No Calculator Is Required...

[@JamNCheez]

Simon, seeing you solve my puzzle and gush so heavily has absolutely made my year. Though it may have felt like madness, the route you took was indeed the intended solve. You took a slightly harder route though, missing the shortcut on row 7 that other have mentioned, (as well as the pun in the title).Thanks so much for the feature!

[@tonymanngreenwich]

Lovely puzzle - thanks very much! Sorry to be stupid but what is the pun in the title?

[@JamNCheez]

@@tonymanngreenwich not stupid at all. A gross is an old fashioned term for a dozen dozen or 144. The title was intended as a subtle 'check' that you were correct (gross misconduct) but it wasn't required to solve

[@tonymanngreenwich]

Thanks @JamNCheez! I get the pun now. It's a great puzzle - one of very few when my time was quite a lot faster than Simon's (though if I had been explaining number theory out loud as I did it, it would have taken me a lot longer). Looking forward to your next puzzle!

[@nathanmays7926]

Why did you name it Misconduct?

[@paulwatson746]

Great puzzle thanks! and I beat Simons time, that has made my day

[@pardox28]

This is the only time I've ever truly understood the whole concept of prime factors as atoms of numbers when it came to multiplication. I don't know how Simon was able to get me to see/visualize it, but solving this puzzle was way easier once I broke things down in "I need four atoms of 2s, I need two atoms of 3s when I make 144."

[@annek3296]

I think that possibly the ancient Greeks' appreciation of prime numbers as basic building blocks for numbers might have led them to contemplate the notion of matter having basic building blocks, i.e. atoms.

[@annek3296]

I loved Simon's realization that the important approach was to balance out the occurence of the prime factors 2 and 3 - the actual product of the entries on the line was not important. BTW, JamNCheez irritated me by using the word "total" instead of "product". The SUM of numbers ADDED together is the TOTAL; when you MULTIPLY numbers together you get the PRODUCT.

[@CrackingTheCryptic]

Thank you for this comment. It means a lot to me. Simon

[@pardox28]

@@CrackingTheCryptic you're welcome, Simon. Have a great day!

[@RichSmith77]

​@@annek3296You can always view a multiplication as just a repeated addition. 4 x 5 is the same as 5+5+5+5 after all, and that has a total of 20. I think a multiplication can still be said to have a total.

[@chrismcdonald6195]

I'm actually in awe of Simon, I really am! I have no idea, NO IDEA, how you can look at the rules of this puzzle, look at the lines and go "oh yeah, there's no 5s or 7s on the lines...."! Like, how? I'm gobsmacked!

[@francoisduez601]

I haven't seen the video yet, but that is how I broke in as well... Not sure it is possible to do otherwise 🤔

[@sillvvasensei]

The thought about looking at prime factors (1,2,3,5,7) is the key. Combined with the 3 lines in boxes 3 and 6.

[@francoisduez601]

Either that or counting all the lines, there are 11 so it is not possible to have a 5 or a 7 on a line without putting 11 of them...

[@annek3296]

Very elegant! @@francoisduez601

[@DekarNL]

Because he's been doing sudokus every single day for decades. You get good at anything if you try hard enough.

[@All-Ireland-Mahjong]

Great to see an outing for the Fundamental Theorem of Arithmetic (every integer greater than 1 is either prime, or is the product of a unique combination of primes)

[@tmhood]

No calculator required, but an undergraduate course in number theory is helpful.

[@agitatorjr]

Everything in here is middle school math.

[@sonalita_]

it's elementary prime factorization you learn as a young teenager (in my day, for 'O' level maths)

[@pranavsetpal]

Seriously feels like number theory or something will make the logic much easier. I tried attacking this problem with combinatorics, counting the number of 2 and 3 primes are possible, all in my head and the sudoku board. It's been 80 minutes and i'm just seeing his solution now. For others who have commented, number theory is not technically required as showcased (probably), but I'm sure it would help with some of the logic as that deals with primes extensively. Prime numbers are deceptively basic (for eg. p-adic numbers, modular arithmetic with prime mod, gaussian primes)

[@agitatorjr]

@@pranavsetpal none of that is required at all and is probably overthinking the issue making it a longer solve. It's just prime factorization as the guy above said. And it's a simple deduction to make regarding 5 and 7 that doesn't require any advanced math.

