Some peak Simon there near the end, when he _finally_ decided he could delete his test examples and random colors, and unconcernedly left behind a single blue square to drive us all mad. 😂
@stangerrits6712
4 ай бұрын
Once the 1-9 cycles where found, you can use the modularity principle that Simon often explains in the 1-5-9 indexing puzzles: in row 1 you need a low, middle and high digit in each box, to make sure you won’t get the same digit twice within a box.
@Sidnv
4 ай бұрын
Not quite low-middle-high, it's more powerful than that. 5 and 7 can't be in the same box in row 1 for instance, anything in the same box has to be separated by at least 3. So you end up forced with 147, 258, 369 in the same box as the only possible arrangement of digits, as otherwise some number would be within 3 of something else in the same box.
@HunterJE
4 ай бұрын
Indeed, by the action of the rules and clues this *is* a 159 puzzle, though rotated 90º from the usual orientation
@Zerotan
4 ай бұрын
@@Sidnv mod 3 go brrr
@AREmrys
4 ай бұрын
@@HunterJE It's even more than that. Every line is an indexing line.
@AaronSmith-i8y
4 ай бұрын
Every cell is an indexing cell for its column.
@emilywilliams3237
4 ай бұрын
I never, ever, ever get any puzzle faster than either you or Mark, Simon. But this one just tripped in my mind and I had it done in 3 minutes. I actually started with thinking about where the 1 would have to be, and then the 2, and recognized something that made me think about the sum of 165, and then a tiny moment gave me modular sets, and then it was simply finished. Very, very fun. I feel as if I can explain it logically, but I could not have done so while solving it because my brain was simply seeing what had to happen. It is so interesting how different people's minds work. Thanks for the wide variety of puzzles featured here on CtC.
@UnaturalShadows
4 ай бұрын
well he does have to explain himself as he does it
@pouletbelette
4 ай бұрын
Congratulations Emily! That's quite impressive.
@psymar
4 ай бұрын
Basically: once you figure out what the 9 ?s have to be (without consideration for their order), The top row has 1..9. The 2 must have a 1 directly below it, the 3 must then have a 2, the 4 must then have a 3, and so on up to the 9 having an 8, leaving only the possibility of 9 under the 1. Similar logic gives you how all 9 columns go and now it's just a matter of what order they go in.
@emilywilliams3237
4 ай бұрын
@@pouletbelette It was an epiphany. And quite fun. But I still enjoyed watching Simon solve it and explain in words what my brain, today, in this one isolated instance, just saw had to be true.
@emilywilliams3237
4 ай бұрын
@@UnaturalShadows Right! Which is why he has a sudoku-solving channel and I don't!
@Darkstar2342
4 ай бұрын
16:34 he basically did the correct reasoning befire to show that the 13 cage cannot be 8-5... so it is 9-4. so if the 4 was in the left cell of the cage, it would have a 5 above it which would clash with the 5 in the center green strip. So the 4 is in the right cell
@emanuelfer456
4 ай бұрын
I was shouting that for 3 minutes while Simon just looked at 9 instead of looking at 4
@spatulamahn
4 ай бұрын
Came here for this comment! LOL - Simon saying that we need to look at the 11-cage when the 13-cage was giving him the answer already! :)
@In_42_Space
4 ай бұрын
Surely Simon this has to be one of your favourite puzzles as you were not really forced into doing any actual sudoku 😂😂.
@BryanSarlo
4 ай бұрын
Reminds me of a sudoku featured on here about a year ago on which the rules were along the lines of 9 invisible vertical thermos whose bulbs are in row 9. Similar solves in this one and that one from last year, but both are great and this comment is not meant to take anything away from this puzzle!
