-in where I figured out that because the snake was a same-sums line AND a product sum line that the 2 ends had to be singletons which limited the possibilities of the ends to be in box 1 and box 3, because they can't add up to more than 9 since it's a product sum with at most 9*9 and it had to go through each box and box 1 had to go down because otherwise there would be 4 cells in a same sum line that can only add up to 9. My 2nd moment, was figuring out that the circles could be the same digit. For some reason, I thought that they had to be different digits, but after banging my head for a while trying to figure out what the other digit could be, I realized that it could be the same digit in both circles. Fun puzzle!
IcyFruit did it again. Man, I live Snake Sudokus and this one is simply amazing. I can't imagine how IcyFruit is able to make someting like this. Just perfect.
@59:33. Simon:- "4 is in one of these cells by Sudoku" ...seconds after having put a 4 directly in the column above. There are times that I wonder quite how he actually solves some of these puzzles!
I found your channel a week ago and have been bingeing and learning your techniques since. Today I solved this puzzle in 2 hours, which means I’m about half the genius you are, which I’m SO PROUD OF, because you’re an absolute master. I used letters instead to denote individual digits (aside from 5) and used colors for the dominoes. It made for a prettier overall result but I did do sudoku with letters A-H all the way through, yes the whole thing, before finding how to turn them into actual digits. 😅🤦🏽♀️
Just so you know, I'd watch a 24h video, just give me a heads up first, since I don't usually have enough beer and snacks available. Also, both of you have such good diction that I can play the videos at 1.5x speed without losing anything. Mark can speed up his flow of words from time to time, but I always catch everything the first time, even with increased speed.
So I got kind of distracted near the start thinking about how the product sum lines reminded me of factoring quadratics because in x² - Bx + C, you're looking for numbers that sum to B and multiply to C. Thinking in terms of product sum lines, you have the middle of the line summing to some value N and the ends summing to some value C, so you can set up a quadratic equation where you're looking for endpoint numbers that sum to C and multiply to N+C. That is, x² - Cx + (N+C) = 0. Using the quadratic formula, you get x = C/2 ± √(C² - 4(N+C))/2. Since the solutions are the two endpoint values, you know you need two distinct, real solutions, so the discriminant is positive. More than that, the solutions are sudoku digits, so the discriminant must be a perfect square. We can generate some solutions by noticing that there's a multiplier of 4 in the discriminant as the difference between C² and the final perfect square we need, so we're looking for two perfect squares whose difference is divisible by 4. For example, we could use 16 and C²=100, which has a difference of 84, giving N+C = 21, C = 10 (the sum of the endpoints), and N = 11 (the sum of the middle). Plugging those into the overall formula gives 3 and 7, so the endpoints are 3 and 7 and the middle adds to 11. We can quickly verify that 3*7 = 21 and 11+3+7 = 21. I doubt any of this is particularly useful, but I found it pretty neat to at least take the guesswork out of coming up with possibilities. Not that this is the easiest way since you can pick two endpoints to multiply and then figure out what N has to be very easily, but this could reveal something about when you have the middle and need the endpoints. Maybe someone else has ideas to take it further.
This one was wild!!! And my wife and I watch together and we love the longer videos -- I know some people prefer the shorter ones, but count us in for the longos! 🎉
I finished in 134 minutes. I was a little late to discovering the break-in involving multiplying the total number of boxes by the minimum number the region could be. It took me until 54 minutes to see that, despite it being obvious. Luckily, all my logic I thought before that helped me zoom along. I made a mistake in the bottom left line and put two 6's on the ends and when I completed the puzzle, I was shocked to not get my tick. I realized that I forgot to count the 6's in that total, causing me to have to rewind quite a while. Luckily, again, I was able to use my previous logic. I enjoyed this one, especially drawing the snake and figuring out the contents. Great Puzzle!
@1:09, after finding the 6789 quad in column 9, you show that 6 can only go in column 9 in box 6. That would eliminate it from the region sum line in column 8, giving you a 7, which eliminates the 2 on that line in box 3, forcing orange in box 9 to be a 2. (Now I feel like the guy who opens the pickle jar after the Rock has loosened it).
At around 1:02:00 I think the easiest next step is to ask if a 2 can be on the product line in box 5. The maximum product would be 2*8 = 16 and then the minimum sum would be 2+8+4+5=19. So (4,4) can't be a 2 and has to be a 3.
@@jimmyporter8941 8 in (3,2) maximizes the product, if you try 7 you get product of 14 sum of 18 and the lower the number the worse the difference becomes.
48:52 finish. Was able to pick up on the snake logic right away, but I missed a couple of obvious bits of sudoku near the end. An outstanding puzzle, so much fun!
That is a brilliant puzzle with some delightful deductions - I think may favourite was the circle. Starts off looking very open-ended so its something of a revelation to find how constrained is the snake.
42:28 the circled digit cannot be a '3' for the extremely simple reason that the circled digit itself would be the 4th '3'. But of course Simon found a much more complicated explanation.
72:30 with two looks at the video. I needed help to see how the 1 had to be in the top of Box 6 and that there was a 2 or 3 on the blue line in Box 3. I got the initial snake line really quickly, so I thought the rest would go smoothly. It didn't.