[@pranavsetpal]

@@agitatorjr The 5 and 7 is basic ofc. It's the rest! I'm sure there's a "simple" way to deduce further with number theory and combinatorics I just doe't know yet

[@FirHydrntsRFirEaters]

I think the title is a play on "gross misconduct," "gross" being a synonym for 144

[@bluerizlagirl]

That was what I thought, too, as soon as I worked out what the product on each line had to be! I started out just watching Simon, but while he was colouring fives and sevens I had already started thinking 1*2*3*4*6*8*9=10360 = 2**7 * 3**4, got the secret for this puzzle, begun working out all the possible ways to fill the lines, and ended up finishing the whole puzzle myself .....

[@JamNCheez]

You're absolutely right, Have an internet gold star for being the first to mention this :D

[@Zeekfox]

Oh that's clever!

[@pouletbelette]

​@@JamNCheez Great puzzle! Please, excuse my ignorance, but can you explain the relationship between the word "gross" and the number 144? I'm a bit lost. Thank you very much!

[@tessabrisac7423]

Same here, I have no idea what you mean

[@SamThe1stOfMany]

I am deadly serious here, if there ever is a 15 hour video, I will get out the popcord, order a pizza and watch every second of it. Probably at 2x speed, but I WILL watch it. XD

[@BaldorfBreakdowns]

Puzzle: "No need for a calculator" Simon: "Let me explain prime factors, in case you're unfamiliar" Me: "I'm way to dumb for this..."

[@longwaytotipperary]

@BaldorfBreakdowns me too!!! 🙃

[@JohnRandomness105]

Come now, it's not so hard.

[@Vorash00]

I’m gonna say your not to dumb for this, but I can see how it may be daunting to someone who’s fearful of mathematics. You got this! It’s easier than some of the killer sudokus you come across. Once Simon works out what the number is he can more eloquently explain what the factors are. I like his idea of “atoms”.

[@jimdavis2683]

Upon determining the prime atoms on each line, around 32:00 in the video for Simon, I found the easiest next step was realizing that the line from r7c3 to r7c7 had to be 12346. That puts 9 in r7c1 (since it can't be on the line with a 3) and 8 in r7c9. etc.etc.

[@kajacx]

This puzzle was simply brilliant. From finding the 2 digits that cannot go on the line, then to figuring out what the product can and cannot be to finding out all the beautiful little things that give you a digit here and there. People who make these puzzles are on a whole different level.

[@danielrhymer1762]

24:08 for me! With all multiplication rules, prime factors become key and that’s how you realise there’s no 5’s or 7’s on lines as if they are on one line, they’d need to be on every line which doesn’t work as there’s 11 lines

[@matt5075]

Ohhhhh. Thank you. This explanation actually made sense to me.

[@nkorppi]

@@matt5075 Even easier is just to note that if the top right line has it, then the box below it has it outside of a full line. Then invoke uniqueness of prime factorisation. Done.

[@sonalita_]

@@matt5075 Exactly how I did it! counted the lines and realized there could be no 5s or 7s

[@SenselessUsername]

Or closer together: Boxes3+6 together already contain three lines --- they'd need three of those 5s and/or 7s to put them on any line. But now you're thinking prime factors, you immediately see that the "tail" of the line that starts in Box3 but "overhangs" into Box6 must be a 2, 6 or 8 necessarily, because (to fill up Box3) there's an odd number of powers of 2 in the set (1,2,3,4,6,8,9) --- that overhanging tail has to compensate; but the 6 is ruled out because there's an even number of powers of 3 in the available set. If you do it like this, you find the solutions in a very different order from Simon's method. If the "tail" is 2, each line is 12x12= 9x16 = 144; if it's 8 it's twice as much, 288... As someone else pointed out, the straight line in Box8 then clearly must be (1,2,3,6) plus a 4 or 8 as 9 would be too much (namely at least 360), and the bottom right line can only work if it's 144.