@damadclown
4 ай бұрын
3:40. First time I managed to get a decent time compared to other viewers. It helped that this puzzle reminded me of another one with a similar "structure" and everything fell in place from there
@jurgnobs1308
4 ай бұрын
yea there was a similar logic one a few days ago, right? where it would also end up with the numbers being in order
@MattYDdraig
4 ай бұрын
Sum of the first n triangular numbers is the nth tetrahedral number: n(n+1)(n+2)/6
@markfinnicum8340
4 ай бұрын
Fun Fact for Parties: nth tetrahedral number is a 3rd degree polynomial because the summation of a polynomial function results in another polynomial function with one higher degree. The nth triangular number is a 2nd degree polynomial: n(n+1)/2. And obviously, the nth natural number is a 1st degree polynomial: n
@andy-kg5fb
4 ай бұрын
Another fun fact for parties, summation of tetrahedron numbers is n(n+1)(n+2)(n+3)/24 and the pattern repeats!!
@Anne_Mahoney
4 ай бұрын
@@andy-kg5fb I want to get invited to your kind of parties! 😺
@HunterJE
4 ай бұрын
Fun coincidence, friends of the channel Numberphile released a video about tetrahedral numbers today!
@MattYDdraig
4 ай бұрын
Thanks for that!! Fun bonus coincidence: The current year 2024 is a tetrahedral number. The most recent previous year this was true in was 1771, and the next will be 2300, so revel in our current tetrahedral glory! (For typical western calendars, of course)
@derekpangelinan4229
3 ай бұрын
The blue square!! The most uncomfortable moment in any CTC video ever!!
@vandelay33
4 ай бұрын
4:21 for me. Definitely the fastest ive ever done a CtC puzzle but very fun nonetheless
@ilyrm89
4 ай бұрын
So happy Simon finally removed the blue highlight at 19:19, thank you!
@HunterJE
4 ай бұрын
Simon started looking at the disambiguating cages on the right then changed course to look at the left first instead, but it's also possible to solve the right first on its own-stepping off from the deduction that the 13 cage must be a 49 pair you can then see that it breaks if you put the 9 in r8c7; it would have an 8 below it, which would need a 1 in r9c8 to finish the 9 cage, BUT the 9 r8c7 puts another 1 in r7c7 which clashes in the box. Therefore the 9 has to be in r8c6 and things flow from there.
@willemm9356
4 ай бұрын
Even simpler, if it's 49, the 4 would have a 5 above it which clashes in the box.
@IguitarVreakI
4 ай бұрын
Haha, I looked at the 4 instead and realized that it would have a 5 above it and you'd have two 5's in Box 8
@AaronSmith-i8y
4 ай бұрын
I worked out that the 6 in box 8 was flanked by 3 and 9. Try putting a 3 into a two cell 13 cage.
@goldenera7090
4 ай бұрын
wow congratulations to Simon and Mark almost reaching 600k subscribers... I remember how this channel started so well done on your journey
@chipsounder4633
4 ай бұрын
Vertical and horizontal drive entropic roping ❤ yet another masterpiece... Oops , i always mix up entropy with modularity.. but the roping still holds true 🎉🎉
@ironalice9452
4 ай бұрын
Beautiful logic! As always a joy watching you ponder and solve as well as listening to your explanations! I don't really solve Sudokus nor am I good at math. But seeing you solve these manages to relax me every time and tingle just the right parts or the brain. 😊
@davidenas
4 ай бұрын
After you conclude how to fill in an entire column from just a single digit and doing it for column 5, you can actually conclude that columns 4 and 6 must start with 1 and 7 in some order to not break box 2. And only one of those orders avoids breaking a cage, so you fill those in. Then the cages solve the rest of the puzzle, that part is the same.
@Turalize12
4 ай бұрын
Exactly what I did!
@vanguard2960
4 ай бұрын
Never get a puzzle done faster than you guys, but this one just worked for me and I noticed the pattern + that the 3 numbers in the same row in a given box had to be 3 apart. Very fun puzzle!
@Ravenishish
4 ай бұрын
The formula of the sum of triangular numbers is (n(n+1)(n+2))/6 and you're right, you can take multiple copies of them and make a cube.