I did both this and yesterdays puzzle tonight. Both pretty darn challenging, thankfully I did ok with an hour and a half on this and on the other I'm not sure since I left it open while dealing with other stuff but under two hours I think. Both were great.
I have now gone to "parallel solving", where I start out doing the solve myself, and when I get horribly stuck, I watch Simon's video for some ideas. This works quite well, I have been able to solve some of these wil relatively little "help". Here I spotted the form of the snake quite quickly, because there is a much faster way to work out that there should be two one-digit single 9s at the end of it (if there is one that is 9, all the boxes are 9, and presto, we know the two ends).
we can confirm the snake was a cobra as the title said and specfy the species because of the one only eye (circle) back on her neck. Beautiful monocled cobra.
55:15 I don't think I've encountered product lines before but I suspect if they catch on this kind of thing is probably going to a recurring theme, using the fact that the product of two sudoku digits tend to grow faster than their sum to constrain the ends by blowing up the middles
I found that the endpoints had to both be 9s by just arguing like this: "the product must be 9 * X since there are 9 regions of X. X must be at least 6, since it has to have 3 cells. product is possibly 54,63,72,81. To have X be anything less than 9, it would then be broken in a region into X+Y. then 9*x would have to equal 9*(X+Y) since each region sums to X+Y. So Y must be 0 and the product is 81". I messed up the snake connection in region 7 though, and then got lost. Great puzzle!
At a certain point I pulled out wolfram alpha to give me integer solutions to a messy equation. It was then that I realized that product lines are not for me yet!
Yeah definitely good instincts to avoid solving over the dark grey cell color, any very dark shading makes it very hard to read pencil marks on smaller screens or at lower quality settings
Love your vids! Just thought i’d give another proof as to why the snake must have 9s at both ends. As you said early in the video, the snake’s sum must be a multiple of 9 (as snake_sum=sum_of_regions=9*region_sum which is multiple of 9). Now you take into account that ends_product=snake_sum=9*region_sum to get that the product of ends must be a multiple of 9. Suppose, for contradiction, that 9 does not exist on either end. Then biggest the sum of snake that has a factor of 9 is 36 (from 6*6), meaning that there is a 6 on both ends and that sum of each region is 36/9=4 in contradiction to 6 being on snake. Therefore, at least one 9 exists on snake and therefore the sums’s region is at least 9. As there are at least 9 regions, the sum of all regions is at least 9*9=81. But it is also at most 81 as 9*9 is max possible. Therefore, both ends contain a 9.
i think you missed (at least for a long time) that the snake needs a multiple of 9 because it sums 9 of on number. there are only a few ways to get a multiple of 9, which is 3*3,3*6,X*9, 6*6. if it has one *9 in it, that means the sum of that grid is at least 9, which means the it is 9*9, and so the start and end cell are the only cell in this box 6*6 isn't possible, as the sum of each box would be 4, do that 4*9 is 36, ehich is lower than the 6 at the end
You could've find out about double 9 in snake ends in the begining of the solve. It's sum is divisible by 9, so either one of its ends is 9, or they are from 3 and 6. Clearly 3*3 and 3*6 are definetely too small, 6*6=36 means each box sums to 4, but that's impossible as one of the ends is 6. So we know that one of the ends is 9, that means that region sum of the snake can't be less than 9 so it is equal to 9 and 9 boxes of sum 9 is 9*9 that are the ends of the snake. Regardless any other clues.
@1:21:38 Simon concludes we need to put a 123 on the snake in row 7, but I don't understand how he concluded this.... Then @44:25 Simon concludes that there are only 4 places to put a four. He wound up choosing the correct boxes, but at this point in the solve, I was still not able to rule out a 4 on the snake in box 7 column 3. Can anyone explain how he ruled it out of row 7 so early?
Well, I'm proud of myself building snake pretty fast. It took me just 25 minutes. The rest of the puzzle, though... Total time is almost 2 hours, and that's with the clues from Simon, cause I just could not see all of those intersecting dependencies, and just didn't have much more time to look for them. Even though, it's not for the reasons you mght think, that puzzle is really hard!!
By the region sum rule, the sum of digits on the snake is a multiple of 9; so either the head or the tail of the snake must be a nine. Then the sum in each region must be at least 9. But 9 is also the maximum possible digit in the other end of the snake; so *both* ends are single digit nines, and the strings of digits in each of the intermediate boxes sum to 9 (meaning, there can only be 3 of them). R3C2 and R2C7 are the only possible squares for the head and tail, and most of the rest of the cells on the snake are fixed.
"so either the head or the tail of the snake must be a nine." not exactly, you could have had (6 ; 6) or (3 ; 6) or (3 ; 3) as tail and head to get a multiple of 9
@@thefallenarm589 One more step to rule those out. If you have two sixes, then the snake's overall sum is 36, meaning it sums to 4 in each box, so you can't have a 6 on it. Similar logic rules out the others.