[@dragonx254]

This video single handedly helped me grasp prime factors better than any math class

[@maartenmarien]

The 5-cell line in row 7 deserved its own deduction too, I feel. Since 1x2x3x4x6x8x9 = 2^7 x 3^4, and the line is 2^4 x 3^2, the two outs are 2^3 x 3^2 straightaway, which can only be done as a 89 pair.

[@J7Handle]

I actually started with that one as well. Don’t know if it was the better start, though.

[@steve470]

21:14 for me. That was a really fun solve. A bit sad to not see Simon use the secret... the multiplicative secret: each row, column, and box contains seven 2s, four 3s, a 5, and a 7. I'm actually kinda surprised that the solve was still manageable without using that.

[@JamNCheez]

The working title for this puzzle was "Shh, it's 362,880" but I thought that would encourage the calculator route

[@longwaytotipperary]

But that adds to 38?.?🤔

[@mc_davit]

​@@longwaytotipperaryhe means 2^7 * 3^4 * 5 * 7( * 1 which we can left out

[@jacobhanna]

This puzzle made my day. This is just impressive to setup and solve. Iconic!!!

[@ronjohnson6916]

Loved the break in and the solve. And how much fun Simon had.

[@Zeekfox]

@48:49 Simon: "I think I'm doing this in the most mad way!" Haha, I would agree. You found out quite some time ago that the product each line must reach was 144, but didn't conclude that a straight line of 5 digits must be 1-2-3-4-6. You already knew about the 5 and 7 going in non-line cells, which would have given you that 8-9 pair in the row quite some time ago! I also find it funny that Simon doesn't think of the sets of digits on a product line the way he does for sums. I guess it's just repetition and memorization, because if I said we were looking for two digits that sum to 9, Simon would immediately list off each pair. Here, there's only one set of digits for the straight line of 5-length, two sets of digits for the straight line of 3-length, three sets of digits for a 4-length line completely contained within a box, and three more sets of digits for 4-length lines if you're able to repeat a digit. It's a very manageable amount of digit sets, and having that is super useful towards reaching conclusions on what digits are on various lines.

[@davidrattner9]

Wonderful debut! Simon, your teaching and explanations of prime numbers and atoms was a stroke of genuis!

[@zawwadmaan1472]

I love the sheer excitement you show for these beautifully crafted puzzles. Loved to see prime factors incorporated into sudoku. In awe of peoples' creativity and kudos to yours as well!

[@longwaytotipperary]

As a not very math savvy person, I enjoyed watching Simon determine how to come up with the combinations- and seeing his fish impersonation (very good! 🐟) 😜

[@davidrattner9]

I bet your fish impersonation is lovely also. 🤪

[@longwaytotipperary]

@@davidrattner9 🤪

[@laurasmith2173]

This would be a great puzzle during a prime factor math lesson or even for chemistry students and when they get stuck give them a hint of prime factors.

[@studgerbil9081]

Mark isn't being mean ... it's "Mark for the GAS and Simon for the torture". I loved this solve but it was honestly way easier for me to just do the multiplication while filling in the lines. We knew from Box 3 what the product of the lines had to be. It also made the "clean-up" and Sudoku way easier. But no one on this platform is as entertaining as Simon doing things in 24D.

[@Tahgtahv]

Usually, but not always (Just refer to yesterday where Simon had a very easy puzzle, and Mark had a much harder one.)

[@studgerbil9081]

the GAS puzzles have been getting harder too.

[@ryxiewuff]

It took all of my self control to not immediately put 7 in r9c7 upon realizing that neither 5 nor 7 could go on a line and the only possible way to differentiate them would be whether or not they could go in an X.

[@dmoc325]

That's valid puzzle logic, I think.

[@Zeekfox]

Simon mentioned in a previous video that this uses the logic of "uniqueness", which assumes the puzzle has a unique solution. He doesn't allow himself to use that logic.

[@ryxiewuff]

​@@dmoc325 It's valid logic, but it relies on knowing the fact that the puzzle has a unique solution. It's more challenging to prove that the puzzle has to have a unique solution while solving it, though. I'm definitely looking forward to the day when a puzzle shows up on this channel with "This puzzle has a unique solution" in the rules that makes you use uniqueness tricks.