@Pathogenus
4 ай бұрын
now thats a proper miracle sudoku unlike the previous one with long ruleset and tricky steps to do along the way
@Kirbyfan87827
4 ай бұрын
Finished in 21:00 with extensive help from the video.
@spin-rg9ib
4 ай бұрын
i had to revert to the puzzle i figured out that the sums were a minimum but couldnt think of how to go from there. i knew there was going to be a 147, 258, 269 combo in the top row and that they would go in descending order but got stuck on where to go from there. then i checked the video and just needed the detail that the bottom of the grid will also follow suite with the order after the x sums.
@Vanziethel
4 ай бұрын
This one filled itself in very nicely! It took me a few minutes to figure out the logic, but it was quite satisfying when I did! Thank you Leonhard!
@Alex6STV
4 ай бұрын
At first, I thought there is no way I was going to be able to solve this. Once I wrote the numbers 1-9 in the first row (just to get an idea how the columns might build themselves out) and figured out that 165 was a minimum value, I was quickly able to see sequential pattern when I worked out where the 1 would be in the 2 column, where would the 2 and 1 be in the 3 column, etc.... Awesome puzzle. Loved it.
@darreljones8645
4 ай бұрын
Finding the maximum possible X-sums total in a row of a finished sudoku is complicated by the fact that X must be present in an X-digit X-sum (i.e., the maximum possible 2-digit total isn't 9+8=17, but 2+9-11), but still, it's not hard to figure it out: 1 + 11 + 20 + 28 + 35 + 39 + 42 + 44 + 45 = 265.
@frankjiang1857
4 ай бұрын
Finished in 7:09. Fairly straightforward sudoku where if you know the trick it solves itself. Fun puzzle!
@SirJefferE
4 ай бұрын
I didn't want to bother thinking about the individual triangle numbers, so I just considered them as a group. If we're minimizing X-sums then: 9 sums must include a 1. 8 sums include a 2. (All but the 1 clue) 7 sums include a 3. (All but the 1 and 2 clues) So the x-sum minimum is the sum of this pattern: 9x1, 8x2, 7x3, 6x4, 5x5, 4x6, 3x7, 2x8, 1x9 The pattern is a palindrome, so I just summed the first four (9 + 18 + 21 + 24 = 70), then doubled it and added 25 for the 5x5 in the middle. Honestly, this approach probably isn't all that different to figuring out the triangle numbers, but it seemed a lot easier to do in my head.
@Xiuhtec
4 ай бұрын
Finished this in about 7 minutes, much of which was "typing" in the values on a phone. Figured out the patterns pretty quickly after a minute or so realizing 165 was just the minimum possible total. Very cool setting!
@katiekawaii
4 ай бұрын
18:07! I don't know how long I would have been starting at the puzzle if I hadn't gotten Simon's suggestion to consider if the sum clue was minimized or maximized, but once I figured that out (with a calculator, not impressively in my head like Simon 😅) I was able to do the whole thing in 18:07. Pretty proud of that one. Doubt I could have done that a few months ago. Thanks for making my puzzle brain sharper, Simon!
@jillyapple1
4 ай бұрын
I spent a couple minute confirming 165 was the sum of triangular sums of 1 through 9, then realized that meant roping descending from the X. The 7 gave me my first column, then my first box, and the cages gave me the rest. 5:49.
@rickwoods5274
4 ай бұрын
I solved this almost entirely in a notepad. Wrote out my logic up to the point where I knew the pattern each column must conform to. Spent an *embarrassingly* long time looking at the grid before realizing the given 7 determines a whole column, then wrote that in. Then worked out the possibilities for the cages, figured out there was only 1, and wrote the remaining 72 digits directly into the grid
@kurtu5
4 ай бұрын
The total number of gifts on the 12 days of Christmas is the "Tetrahedral" number for 12. You are stacking cannon balls in a tetrahedron and the geometric proof is copying the tetrahedron, stacking them so you get a rhombus(skewed box) and then calculating the side lengths.