Why do the intemidary boxes sum to 9 and not atleast 9? If the head and tail both take 2 boxes in there respective boxes couldn't we get 10 for example if it is 1 9, with 9 being the tail/head
And what a clean solve too - as usual Simon (who sometimes thinks he takes "too long" to spot things) finds a way through with extraordinarily crisp logic: true, there was a point at which 6 in column 9 would have saved time. I have solved this twice, and both times less efficiently. Any time I gained was through not having to explain the logic and (first time round) realising that the snake and the circles would have to do the early work right from the start. Simon is a really good expositor of the puzzle logic, and his intuition for weaknesses is well tuned: this solve gets a high rating from me. BTW once 9 is a factor of the snake sum, you have to have either 6x6 (which is easily disproved, as you can nowhere have a run of four cells from 123) or 9x9, because as soon as you have one 9 on the line, the region sum has to be 9 to accommodate that - and that was what saved me early time.
I wasn't expecting to hear the name SmallAnt clicking on a Cracking the Cryptic video!! I've loved both channels for quite a while now so it's funny to see the two know of each other lol, makes me wonder what a CtC Pokemon video might look like, or SmallAnt speedrunning sudoku somehow 😂
Draws the snake almost spot on as an example. Instantly hits the nail on the limits of the snake. With it being something you can divide by 9, but also cannot be more then 10. Proceeds to not instantly get that the snake can only have 1 block at the start and end. Enjoyed it, once you get started, very addictive. Thank you
I really like how you can arrive at the conclusion that the two edges of the snake are 9. Simon came to that conclusion by seeing the 7th and 8th row. While i thought about the fact that due to the snake being a region sum the snake would add to 9 * x, where x is the sum of each region. so one of the two edges needs to be a 9 cause if you don't have a 9 at either end then the other combinations that could work for the result to be divisible by 9 would be either 3*6 or 3*3 or 6*6 all 3 option not possible. (how i came to the conclusion that those are all the available combinations you can think about prime factors) Taking into account that one of the edges is 9, and x being the sum of each region, how can x be less than 9 as in which ever end of the snake the 9 is placed, that region is already summing to 9 so x has to be 9 and cant be greater than 9. and that results in the snake summing to 9 * 9.
The snake also acts as a product-sum line, so the end digits have to multiply together to give the sum along the snake. The equal sums nature of the line tells us it sums to 9 boxes x 9 = 81, so the end digits have to be 9 and 9.
I'm dumb. For some reason I was thinking of the snake as a loop and I couldn't see any possible way that a loop could enter every box without touching itself orthogonally.
Simons way of proving the snake ends are 9 is so complicated when instead you KNOW that the max row/column cell count on the snake in row 9 has to be 6 or fewer cells otherwise you force a number greater than 6 into one of the cells on the snake, this makes the region sum more than 9 in one of the boxes 7,8,9 which it cant be. So you know the path it takes in box 7 as there cant be a 7th cell in row 8 and you know the region sum is 9 without any complicated deduction because theres a 6 somewhere and that region has to be 126.
I love it when Simon talks about The Secret because he typically also uses the word 'avail', which I always associate with Gandalf's speech before he battles the Balrog ("The dark fire will not avail you"). It makes solving sudokus seem much more epic:
"You shall be filled," Simon declared, his voice echoing across the grid. The puzzle paused, and a silent tension filled the air. "I am an envoy of the sacred patterns, wielder of triangular numbers. You shall be filled. The power of The Secret will not avail you, nori nori. Go back to your constructor! You shall be filled!"
What a wonderful comment!!!
Loved this from you!!!
A wizard is never late, Frodo Bobbins
Very epic comment, thank you
Im always smiling face edge to edge when im one of simons favorite people, being told about The Secret 🥰
IcyFruit is slowly training Simon to pencil mark prolifically.
the real long game
Does that mean IcyFruit is actually Mark ?
After Simon explained the rules and then said "do have a go..." I uncontrollably snorted with laugher at the thought of me attempting this puzzle.
That would have been my response two years ago ...
I just solved it. Great fun. Have a go.
Looking at Simon's solve time I also thought that but decided to give it a try anyway. Ended up solving and even got a first break in much faster.
I always follow his sayings like „yeah sure makes sense“ but I couldn’t do any of that work myself - I can solve standard Sudoku. That’s it.
I actually really like when the cells are all colored black. It's like an artificial dark mode and I wish that the website had an actual dark mode now
The snake you drew to show is where is possible was almost bang on
Yes, indeed! :-)
Rules: 04:27
Let's Get Cracking: 09:21
Simon's time: 1h10m46s
Puzzle Solved: 1:20:07
What about this video's Top Tier Simarkisms?!
The Secret: 5x (36:37, 36:46, 36:50, 36:53, 36:58)
Three In the Corner: 4x (1:07:03, 1:07:06, 1:19:17, 1:19:59)
Knowledge Bomb: 1x (44:46)
And how about this video's Simarkisms?!