[@letsmakeit110]

If you continue the logic at 27:00 to 29:00, you can say that 2 sets of the digits 1-9 contain 14 twos and 8 threes. But you need the total number of twos and threes on the lines to each be divisible by 3, otherwise they won't multiply to the same total. One of the lines will have an extra factor. So which two digits can you remove from the set 1,2,3,4,6,8,9 to have 12 twos and 6 threes so that the lines work? Those are the non-line digits in box 6.

[@nyxicsulfur]

one of the rare CtC puzzles where I didn't need to peek in the video for a hint! beautiful solve from start to finish!

[@icepyrox]

I find it interesting that you kept the prime factors straight... once you got the total, I just broke things down to it's factors in a different way. it has a square root which each have many factors, so I found it easier to shift factors between two "sides" of its square root than to think of the "atom" count. This worked further since most lines were length 4..

[@jonhansen9622]

What about an abacus??

[@anaayoung9142]

What a beautiful solve Simon! You are so smart playing with numbers like atoms, thank you for the lovely puzzle! 🤗

[@grahamrskelly6042]

I feel slightly robbed of maths education, that i didnt have this puzzle to help me understand the atoms of numbers till now.... Lovely puzzle.

[@KhanuuG]

I'll admit I stared at this puzzle for an hour just not getting it. I came back to the video and once Simon explained the factor logic, it all just fell into place. I immediately paused the video, went back to the puzzle, and after almost another hour, I finally solved it. Next time I hope to breakthrough to the puzzle without assistance!

[@Fun_maths]

What a delightful puzzle! Figuring out the 5s and 7s and everything else after was a joy as well

[@okimhin]

I think doing crazy crazy hard puzzles would be great on stream and can then be turned into a great video. Please do the really really impossible puzzles.

[@Sponsie1000]

maybe in theory, but there'd probably be a constant deluge of backseat-solvers who'd just shout answers/correct deductions throughout the whole stream

[@okimhin]

The viewers of the channel usually honors a no spoilers request, and the rest can be moderated @@Sponsie1000

[@coherentramblings7326]

After you get the 2 in box 6, there’s a weird SET trick you can use to get R5C6 and R5C7. Let’s say all the digits besides 5&7 multiplied together equal Z, the value represented by each gray line equals X, and Z divided by X equals Y... This means that in box 6, R4C8 X R5C8 X R5C9 = Y This also means that in row 5, R5C6 X R5C7 X R5C8 X R5C9 = Y You can remove R5C8 and R5C9 to make the equation R5C6 X R5C7 = R4C8. Since R4C8 is a 2, the equation only works as 2X1=2.

[@kristad8129]

You are so brilliant at explaining your thought process through your more difficult videos. I just love looking through your old videos and clicking on the longest solves, because I just know I’ll get to see you explain something amazing! And your enthusiasm is absolutely infectious. You make me love these puzzles!

[@theashen]

This was wildly beyond me, but great to watch Simon solve it and explain it so well.

[@joeg451]

A 9 has to appear on a line, so the mystery number must be a multiple of 9. An 8 has to appear on a line, so the mystery number must be a multiple of 8. Therefore the mystery number must be divisible by (9x8) = 72. That narrows the possibilities immensely.

[@FrancisFjordCupola]

I love how Simon at 20:00 in goes "I'd much rather all the digits were confined to [the top-right] box without spilling over..." but that spill is going to give at least a single digit. It really comes down to seeing 3x6=2x9 and 1x8=2x4 and those eight digits include two two's. No calculator needed.

[@jamesbrady3471]

I like your method better than mine, I looked at the prime factors, saw an odd number of 2s but an even number of 3s (which eliminated 6 on the outside cell) and concluded the outside cell was either 2 or 8 but that 8 would break the ability to fit the required number of 2 and 3 factors on a three cell line (my line of thinking mirrors Simon's but I don't have to explain myself to viewers so I got it quickly). your method flows more intuitively I think

[@frankjiang1857]

Finished in 29:51. No calculator is required as you only care about factorization for the line products. The break-in was relatively easy since the 3 lines in boxes 3 and 6 constrain what factorizations you can have (no 5 and 7 since you have 3 lines completely in 2 boxes and 5 and 7 are the only factors available which give you 5 and 7 and only 2 threes and 4 twos allowed since you only have access to 8 threes and 14 twos total in 2 boxes for 3 lines, so 3 threes per line would require 9 threes and 5 twos per line would require 15 twos) along with the line in row 7 (setting 2 threes and 4 twos per line as the minimum). Everything follows once you have the factorization down. Fun concept!