@davidhughes7174
4 ай бұрын
The first columns comedy! thank you.
@brianarsuaga5008
4 ай бұрын
Proud of my performance here! I spotted the 165 constraint immediately, then fooled around to prove the low-middle-high snookering from 1-5-9 puzzles, then figured out the descent. Really fun how it just completely falls apart after that, I've never filled so many squares back to back!
@AngelWedge
4 ай бұрын
4:20 for me; about half of which was double-checking my arithmetic before starting :p
@HunterJE
4 ай бұрын
Weird thing to notice: This setup results in a secret 1-5-9 puzzle, though rotated 90º from how those are usually presented - the "slot machine" arrangement results in every digit in row 1 indexing the position of the 1 in its column, every digit in row 5 indexing the position of the 5, and every digit in row 9 indexing the 9
@attker89
4 ай бұрын
I think that pattern extends to every row and every digit. Row 2 indexes all the twos, row 3 indexes all the threes, etc. Very interesting properties in this puzzle.
@jack_2612
4 ай бұрын
nice spot, I didn't notice
@chrishaynes7425
4 ай бұрын
Very satisfying. Cracked it by working out the min and max x-values (in Excel!)
@Caladryus
4 ай бұрын
11:03 My reasoning after getting the centre column was slightly different than the reasoning Simon had. I recognised the cycling nature of the columns, meaning that columns 4, 5 and 6 would, in each box, have the numbers 4-3-2, 1-9-8, 7-6-5 in those orders in their boxes. This would, in box 8, put a 3 or a 9 in the cages. Since a 3 cannot be in the 13 cage, that one has a 9 in box 8 and the 11 cage gets a 3 in box 8, and after that it solves itself by using the cycle and remaining cages
@emptyset1312
4 ай бұрын
Very neat puzzle. I was able to work out that everywhere throughout the puzzle, digits must ascend in order upwards, e.g. if you place a 3, it must have a 4 above it. Once I knew that fact, it was quick and easy to fill everything in starting from the given 7 and then the cages. Very very satisfying.
@martinepstein9826
4 ай бұрын
The sum of the first n numbers, AKA the n'th triangular number, can be found on Pascal's triangle. On the left side of the triangle the n'th triangular number is down and to the right from n itself. The sum of the first n triangular numbers, AKA the n'th tetrahedral number, can also be found on Pascal's triangle. On the left side of the triangle the n'th tetrahedral number is down and to the right from the n'th triangular number.
@geezerama
4 ай бұрын
Good grief! Somewhere between 8:15 and 9:10 I was overcome with a very personal nostalgia whack. That's how I felt many years ago, in another far younger life, within the confines of my mind most of the time. Always trying to draw it all together to make the old model conform to the new. Sorry if I texted that out loud. Great puzzle, thanks to setter and CTC.
@HolyChez
4 ай бұрын
9:09 time for me. Once I figured out that 1-9 cycles must be in the same descending order from the top-down, I immediately can fill in from the 7 and the rest just falls in place through the sums.
@jdyerjdyer
4 ай бұрын
Took a minute to work out what I suspected that the 165 sum meant, and sure enough, it meant it. Then I had all the digits in their strips and from there it was just placing which column each strip went into so as to not break the cages or the bottom boxes. Fast and fun "magic"! Amazing!