Snake: 119x (01:04, 06:33, 06:39, 06:43, 06:45, 06:48, 06:53, 07:10, 07:23, 07:29, 07:38, 07:42, 08:01, 08:05, 08:15, 08:35, 08:44, 09:08, 09:13, 12:14, 12:16, 12:16, 12:48, 12:57, 13:02, 13:13, 13:23, 13:39, 14:01, 14:31, 14:39, 14:44, 14:47, 17:00, 17:03, 17:03, 17:08, 17:33, 17:51, 18:06, 18:42, 18:45, 18:55, 19:04, 19:04, 19:46, 19:48, 19:59, 20:18, 20:24, 21:24, 21:35, 21:38, 22:01, 22:03, 22:10, 22:13, 22:39, 22:39, 22:44, 22:46, 23:20, 24:32, 24:43, 25:01, 25:06, 25:26, 25:29, 25:45, 25:52, 26:30, 26:48, 26:51, 28:01, 28:46, 28:56, 28:58, 29:58, 30:02, 30:09, 30:09, 30:33, 31:08, 31:39, 31:44, 31:55, 32:02, 32:06, 32:15, 32:32, 34:09, 34:46, 34:46, 34:48, 35:21, 41:06, 41:08, 41:20, 41:30, 41:52, 42:05, 42:33, 43:17, 43:36, 43:42, 43:48, 44:07, 44:10, 44:13, 44:13, 44:23, 44:26, 52:37, 52:43, 52:50, 52:52, 52:54, 52:57, 1:21:01)
Ah: 17x (13:17, 23:49, 24:02, 36:32, 46:53, 52:18, 58:16, 59:25, 59:50, 1:01:40, 1:04:05, 1:04:22, 1:11:13, 1:12:57, 1:17:05, 1:17:30, 1:19:15)
Sorry: 12x (03:36, 03:48, 13:17, 27:08, 33:10, 40:22, 50:14, 53:00, 58:59, 1:04:05, 1:08:40, 1:18:50)
In Fact: 11x (05:07, 07:48, 14:25, 23:36, 30:14, 31:11, 35:38, 41:22, 42:57, 43:24, 48:15)
Hang On: 9x (09:50, 21:24, 21:27, 23:49, 33:30, 52:18, 58:44, 1:12:48)
By Sudoku: 8x (33:16, 50:35, 53:10, 56:12, 56:32, 59:32, 1:00:16, 1:00:32)
Pencil Mark/mark: 8x (31:49, 51:42, 59:46, 1:04:09, 1:08:48, 1:08:52, 1:10:29, 1:15:16)
Obviously: 7x (10:13, 17:11, 17:36, 20:41, 44:21, 57:50, 59:43)
Beautiful: 6x (21:18, 21:22, 30:30, 50:21, 1:21:03, 1:21:03)
Triangular Number: 6x (29:06, 30:38, 34:36, 35:44, 37:09)
Naughty: 5x (06:50, 16:16, 16:30, 16:40, 16:43)
Touch Itself: 5x (06:35, 06:48, 12:23, 24:32, 25:01)
Cake!: 5x (02:56, 03:06, 03:18, 03:43, 03:50)
Good Grief: 4x (42:17, 55:15, 1:18:17, 1:18:37)
Goodness: 4x (57:36, 1:04:09, 1:12:06, 1:12:13)
Nonsense: 4x (15:39, 15:41, 16:26, 46:53)
Brilliant: 4x (02:59, 03:16, 26:45, 28:40)
Naked Single: 3x (45:08, 48:17, 1:17:09)
Shouting: 3x (01:56, 03:34, 03:50)
What Does This Mean?: 3x (18:22, 45:05, 1:11:56)
Weird: 3x (05:28, 36:46, 55:20)
Famous Last Words: 2x (1:05:04, 1:14:38)
Useless: 1x (40:31)
What a Puzzle: 1x (1:19:55)
Bother: 1x (49:58)
Clever: 1x (1:12:13)
Missing Something: 1x (1:08:36)
In the Spotlight: 1x (1:20:02)
Lovely: 1x (50:24)
Incredible: 1x (02:37)
Shenanigans: 1x (00:19)
Surely: 1x (1:17:36)
Unbelievable: 1x (26:42)
Box Thingy: 1x (53:10)
Phone is Buzzing: 1x (32:24)
Progress: 1x (32:48)
Most popular number(>9), digit and colour this video:
Fifteen (12 mentions)
Three (103 mentions)
Blue (7 mentions)
Antithesis Battles:
High (8) - Low (8)
Even (22) - Odd (3)
Higher (2) - Lower (0)
Black (2) - White (0)
Row (22) - Column (16)
FAQ:
Q1: You missed something!
A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn!
Q2: Can you do this for another channel?
A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!
One way to see the endpoints are 9:
A, B = endpoints
R = regional sum
T = total sum
0.) Without loss of generality, A= B (B is contained within R)
4.) T >= 9*B (equations 2 & 3)
5.) A*B >= 9*B (1 & 4)
6.) A >= 9 (cancel B)
7.) A
I'm satisfied with just figuring out the 9 in each end of the snake within 1 minute of looking at the possible, and knowing full well the rest of the puzzle would still take me well over an hour.
9s were obvious because the moment you put a digit on the end of a line (say 6 for an example), the region sum for the snake is at least that number, so the total sum of the snake is at least that number times 9 (so in this case 6x9, 9 on the other end), and the moment you place the 9 on the other end, which again forces the same logic the other way, by making the region sum at least 9 and therefore the total sum at least 9x9.
Great solve as usual, Simon. Well done!