[@titusadduxas]

1:24:24 - Wow! What a great puzzle! Congratulations JamNCheez. 👏👏👏 It took me about 45 minutes to finally get my head around box 3 but once I eventually did the logic was magnificent.

[@kobe11111]

The 5-cell line in row 7 has a min value of 120, once you remove the and 5 and 7 as options, the min value changes to 144. From there you could determine that in fact it had to be 1,2,3,4,6

[@Gonzalo_Garcia_]

15:52 for me. Great puzzle, I enjoyed it a lot!!

[@reubenmckay]

More extra-long Simon solves? YES PLEASE!!!

[@kevinmartin7760]

Starting around 35:00, once the 2 was placed in box 6 and we knew the line product was 144, you can also calculate that the cells in a unit (box, row, or column) which entirely contains a line but are not on that line (and not 5 or 7) must multiply to 72. This means R5C8 and R5C9 must be 4 and 9 (the only 2 digits that multiply to 36, which, with the 2 in R4C8 gives the 72 for non-line cells). You can also get that R7C1 andR7C9 must be an 8/9 pair, again multiplying to 72. I found it natural to use this to find the choices for box 6 and that the line in box 9 contained 1/6/8 in column 9, placing 2/4/9 in R2C9 and R3C9. Testing how the right-hand line in box 1 can complete eliminated the 4 from this and things were simple from there.

[@imblackmagic1209]

it was a very beautiful puzzle, thanks for sharing!

[@davidtieman4102]

Fun Puzzle. Enjoyed it. I am sure it was the PRODUCT of a great mind.

[@bobh6728]

Simon is going change the history of mathematics by changing the word “factor” into the word “atom”. So we will soon have terms like: Prime atoms The Fundamental Theorem of Mathematics will state that every positive integer other than one has a prime atomization. Reducing fractions will involve finding the greatest common atom, GCA. Solve a polynomial equation by setting one side equal to zero and atomizing it. (Sounds quite violent!) Sorry, I have too much time on my hands!!

[@tessabrisac7423]

😂😂😂

[@Donrafa189]

Yes please!! Long videos are a treat

[@mostman]

Really elegant way to describe prime factors. I’ll be borrowing that.

[@craigfjay]

My break in, after the 5/7s, was using the 3 lines in box 3 and 6. You must fill 3 lines using 2 sets of 1-9. Adding the powers of 2 and 3 in total gets 2^14 and 3^8. To divide those into 3 lines, each line could have a maximum of 2^4 and 3^2, you can’t have more The 5-line in row 7 shows that the minimum powers of 2 and 3 are 2^4 and 3^2, you can’t have less. So therefore each line has exactly 4 powers of 2, and 2 powers of 3

[@JamNCheez]

This was how I thought of it when setting the puzzle. Dividing 2 lots of factors between 3 lines left only 144 as a viable total. Considering the leftovers - 2 5s, 2 7s, 2 2s and 2 3s forced a 49 pair off the line in box 6, and also the 2 in r4c8 could be reached similarly

[@Danielmoen88]

I'm doubting whether or not anyone is reading these comments, since I'm usually posting a few days late; if you are, I apologize if my comment is hard to understand due to my lack of refinedness as an amateur dabbling mathematician enthusiast ^^ Around 22:00, when you're thinking about box 3 and the product of the lines, and what c8r4 might mean, I figured something out. You say you can't multiply two lines together and divide them by two to get the product of a single line; true, but you can take the square root of two lines multiplied together to get the product of one single line. Sounds scary maybe, but not so much when you break it down to their factors. Since when you square root two lines multiplied together, you have to get a whole numbers of factors (arriving at just one line's product), that means that two lines multiplied together have to have an even number of the factors 2 and 3. Adding together the factors in the product of 1,2,3,4,6,8,9 you get howevermany 1s, seven 2s (one in 2, two in 4, three in 8, one in 6) and four 3s (one in 3, one in 6, two in 9). Now we know that one of the lines enters a single cell in box 6. We can deduce that this number have to include the factors of either one 2=2 or three 2s=8; c8r4 is either 2 or 8, and the product of the lines [1^n] * [3^2] * [2^4 or 2^5] (to take the square root of the multiple of both lines, we divide the number of factors by two to arrive at this). Later on, or at least I couldn't figure it out right here, we deduce which it is. edit: continued watching the video, and see Simon arrived at the same conclusion, but used box 6's line to rule out the 8 at this stage. Beautiful!