@jdyerjdyer
4 ай бұрын
Hint: 45 + 45 - 9 = 81, pretty high sum already just from row 1 and the column with all 9 digits. So I asked how much was left from the 165 and started subtracting the minimums. 165-45-36-28-21-15-10-6-3-1 and found out that there was nothing left. This meant that wherever the x-sums were, they took the minimum digits leaving the higher digits to sit outside the x-sums in the bottom rows. So you get a 9 in the last cell for the 8 x-sum, an 89 pair for the 7 x-sum, but the order is forced by the 8 x-sum...all the way until you end up with the 9 x-sum just counting down to 1 at the bottom. From there, each strip gets the remaining digits filled in such that they count down as well to meet the 9 in each column. From there, you can just place the 7 strip by the given 7, there is only one strip that will work next to that column with the 13 cage. Then it continues just matching which strip is forced by a cage sum or the remaining digits in the lower three boxes. Done!
@Eckbert1410
4 ай бұрын
Nearly got a stroke staring at the lonely remaining blue-colored cell 🤯
@vandelay33
4 ай бұрын
*spoiler* For others who were curious like me, the sum of triangular numbers are called tetrahedral numbers and thr formula is n(n+1)(n+2)/6
@Sidnv
4 ай бұрын
There's a pretty simple inductive combinatorial proof for this, if you're interested. Let me show you the proof for the triangular and tetrahedral numbers and the induction upward is pretty straightforward. The core idea is that the triangular numbers are also equal to the number of ways to pick out 2 objects from a collection of n+1 objects. n+1 choose 2 is n(n+1)/2. The way to see this is: arrange the objects in a line, and focus on the first object you pick (first as in first left to right). If you pick the one in position 1, you have n remaining choices for the second one. If you pick the one in position 2, you can no longer pick the one in position 1, so you have n-1 choices. If you pick the third, you have n-2 choices. As you add all these up, you see you get exactly the triangular number for n. To get the tetrahedral number for n, repeat this idea, but now pick 3 objects from a pool of n+2 objects (n+2 choose 3 is n(n+1)(n+2)/6). Again, focus on the first you pick left to right. If it's in position 1, you have 2 objects to pick from n+1, which is n+1 choose 2, which is T(n), the triangular number for n. If it's in position 2, you pick 2 remaining objects from n, which is T(n-1). This continues, and you end up summing up the triangular numbers. The is already in inductive form, which shows that the k'th iteration on summing up these numbers will be (n+k) choose k+1.
@olivier2553
4 ай бұрын
To me it is 1+3+6+10+15+21+28+36+45 because after watching Simon for over a year I ended up knowing the triangular numbers :)
@JalebJay
4 ай бұрын
An easy way to find it is using Pascal's triangle. Notably the diagonal right below the diagonal for triangular numbers, or the 3rd.
@katiekawaii
4 ай бұрын
@@SidnvI love CtC viewers. Only here will someone comment "here's a proof for the formula for triangular and tetrahedral numbers you might be interested in" _and be right._ (I was! I was interested! Thanks!) 😄
@seanb7807
4 ай бұрын
Solved in 8:15, first time I've solved faster than Simon. Can't say my solution was the cleanest, but I noticed 165 was pretty small relative to the total sum of 405, and 240 was a lot to cram into 36 digits since 45 digits would have to be in the X-sum per the secret, so I figured the only way it could solve was if the 9 was left out of the 8, the 8 and 9 out of the 7, and so on. Did the math and confirmed it which made the rest just a matter of setting the orders. Fun puzzle!
@compiling
4 ай бұрын
6:10. I tried just filling in the numbers ignoring boxes and cages to see how the columns work, then once I saw the specific sequences are forced the rest of the puzzle was easy. There are only 2 values that can go next to the 4, which the 13 cage disambiguates. The formula you were looking for is 11C3. I remembered that the sum of consecutive triangular numbers is the 4th diagonal of Pascal's Triangle.
@colemanjamie1
4 ай бұрын
Very fun quick puzzle, 11:33 for, this is my very first time getting a Simon puzzle faster than his video time!!
@MarushiaDark316
4 ай бұрын
Puzzles like this make me wonder how fast Simon could solve if he didn't have to explain things.
@RoderickEtheria
4 ай бұрын
6:39. The largest part of this puzzle was checking whether all the triangular numbers summed properly.