That's exactly what I did :) Just explained in words rather than equations.
My version:
(lower end digit) × (higher end digit) = 9 × (region sum)
(region sum) ≥ (highest digit on line) ≥ (higher end digit)
combining these:
(lower end digit) × (higher end digit) ≥ 9 × (lower end digit)
and cancel:
(lower end digit) ≥ 9
Pretty sure that's the same logic expressed differently
Yep, noticed nines too.
this was also obvious to me and i have been on the edge of yelling at the screen for so long waiting for simon to catch up. you need to enter 9 boxes your max is 9x9. but there is no way to have less than 9 on the ends of the snake if you have 1+8 and a 9 on the end boxes you will always be 9 short. 8x8 on the ends 64 cant be divided into 9 boxes. almost frustrating to watch
@@aj_cheeze7263 haha did he use too much time on that? Simon is a genius, but sometimes I get very annoyed with him. Hahahahahaha. Your logic is the best.
Yep I followed pretty much the same logic as you and @AngelWedge to determine not only that both end digits had to be 9, but that those digits would also be the only snake digit in the end boxes.
the inner machinations of simon's mind truly on full display today! loved that today simon actually said "good brain" and hope those two can keep on solving these wonderful puzzles for us.
I love Small Ant's content and knowing that Tanner watches CtC makes me love him even more. It's always a treat discovering people who also watch this channel. Like the other day, I was working on a tool for Zelda speedrunning and someone name-dropped WooferZFG and I was like, "Hang on, I know that name from sudoku!"
The irony of apologising for long videos only at the point where those of us who DO watch the whole long video would see :) It's a tough balance, finding puzzles that are interesting but don't take too long! I don't envy you, and if I'm too busy to watch a long video on the day, I often come back to it later at least.
The puzzles I find most fun are those just within or beyond my grasp. Having 80 mins + several nights in a row is testing my sleeping hours.
Almost three hours for me, but I must confirm they were definitely _"brim full of gorgeous, innovative logic."_
Incredible construction. Thank you CTC for selecting and featuring so many mind-blowing puzzles.
Finished in 47:42. I had 2 lovely Ah-ha! moments. One was the break-in where I figured out that because the snake was a same-sums line AND a product sum line that the 2 ends had to be singletons which limited the possibilities of the ends to be in box 1 and box 3, because they can't add up to more than 9 since it's a product sum with at most 9*9 and it had to go through each box and box 1 had to go down because otherwise there would be 4 cells in a same sum line that can only add up to 9. My 2nd moment, was figuring out that the circles could be the same digit. For some reason, I thought that they had to be different digits, but after banging my head for a while trying to figure out what the other digit could be, I realized that it could be the same digit in both circles.
Fun puzzle!
I like that the snake ended up being very snake-shaped.
As snakes go, this one was pretty cute!
In fact we can confirm it was a cobra as the title said because of the eye (circle) back on her neck. Beautiful monocled cobra.
I always love long video, as long as a wonderful puzzle got featured. Great solve!
Loved the fight berween the good part and the naughty part of Simon's brain 😂
Having a brain that argues with itself will always keep you entertained! 😉
It sometimes reminds of the struggle of good vs. bad Smeagol, albeit infinitely more benign.
Can we have a comedy show about Simon discussing stuff with his brains, please?
IcyFruit did it again. Man, I live Snake Sudokus and this one is simply amazing. I can't imagine how IcyFruit is able to make someting like this. Just perfect.
59:26, Simon... how? LOL
@59:33. Simon:- "4 is in one of these cells by Sudoku" ...seconds after having put a 4 directly in the column above. There are times that I wonder quite how he actually solves some of these puzzles!
please release the 3.5 hour masterpiece because that is all we want to see
throwing triangular numbers around like crazy for 15 minutes and then calling the triangular number of 9 a "secret" is just ridiculous.
I found your channel a week ago and have been bingeing and learning your techniques since. Today I solved this puzzle in 2 hours, which means I’m about half the genius you are, which I’m SO PROUD OF, because you’re an absolute master. I used letters instead to denote individual digits (aside from 5) and used colors for the dominoes. It made for a prettier overall result but I did do sudoku with letters A-H all the way through, yes the whole thing, before finding how to turn them into actual digits. 😅🤦🏽♀️
Just so you know, I'd watch a 24h video, just give me a heads up first, since I don't usually have enough beer and snacks available. Also, both of you have such good diction that I can play the videos at 1.5x speed without losing anything. Mark can speed up his flow of words from time to time, but I always catch everything the first time, even with increased speed.
63:03 for me. Snake was super fast for me and then my terrible maths skills really slowed me down on those product sum lines. That hurt my brain
The snake's position and value being entirely forced at the start is interesting.
So I got kind of distracted near the start thinking about how the product sum lines reminded me of factoring quadratics because in x² - Bx + C, you're looking for numbers that sum to B and multiply to C.
Thinking in terms of product sum lines, you have the middle of the line summing to some value N and the ends summing to some value C, so you can set up a quadratic equation where you're looking for endpoint numbers that sum to C and multiply to N+C. That is, x² - Cx + (N+C) = 0.