[@danielepicone1480]

This is one example of a puzzle that totally collapses immediately once you start get it going. Very fun overall.

[@xChikyx]

This is one of the hardest sudokus to follow for sure

[@emilywilliams3237]

This was very fun and so interesting - and I think, possibly, maybe, I can do this puzzle! I will give it a try very soon. Your delight and enjoyment and chortling make for a fun video, Simon - thank you!

[@longwaytotipperary]

Yes, Simon’s enthusiasm is sometimes the best part of the video (particularly when the the logic eludes you!).

[@_kyarumii_]

A simple explanation for people like me who are slow with understanding the 5/7 rule: If a line's total is divisible by 5 (like Simon's example of 100) then the total can't be reached in sudoku without using 5 and because the total of each line is the same, you would need to put a 5 on every line which you will eventually find won't work. This applies with 7 too because they're both prime numbers which can't be divided by anything smaller.

[@JudithRachelD]

I never studied prime factorisation in school so this concept was completely new to me. After seeing how 5 and 7 could not be included, I deluded myself into thinking I could take it from there, and brute-forced my way through prime theory 😪 The RUSH I felt once I cracked it!!

[@kempisthomasa7311]

sadly, I have no head for mathematics, but I will kindly say that I enjoyed Simon’s enthusiasm for the number atoms.

[@erwilleke]

First one I solved on my own after finding this channel a week ago!

[@eve_the_eevee_rh]

20:23 I'm getting better at some of these easierish math-logic puzzles! Proud of myself

[@Poet13xRatedRKO]

Solved in 26:43. I just knew 5 and 7 would not be on a line and one of them was connected with an X.

[@Zeekfox]

That uses the logic of uniqueness, which Simon disregards.

[@JohnRandomness105]

The easiest part was placing 5s and 7s. If a line had either digit, then every line had to have that digit, but there were too many lines. The rest took a heck of a lot longer than it takes to summarize. Box 3 with two lines limited the products. The product-squared required an even number of 2s and 3s, requiring the outside digit to be 2 or 8 -- giving 144 or 288 as the line product. Box 6 resolved which, as it was impossible for the line to multiply to 288 without an 8. The line was 144, with two factors of 3 and four factors of 2. 15:00 I think that I made life easier for myself by letting P and Q be 7 or 5. I placed all the Ps and Qs, and disambiguated when one landed on an X-domino. That also gave me a 3 on block 9's line. 20:30 Take the geometric mean: multiply them all out and take the square root. Require an even number of all factors in the square. 25:30 In the product of the digits in box 3 on the lines, you have seven 2s and four 3s. You need an even number of 2s total. 2 and 8 work in that outside cell. You can't include another even number of 3s in that cell. It's limited to 2 or 8.

[@AlRoderick]

144 is a gross. Gross Misconduct. JamNCheez, I love and hate you.

[@tessabrisac7423]

Thanks, I had no clue!

[@billystevenson9042]

I hate to say that the way I got the total for these lines was by looking at the title of the puzzle. "Misconduct; that's a funny name for a puzzle. The only time you usually hear that word is in the phrase Gross Misconduct. I wonder if the sum for these lines in a gross. A gross has a lot of combinations to be made using sudoku digits, it's probably that." I'm not very good at logic puzzles.

[@tessabrisac7423]

Oh, OK, thank you, I had no idea how “misconduct” could relate with 144!

[@francoisduez601]

26:15 for me. Very nice factorizing puzzle 😊

[@williamsemmer3544]

Considering I just looked up the rules of DarthParadox's puzzle on LMG and cannot even begin to think about where to start, I would love to see you tackle that puzzle!