@Michael-hs7pr
4 ай бұрын
2:44 for me. Just had to check that the sum of triangular numbers is 165 and immediately knew it was a roping puzzle. Rest is just filling in the digits.
@trainzack
4 ай бұрын
I generally take about 3 times as long to solve these, so I'm super proud of my 11:48. It's the first Sudoku I've ever solved where I figured out what all of the columns were before I placed any of the digits. I only had to figure out which order they went in!
@penningmeestercgkdelft9159
4 ай бұрын
Solved it in 9:14. :-) A true miracle sudoku indeed, and it fills itself in immediately as soon as you see the trick!
@PathOfShrines
4 ай бұрын
Haha, very clever idea. Immediately saw the top half of the induction, then figured out the bottom half a few minutes later. Finally convinced myself the starts had to be not just in separate high/middle/low per box but actually modularly related, and then it was done. 13:46
@shortfatboy
4 ай бұрын
Many has pointed out the formula for the sum of the first n triangular numbers aka n-th tetrahedral number. Perhaps, here is a quick way to rederive it. Essentially, the n-th triangular number is a binomial coefficient with lower entry two and the n-th tetrahedral number is a binomial coefficient with lower entry three. To see why this is true, visualize the pascal triangle and recall how the entries are generated (details are grossly omitted). This explains the lower entry of the binomial coefficients and with some more work, you can figure out the top entry of the binomial coefficient.
@psiphiorg
3 ай бұрын
I spotted the trick immediately, and was able to solve it in 1 minute, 43 seconds! 165 is a tetrahedral number, specifically the sum of the first 9 triangular numbers (1+3+6+10+15+21+28+36+45). Therefore, the X-Sum with a 1 in its first digit is free to have any numbers below it, the 2 must have a 1 below it, and the 3 must have a 2 and 1 below it. The key deduction here is that the 3 must therefore have a 2 directly below it, and a 1 directly below that. This sequence continues such that the 9 column must be 987654321. Now, working your way back down the numbers, the 8 column must start 87654321, which leave only 9 for the final digit. Then the 7 must have 8 and 9 below it, in descending order, and so on. So that means that each column is 987654321, just rotated through one way or the other. Figuring out which side is which in the fourth and sixth columns is solved with the 13 cage, since the cell in it in box 8 would be either a 3 or a 9. The 3 isn't possible there, so it's the 9, and the 3 goes into the 11 cage instead. Solving the cages shows the next columns over, and the cages in row 9 go out one more. Then there are only two columns left, the first and the ninth, which just get the remaining three digits from their boxes in descending order. I was solver number 9844.
@deadlybee111
4 ай бұрын
the sum of Triangular numbers are tetrahedral numbers and you can get them just like triangular numbers with pascals triangle, its the "diagonal" right underneath triangular numbers exactly the same as triangular numbers are in relation to natural numbers
@AugustoValentini
4 ай бұрын
9:15 to solve the puzzle itself, I did the 165 sum while taking a shower so the timer wasn't on yet 😅 A simple and fun mathematical puzzle, just the kind of sudoku I love
@10prozenthimmel
4 ай бұрын
This very strongly reminded me of amother puzzle that Simon solved maybe a year ago or so. It had the same rotational symmetry. Probably just had a different break-in but resulted in the same pattern or a permutation of it.
@Paolo_De_Leva
4 ай бұрын
I can remember a very similar but more interesting puzzle in which the *1-9* cyclical sequences were horizontal, rather than vertical as in this case, and the ruleset was slightly more interesting. I believe it was published in one of the volumes of *CTC Greatest Hits.*
@eve_the_eevee_rh
4 ай бұрын
4:24 woah. A miracle!
@Michaelzehr
3 ай бұрын
Beautiful!
@daniellucas5522
4 ай бұрын
4:59 for me - and about half of that was finding that 165 is the minimum.