Using the quadratic formula, you get x = C/2 ± √(C² - 4(N+C))/2. Since the solutions are the two endpoint values, you know you need two distinct, real solutions, so the discriminant is positive. More than that, the solutions are sudoku digits, so the discriminant must be a perfect square.
We can generate some solutions by noticing that there's a multiplier of 4 in the discriminant as the difference between C² and the final perfect square we need, so we're looking for two perfect squares whose difference is divisible by 4. For example, we could use 16 and C²=100, which has a difference of 84, giving N+C = 21, C = 10 (the sum of the endpoints), and N = 11 (the sum of the middle). Plugging those into the overall formula gives 3 and 7, so the endpoints are 3 and 7 and the middle adds to 11. We can quickly verify that 3*7 = 21 and 11+3+7 = 21.
I doubt any of this is particularly useful, but I found it pretty neat to at least take the guesswork out of coming up with possibilities. Not that this is the easiest way since you can pick two endpoints to multiply and then figure out what N has to be very easily, but this could reveal something about when you have the middle and need the endpoints. Maybe someone else has ideas to take it further.
The snake isn’t just an adder then!😀
Maybe it is an adder, it's just multiplying
@@michaurbanski5961 So this snake is in fact both an adder and a multiplython!
@@Imperial_Squid😃
94 minutes for me. What a gorgeous, absolutely brilliant puzzle!
Simon ruled out a 3 in the circle in the top right corner but I think it was possible at that point for there to only be 3 3's on the snake.
I thought so too initially but that point there was a 3 in row 8, row 7, box 4 and box 6. So already four 3s on the line, just a bit hard to see :)
The 123 triple in row 7 ruled that out, as the only way for there to be only three 3s is if the snake was made up of a 126 triple in both box 7 and 9.
This one was wild!!! And my wife and I watch together and we love the longer videos -- I know some people prefer the shorter ones, but count us in for the longos! 🎉
I finished in 134 minutes. I was a little late to discovering the break-in involving multiplying the total number of boxes by the minimum number the region could be. It took me until 54 minutes to see that, despite it being obvious. Luckily, all my logic I thought before that helped me zoom along. I made a mistake in the bottom left line and put two 6's on the ends and when I completed the puzzle, I was shocked to not get my tick. I realized that I forgot to count the 6's in that total, causing me to have to rewind quite a while. Luckily, again, I was able to use my previous logic. I enjoyed this one, especially drawing the snake and figuring out the contents. Great Puzzle!
hahahaha. I loved the inner dialog between the nice and naughty parts of your brain. Actually made me laugh out loud!!
I enjoyed that as well! 😄
yes, me too.
@1:09, after finding the 6789 quad in column 9, you show that 6 can only go in column 9 in box 6. That would eliminate it from the region sum line in column 8, giving you a 7, which eliminates the 2 on that line in box 3, forcing orange in box 9 to be a 2. (Now I feel like the guy who opens the pickle jar after the Rock has loosened it).
At around 1:02:00 I think the easiest next step is to ask if a 2 can be on the product line in box 5. The maximum product would be 2*8 = 16 and then the minimum sum would be 2+8+4+5=19. So (4,4) can't be a 2 and has to be a 3.
Yes, R4C9 cell was essential to block 2*7=14=7+4+2+1
Not sure where your 8 in the 19 sum has come from. Not at that stage of the puzzle. Which no doubt means I'm missing something.
@@jimmyporter8941 8 in (3,2) maximizes the product, if you try 7 you get product of 14 sum of 18 and the lower the number the worse the difference becomes.
Yeah I was screaming that 😂
Internally suffering after the 4 pencil mark in box 4
what a FUN puzzle! loved the solve
48:52 finish. Was able to pick up on the snake logic right away, but I missed a couple of obvious bits of sudoku near the end. An outstanding puzzle, so much fun!
That is a brilliant puzzle with some delightful deductions - I think may favourite was the circle. Starts off looking very open-ended so its something of a revelation to find how constrained is the snake.
Solved it with much help from the video.
42:28 the circled digit cannot be a '3' for the extremely simple reason that the circled digit itself would be the 4th '3'. But of course Simon found a much more complicated explanation.
I think you may have made a mistake here as there isn’t a 4th ‘3’ on the snake. Simon’s reasoning is in fact correct and necessary to the solve.
72:30 with two looks at the video. I needed help to see how the 1 had to be in the top of Box 6 and that there was a 2 or 3 on the blue line in Box 3. I got the initial snake line really quickly, so I thought the rest would go smoothly. It didn't.
I did both this and yesterdays puzzle tonight. Both pretty darn challenging, thankfully I did ok with an hour and a half on this and on the other I'm not sure since I left it open while dealing with other stuff but under two hours I think. Both were great.
I loved solving this! It was a real test of everything learned so far + some new things. PS. I solved the leftmost brown lines in the opposite order.
Longer video the better!
So now we have
• Simon,
• his good brain (in good and bad mode) and
•his bad brain.
This is getting out of hand
1:16:47 the 8 doing a little bit of work. It did more, it determined the 8 in box 3.