[@Danimrich]

Enjoyable! Took me about of time to realize the thing with the 5s and 7s, but from there it was quite smooth. 58 minutes.

[@nkorppi]

Solved it easily the same way. The only difference being that I coloured in various sets which were the complement of a line in a box or row (ignoring the 5 and 7), since these all needed to multiply to 72. This offered some nice set theory equivalences. Dealing with complements of lines was at least as easy as dealing with lines.

[@maavinkayi]

Good job explaining prime factors!

[@karsaanita]

30:56 for me. It took me a while to notice box 3 but after that it was smooth sailing. This was really fun puzzle. Thanks for the treat!

[@frozenzenberry4101]

I’ve actually never had prime factors explained to me. Now I’m going to be compulsively trying to find prime factors of numbers now :p

[@averygaron994]

We like the really long solves because those are puzzles none of us would even be able to start. Personally, I don't even attempt the puzzles unless the video is

[@wuorson5111]

I love this puzzle!!! To me, I have the AHA moment when all 5s and 7s aren’t on the line, and also I worked out: 2 has a 2 in it, 4 has two 2s, 8 has three 2s, 6 has a 2 and a 3, 3has a 3 and 9 has two 3s, which then it’s a simple killer kind puzzle, after you spend some time in box 3 you’ll quickly workout that each line has four 2s and two 3s

[@nathanmays7926]

this puzzle is world class

[@PennyLapin]

solved in 31:39. this was really fun to exercise my brain's ability with arithmetic and use that not only to break into the puzzle with one of the boxes, but to spot the geometry of the cells not occupied by lines. the fact that 5 and 7 have nothing they can be matched with on each line except for themselves, and that the grid has 11 of these lines, really sends the puzzle running when you immediately place all the 5's and 7's in the grid using the fact that they're off the lines, and then open the puzzle using the equivalent product of the two lines in box 3.

[@othafakk]

The product is 144! This puzzle is 'Gross Misconduct'

[@jonh6585]

Amazing number theory, beautifully explained

[@PathOfShrines]

Really cool idea. I stalled out for a long time until I found the power constraint in the top right boxes, but still got a decent time. 42:41

[@philwheatley5057]

Very happy with this. I finished in 13:13 by starting on the straight 5-line at the bottom, as 12346 to make 144, leaving an 89 pair on the wings which disambiguates those two lines in boxes 7 & 9. It just fell out from there. Easy peasy.

[@srwapo]

31:03, I figured 5 and 7 couldn't be on the lines and wrote out the possibilities for the lines in Box 3 until I was sure you had to multiply 8 and 18 (or 2 and 4 and 6 and 3, etc). It took me way too long to take that logic to the most basic and see that our lines had to = 2*2*2*2*3*3, which made it SO much easier at the end.

[@WhoStoleMyAlias]

Pretty clear that primes would pose an issue, especially with three lines confined within two boxes. So [57] was out, leaving only powers of 2 and 3 but I still managed to get confused what power of 2 would end up being on the line and found myself needing to rewind as I locked out the required factor of 9 in at least one line. Tricky puzzle.

[@TehFilmFanatic]

I don't know if Simon notices later in the video, but the puzzle title is a hint at the total!

[@TehFilmFanatic]

This puzzle has some GROSS misconduct 😁

[@Gnarlf]

Regarding Crux. Of course we really want to see those hatd puzzles. There is a big chunk of us, that can't do these on our own. Be it, that we get stuck and need a hint or that it is completely out of our league, for now, and we simply want to ecperience the puzzle and learn from it. And these hard, but brilliant, puzzles deserve to be experienced, by as many enthusiasts as possible. They are a work of art in their own way and through your lense, we can appreciate them. So keep those coming, whenever you run into them. And regarding this puzzle. Very interesting rule set and a beautiful solve as always. I highly enjoyed it

[@fynnoldenburg8082]

I think the reason you might want to use a calculator is to calculate roots of the product from multiple parts, e.g. the two paths in the top right quadrant multiply to 2 x (1 x 2 x 3 x 4 6 x 8 x 9) which is equal to 144^2 (take the square root and get 144). So you could get the value of the path-products that way. If you have three paths take the third root, etc. - at some point you would want a calculator 😄