@richardfarrer5616
4 ай бұрын
n(n+1)(n+2)/6 is the tetrahedral formula (sum of triangular numbers). And 9x10x11/6 = 165.
@Gonzalo_Garcia_
4 ай бұрын
3:25 for me. I think I remember a very similar puzzle being featured not that long ago.
@charliemichael4052
4 ай бұрын
The sum of the first n triangular numbers are called the tetrahedral numbers named after the 3 dimensional equivalent of a triangle for future reference
@LarkyLuna
4 ай бұрын
A proof of sum of triangular numbers for those mathematically inclined, using the formulas for the sum of n numbers and the sum of n squares My trick was realizing that 1 will appear in all n triangular numbers, 2 in n-1 of them (will miss the first), etc, until we get to the nth triangular number where n will appear there and only there, so we get: 1*(n- 0) + 2*(n-1) + 3*(n-2) + ... + n*( n - (n - 1)) = expanding the multiplications: n*(1 + 2 + 3 + ... + n) - (1*2 + 2*3 + ... + (n-1)*n) = expanding the negative part as 2 = 1+1, 3 = 2+1, 4 = 3 + 1, ..., n = n-1 + 1 then multiplying n*n(n+1)/2 - (1² + 2² + ... + (n-1)²) - (1 + 2 + 3 + 4 + 5 + ... + n-1) = square formulas and sums again n*n(n+1)/2 - (n-1)(n)(2n-1)/6 - (n-1)(n)/2 = n(n+1)(n+2)/6 wah, good math warm-up
@Kinada
4 ай бұрын
Yeah, the puzzle literally just filled itself in. It's interesting that the starting digits follow mod3 to keep the lines separated.
@grahamania
4 ай бұрын
00:06:55 for me. While not complicated, it was a very fun puzzle to think through the math vs sudoku issues involved! Kind comment.
@EdDrow
4 ай бұрын
The 7 indicates that the middle column is a 4 which means column 4 and 6 is either 1 or 7 what you can find out with the 13cage and from then on the cages only give you the start of the next cycle.
@abubakr9796
4 ай бұрын
One day, the rules are going to be "Just fill in the numbers and make sure it resembles a sudoku"
@DennisR219
4 ай бұрын
I actually regrets having seen this video. This is such an approachable puzzle, I feel I could have solved it, yet didn't test myself on it hehe. Anyway, fun as always to have Simon solve it for us!
@mhelvens
4 ай бұрын
I did this one in 13:47. Can't complain!
@redstonekid2222
4 ай бұрын
Got it in around 15 minutes. Very fun puzzle, quite similar to the "121" puzzle featured before.
@squallerrleon
4 ай бұрын
Got this pretty quick, just under 6 minutes! I suppose it would take much longer if I had to stop and explain what I was doing logically
@przemekmajewski1
4 ай бұрын
13 minutes and done, rather easy
@Rach881101
4 ай бұрын
16:45 for me. Beautiful puzzle!
@alanscott8245
4 ай бұрын
9:33 for me. This was a fun one.
@josephdlist
4 ай бұрын
20 minutes? What am I supposed to do for the next hour?
@titusadduxas
4 ай бұрын
13:33 - Yay! One of the few occasions I’ve beaten Simon.
@janeflett4971
4 ай бұрын
Cool puzzle!
@KennethBouman
4 ай бұрын
9:33 with a break in the middle to help the toddler wipe her bum 😂 Delightful puzzle!
@ibrahimylgor7365
4 ай бұрын
Around 40mins. I got the idea of 165 very quickly because we need another constraint to solve. However, i had to think about the 1 to 9 and 9 to 1 rule
@_-_-Sipita-_-_
4 ай бұрын
4:45 for me. yup
@dmdeemer
4 ай бұрын
I would have done that much faster if I hadn't messed up the math of triangular sums, I was thinking the minimum X-sum was 160, and that would have been a much harder puzzle.
@57thorns
4 ай бұрын
Too me a total of 8 minutes and 41 seconds, really fun little find.