I have now gone to "parallel solving", where I start out doing the solve myself, and when I get horribly stuck, I watch Simon's video for some ideas. This works quite well, I have been able to solve some of these wil relatively little "help". Here I spotted the form of the snake quite quickly, because there is a much faster way to work out that there should be two one-digit single 9s at the end of it (if there is one that is 9, all the boxes are 9, and presto, we know the two ends).
Apparently Simon's naughty part of his brain thinks of completely different things than mine
@59:30 Simon just went mildly insane ;)
Great rule set!
I actually got the puzzle immediately then started to see how Simon solved it and he took way more time to realize the snakes each end will be 9
You could've calculated double 9 at the beginning just by using math
68:30 for me. Loved the mathematical break in
Simons brain with its good part and naughty part seems to be more difficult than the sudoku itself😂😂😂
I used a spreadsheet to try to narrow things down so it was cool to see it wasn't actually needed.
we can confirm the snake was a cobra as the title said and specfy the species because of the one only eye (circle) back on her neck. Beautiful monocled cobra.
I personally liked the idea of doing the puzzle on "dark mode". Perhaps worth trying some time.
55:15 I don't think I've encountered product lines before but I suspect if they catch on this kind of thing is probably going to a recurring theme, using the fact that the product of two sudoku digits tend to grow faster than their sum to constrain the ends by blowing up the middles
I found that the endpoints had to both be 9s by just arguing like this: "the product must be 9 * X since there are 9 regions of X. X must be at least 6, since it has to have 3 cells. product is possibly 54,63,72,81. To have X be anything less than 9, it would then be broken in a region into X+Y. then 9*x would have to equal 9*(X+Y) since each region sums to X+Y. So Y must be 0 and the product is 81". I messed up the snake connection in region 7 though, and then got lost. Great puzzle!
I don't have time to watch long videos. But I do, cos I love watching you beavering away.
Phisomefel such a genius
now that you mention it, have you ever seen them in the same room together?
At a certain point I pulled out wolfram alpha to give me integer solutions to a messy equation. It was then that I realized that product lines are not for me yet!
Yeah definitely good instincts to avoid solving over the dark grey cell color, any very dark shading makes it very hard to read pencil marks on smaller screens or at lower quality settings
I'd even suggest the green was a little on the dark side. A nice light pastel colour makes reading the pencil marks so much easier.
These puzzles need to be immortalized somehow. Maybe somebody with salon quality hair can make TH-cam videos about them...! LOL
nice you read my comment about using dark blue with blue digits
Wow, that's masterpiece.
@13:45 If the snake takes four squares in any box then it sums to a minimum of 90.
SmallantxCTC crossover was not on the bingo card but honestly it should have been. Love you both!!!
Love your vids!
Just thought i’d give another proof as to why the snake must have 9s at both ends.
As you said early in the video, the snake’s sum must be a multiple of 9 (as snake_sum=sum_of_regions=9*region_sum which is multiple of 9).
Now you take into account that ends_product=snake_sum=9*region_sum to get that the product of ends must be a multiple of 9.
Suppose, for contradiction, that 9 does not exist on either end. Then biggest the sum of snake that has a factor of 9 is 36 (from 6*6), meaning that there is a 6 on both ends and that sum of each region is 36/9=4 in contradiction to 6 being on snake.
Therefore, at least one 9 exists on snake and therefore the sums’s region is at least 9. As there are at least 9 regions, the sum of all regions is at least 9*9=81. But it is also at most 81 as 9*9 is max possible.
Therefore, both ends contain a 9.
i think you missed (at least for a long time) that the snake needs a multiple of 9 because it sums 9 of on number. there are only a few ways to get a multiple of 9, which is 3*3,3*6,X*9, 6*6.
if it has one *9 in it, that means the sum of that grid is at least 9, which means the it is 9*9, and so the start and end cell are the only cell in this box
6*6 isn't possible, as the sum of each box would be 4, do that 4*9 is 36, ehich is lower than the 6 at the end
Great video
Wow, SmallAnt watches CTC? Thats really something I didn't expected
You could've find out about double 9 in snake ends in the begining of the solve. It's sum is divisible by 9, so either one of its ends is 9, or they are from 3 and 6. Clearly 3*3 and 3*6 are definetely too small, 6*6=36 means each box sums to 4, but that's impossible as one of the ends is 6. So we know that one of the ends is 9, that means that region sum of the snake can't be less than 9 so it is equal to 9 and 9 boxes of sum 9 is 9*9 that are the ends of the snake. Regardless any other clues.
@1:21:38 Simon concludes we need to put a 123 on the snake in row 7, but I don't understand how he concluded this.... Then @44:25 Simon concludes that there are only 4 places to put a four. He wound up choosing the correct boxes, but at this point in the solve, I was still not able to rule out a 4 on the snake in box 7 column 3. Can anyone explain how he ruled it out of row 7 so early?
Well, I'm proud of myself building snake pretty fast. It took me just 25 minutes.
The rest of the puzzle, though... Total time is almost 2 hours, and that's with the clues from Simon, cause I just could not see all of those intersecting dependencies, and just didn't have much more time to look for them.
Even though, it's not for the reasons you mght think, that puzzle is really hard!!