[@samuelcourtney2118]

"The Hardest Sudoku Of All" 2:18:38 362k views "Normal Sudoku Rules CANNOT Apply" 1:53:38 342k views "Only ONE Person Has Solved This Puzzle..." 2:13:13 273k views "The Most Incredible Sudoku Rules EVER" 2:37:44 268k views "The Odyssey" 2:34:43 172k views I think its safe to say we like the long videos 😁

[@NeilGirdhar]

27:19 for me :) (with the conflict checker/resolver)

[@bobh6728]

When you were looking at box 3, you can multiply all of them together and take the square root, which is the equivalent of adding and dividing by 2. That is similar to the geometric mean vs the arithmetic mean.

[@tessabrisac7423]

but not very comfortable if you are not familiar with square roots, and mental multiplication… certainly, we are all geniuses here, but from various tribes 😂

[@Swisswavey]

A really clever puzzle, took me 45 minutes cos i messed up some mental arithmetic more often than i like to admit (it's early and I'm only on my first coffee!), but i loved it. Very clever.

[@OlafDoschke]

42:59 That's Pencil Mark in the corner, that's Pencil Mark in the spotlight, losing his position.

[@khronosh4954]

Amazing puzzle, but was disappointed that Simon didn't call out the banding in rows 5-7. Great solve!!

[@diacor4life489]

It amazes me how someone's brain can work like that 😵

[@markp7262]

32:29 finish. I got out my calculator, just for spite. And the answer is.... 17! A very fun puzzle, well done!

[@longwaytotipperary]

Are you Sue it isn’t 🙃

[@BrentDeJong]

If cages were marked with their product written in prime factorization, killer sudoku would be way easier for me. This puzzle took me 37 minutes

[@zergrush8709]

loved this puzzle. I am very much a maths person, and for once I managed to beat you! 45:59 was my solve. You are usually faster than me though.

[@kilimanjarocruz660]

17:49 for me. This one really clicked with how my brain operates. Great puzzle.

[@michaelhoffman2011]

Think I solved it a little different to Simon, I got the 5 and 7 since they are prime factors but then i expanded everything into factors eg 1 x 2^7 x 3^4 Then figured out the minimum and maximum for the line of 3 and the line of 5. and was able to figure out the values for each line after that. (value = 2^4 x 3^2 difference = 2^3 x 3^2) Have to admit a super clever puzzle, pretty sure i solved it the hardest way, but no calculator needed. Very clever and enjoyed it a lot also took me 43 minutes

[@douglasmagowan2709]

One of the rare times I beat Simon! I took a rather different line to the solution.

[@pelahnar4]

I'm always intrigued when Simon says he has more trouble with a puzzle when he has to leave in the middle of it. Maybe it's a case of having to leave to do something else (like kids or a phone call), but I had to take a break twice while working on this puzzle - to go to the bathroom and to take a shower - and both times came back having had epiphanies about it. I think I have more difficulty considering over-arching ideas when I'm looking at the whole puzzle, so when forced to just be thinking about it, I'm more likely to realize "if there's a 5 on any of the lines, there has to be one on every line. I don't remember how many lines there are, but if there's more than 9, 5 (and 7, for that matter) can't appear on any line"

[@Xiuhtec]

Took me 70 minutes. I didn't try coloring the 57 pairs so didn't place them all and thus had a harder time proving whether the X in box 9 was 37 or 19 but even without that it becomes quickly obvious there are four 2 and two 3 prime factors per line and things like every line having either 36 or 9 and the difficulty of placing 4s comes in handy all over the grid.

[@dontdreamon9026]

22:44 for me. Nice puzzle! It came down to counting 2 and 3 factors in the digits. As I’m writing this I’m watching Simon who is doing the same thing 🙂

[@darkgrach40]

It's funny how clever I feel myself when pause video and found the idea of 7 '2' and 4 '3' and all this logic by myself. Like u make little piece of puzzle with help with idea, but it still good job

[@asherhiggins7853]

This is the first time I caught on to the solution process before Simon.