@gibbbon
4 ай бұрын
finished in half your time! i rock! i quickly calculated that the minimum sum of all the clues on top was 165, and quickly figured out the 3 groups of 3 strips of numbers from top to bottom, then used the clues at the bottom to line them up, and done! easy, time of 9:03
@LucaSalemi
4 ай бұрын
Cojectured a possible solution in the first minute, and found it in 7:12. Minute 16 to do a proper reasoning rather than noticing the solution.
@darthrainbows
4 ай бұрын
It took a minute to figure out the logic in this one, but then the rest of the solve was just filling out digits.
@vborja3877
4 ай бұрын
I wish I knew how to do this😢I don’t understand. You guys are too smart for me. I love sudoku but I just put the numbers in the regular way😢😊
@olivier2553
4 ай бұрын
The opening was easy (sort of, I had to quickly confirm the hunch) but applying with not making mistake was more difficult, I had to count and recount the cells every time. 22:43 should have been faster.
@six_5000
4 ай бұрын
could that title be screaming at me any louder? 22:15
@veggiet2009
4 ай бұрын
I don't get why the cycles are mandatory, because the x-sum clues simply divide each column into two sections, the first section summing to X and the second to 45-x, saying nothing of the ordering of the digits within each section.
@jonathansperry7974
4 ай бұрын
Surely we will see a puzzle titled “265” soon. Should I be surprised that maximizing the x-sums is exactly 100 more?
@victorfinberg8595
4 ай бұрын
i remember this one, and i remember thinking "simon will get a giggle out of this one"
@victorfinberg8595
4 ай бұрын
the way i did this was technically quite different from what simon did. i started entirely on paper. 1) an x-sum of one cell is 1. an x-sum of 9 cells is 45. then, by playing with the numbers, i very quickly realized that all the x-sums had to be MINIMUM for the string length. 2) now i made a 9x9 blank grid and started filling in the possibilities randomly. a) place a 1 anywhere in the top row. b) next, place a 2 anywhere in the top row, with a 1 below it, which restricts the box. c) continue with 3-2-1 and keep going. you see a pattern develop 3) in the final phase, fill in the columns from the "test" grid as appropriate into the final puzzle.
@nemoyatpeace
4 ай бұрын
Real quick solve once I realized that the 7 defined the column, and in general any single digit defines the full column. 7:42
@anaayoung9142
4 ай бұрын
The great thing was: I knew how the puzzle was going to look like! The bad thing was: I didn't know how to start the solve 😅
@adipy8912
4 ай бұрын
Funny enough you are talking about adding triangle numbers together and one day after Numberphile uploaded a video about tetrahedral numbers
@roccov3614
4 ай бұрын
The fastest one I've done and the first time I didn't use any pencil markings
@BinarySecond
4 ай бұрын
Why do they have to be in those cycles? I did not understand why column 5 had to be the 4. Can't the digits just be in any order?
@steve470
4 ай бұрын
One column has a 1 in the top row. Another will have a 2 in the top row, and to keep the sum of sums down to 165, that column must have a 1 in the second row. Another column will have a 3 in the top row, which needs a 1 and a 2 immediately below it. By sudoku, the 1 can only go in the third row, so the 2 must go in the second row. Similar logic shows that, starting from the top row, every column descends sequentially from its topmost digit down to 1. Now, look at it from the other side. Whichever column has an 8 in its top row, must not be counting the 9 in its sum to keep the sum of sums down to 165, so the 9 must be in the bottom row. (By the earlier logic, this puts 9 directly below that column's 1.) Whichever column has a 7 its top row, must not be counting the 8 or 9. By sudoku, the 9 can only go in the second-to-bottom row (directly below *that* column's 1), and the 8 must go in the bottom row. Continuing this logic, every column must descend sequentially from its topmost digit down to 1, then have a 9 below it, and continue sequentially downward from there.
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