16:00 I'm loving this sudoku induced psychoanalysis 😂
By the region sum rule, the sum of digits on the snake is a multiple of 9; so either the head or the tail of the snake must be a nine. Then the sum in each region must be at least 9. But 9 is also the maximum possible digit in the other end of the snake; so *both* ends are single digit nines, and the strings of digits in each of the intermediate boxes sum to 9 (meaning, there can only be 3 of them). R3C2 and R2C7 are the only possible squares for the head and tail, and most of the rest of the cells on the snake are fixed.
Had worked that out first... was thinking whatever the region sum was one end of the snake and and 9 the other
"so either the head or the tail of the snake must be a nine."
not exactly, you could have had (6 ; 6) or (3 ; 6) or (3 ; 3) as tail and head to get a multiple of 9
@@thefallenarm589 One more step to rule those out. If you have two sixes, then the snake's overall sum is 36, meaning it sums to 4 in each box, so you can't have a 6 on it. Similar logic rules out the others.
@@steve470yep, it's a simple step, but an important one for getting an accurate solve.
Why do the intemidary boxes sum to 9 and not atleast 9? If the head and tail both take 2 boxes in there respective boxes couldn't we get 10 for example if it is 1 9, with 9 being the tail/head
If one of the ends absolutely has to be 9 because of the region sum on 9 boxes, doesn't the region sum automatically have a lower limit of 9?
This is a great puzzle.
And what a clean solve too - as usual Simon (who sometimes thinks he takes "too long" to spot things) finds a way through with extraordinarily crisp logic: true, there was a point at which 6 in column 9 would have saved time. I have solved this twice, and both times less efficiently. Any time I gained was through not having to explain the logic and (first time round) realising that the snake and the circles would have to do the early work right from the start.
Simon is a really good expositor of the puzzle logic, and his intuition for weaknesses is well tuned: this solve gets a high rating from me.
BTW once 9 is a factor of the snake sum, you have to have either 6x6 (which is easily disproved, as you can nowhere have a run of four cells from 123) or 9x9, because as soon as you have one 9 on the line, the region sum has to be 9 to accommodate that - and that was what saved me early time.
I didn't even finish watching your video yesterday, if was to mind splitting for me to understand.
Well done brain!
40:56 for me today. had to write down some numbers could not keep them in head.
"so my good brain was being a bit naughty" hahaha
OMG Smallant. I love this crossover
Not so hard but not easy for me! I could make it with a lot of help... thank you! 😀
I wasn't expecting to hear the name SmallAnt clicking on a Cracking the Cryptic video!! I've loved both channels for quite a while now so it's funny to see the two know of each other lol, makes me wonder what a CtC Pokemon video might look like, or SmallAnt speedrunning sudoku somehow 😂
Draws the snake almost spot on as an example.
Instantly hits the nail on the limits of the snake. With it being something you can divide by 9, but also cannot be more then 10.
Proceeds to not instantly get that the snake can only have 1 block at the start and end.
Enjoyed it, once you get started, very addictive.
Thank you
I did the puzzle, but gave up „for a filthy reason. Good grieve!“ 😅
i love small ant. It was cool to find out that he watches your videos. I also really enjoy your sudoku videos and let’s get cracking :)
Cool puzzle. 99:30. Spent way too long with my eyes glazing over that last rule about the snake.
I'm quite tired of snakes... and regions...
Same
I could tell from the title it was going to be an IcyFruit puzzle.
I really like how you can arrive at the conclusion that the two edges of the snake are 9. Simon came to that conclusion by seeing the 7th and 8th row. While i thought about the fact that due to the snake being a region sum the snake would add to 9 * x, where x is the sum of each region. so one of the two edges needs to be a 9 cause if you don't have a 9 at either end then the other combinations that could work for the result to be divisible by 9 would be either 3*6 or 3*3 or 6*6 all 3 option not possible. (how i came to the conclusion that those are all the available combinations you can think about prime factors)
Taking into account that one of the edges is 9, and x being the sum of each region, how can x be less than 9 as in which ever end of the snake the 9 is placed, that region is already summing to 9 so x has to be 9 and cant be greater than 9. and that results in the snake summing to 9 * 9.
Ah the age old battle between good and naughty. Kind Comment.
Your naughty brain was puttimg in work
at 32:10, why couldnt there be a 4 5 in box 3?
The snake also acts as a product-sum line, so the end digits have to multiply together to give the sum along the snake. The equal sums nature of the line tells us it sums to 9 boxes x 9 = 81, so the end digits have to be 9 and 9.
@@RichSmith77 i forgot about the product part ty
I'm dumb. For some reason I was thinking of the snake as a loop and I couldn't see any possible way that a loop could enter every box without touching itself orthogonally.
and the snake may not touch itself- XD
Simons way of proving the snake ends are 9 is so complicated when instead you KNOW that the max row/column cell count on the snake in row 9 has to be 6 or fewer cells otherwise you force a number greater than 6 into one of the cells on the snake, this makes the region sum more than 9 in one of the boxes 7,8,9 which it cant be. So you know the path it takes in box 7 as there cant be a 7th cell in row 8 and you know the region sum is 9 without any complicated deduction because theres a 6 somewhere and that region has to be 126.