A Bizarre Sudoku Set-Up - Numberphile

Featuring Mark Goodliffe from Cracking the Cryptic. See brilliant.org/numberphile for Brilliant and 20% off their premium service & 30-day trial (episode sponsor). More links & stuff in full description below ↓↓↓
Cracking the Cryptic (featuring Mark and his off-sider Simon): / crackingthecryptic
See Simon crack this puzzle at: • We'd Not Seen This Sud...
More from CtC on Numberphile: • Cracking the Cryptic o...
James Grime talks about Sudoku on Numberphile: • 17 and Sudoku Clues - ...
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[@MegaMisch]

Holy, Mark on Numberphile?! Two of my favourite channels doing a cross over. This is awesome!

[@TheNethIafin]

Simon was also here

[@MajinBlayze]

What is this, a crossover episode?

[@wyattstevens8574]

Simon was in another video!

[@Tehom1]

And shortly after Simon's Numberphile, CTC did a Numberphile-themed puzzle. So it's a true two-way crossover.

[@Systox25]

Simon’s video is only 2 months old? I could swear it was about 2 years old. Probably because I watched a lot from them about 3 years ago.

[@MrForbinator]

I can't believe Mark just blurts out the secret so casually!

[@AkshayKumarX]

Time to take the dear leader out, with regret.

[@JPKocher]

Well, it's not THE secret.

[@williamnathanael412]

​@@JPKochershush, we gotta keep the non-favorites in the dark. A little misdirection will go a long way.

[@TommiHimberg]

Surely Numberphile viewers are among everyone's favourite people?

[@derekjc777]

Shocking! Being on Numberphile has obviously gone to his head!

[@CatzHoek]

I have not solved a single Sudoku in my live but since Simon was on the channel i am addicted to watching Simon and Mark solve them.

[@martysears]

You’re one of us now 🤓

[@guillermojperea6355]

Wait what how??

[@TheCollapsedPsi]

That's how it starts. Then you'll solve alongside them. Then you'll solve it yourself after they break it in. Then you'll be doing them on your own.

[@stevefrandsen7897]

If you want to try New York and LA Times newspapers have a new one each day online. I can only do the Easy version but you can ask for hints, check the cell or the whole puzzle and it shows you your errors. Give it a try if you like but Sudoku can be addictive. At least you are using your brain.

[@Pulsar77]

@@TheCollapsedPsiThen you try constructing sudokus yourself. And then you start coding your own sudoku app (yes, I'm at that stage. Help!)

[@Fallub]

Inreally hope many people find these Sudokus interesting and discover all the wonder the CrackingTheCryptic channel has to offer. Thanks for the collaboration.

[@davidgillies620]

It's hard to think of a simple but non-trivial operation in mathematics that has more applications than modular arithmetic.

[@steve470]

For one, it certainly makes dealing with time easier. If it's November, and something is 5 months away, what month will that be? November = 11 11 + 5 = 16 16 = 4 mod 12 4 = April That can be done really quickly with practice. (Having practiced a lot, my internal monologue would go "November; 11 to 4; April", faster than I can speak.) And similar techniques work for adding and subtracting times within a day, using mod 12, 24, or 60, as appropriate.

[@fatsquirrel75]

I'd say logs are exponentially more common. 🫢

[@stevefrandsen7897]

I've been watching Numberphile for 10 years. It renewed my love of numbers and Math, made me think clearer, I've learned about concepts I never heard of like Benford's Law, Mandelbrot Set and Pascals Triangle, introduced me to some brilliant and fun instructors like James, Holly, Matt, Tony, Hannah, Simon and many others. I have done Sudoku for about 2 years and am much better than then, recognizing patterns and applying rules but I'm no expert. I have set up exactly 1 Sudoku in my life, the easiest one you can imagine. When I saw this vid and the 2 Sudoku vids 2 months ago I realize how far I am behind the Sudoku curve. Oh well. I'm not competing with anybody else, just having some fun and applying some thinking, math and logic skills. Thanks Brady!

[@Pulsar77]

I started watching Cracking The Cryptic two years ago, and my sudoku skills have gone from basic to the point where I can do nearly every puzzle on the channel (albeit much slower than Simon and Mark). If you enjoy sudoku, I highly recommend following their channel, and you'll be amazed how fast your skills will improve. And the stuff that constructors are able to come up with these days is just incredible. A few days ago Simon posted a video called "This Sudoku Has The Most Terrifying Rating!". It's two hours long, I won't tell you how long it took me to solve it (but I did!), and it's just stunning.

[@JohnDoe-ti2np]

Solving a puzzle is absolutely an actual application! It's an activity that some people want to do, and all that any "application" is, ultimately, is something that helps someone do something they want to do.

[@davejacob5208]

yes, but that is not what we usually mean when we ask about applications of scientific knowledge. we usually mean something that contributes more to human life than yet another version of some type of game.

[@k0pstl939]

So games dont provide benefits to life?​@@davejacob5208

[@Gakulon]

​@@davejacob5208To be fair, leisure and enjoyment are absolutely vital aspects of the human life. We do have a lot of different games at this point, yeah, but without them I think we'd be much worse off

[@SwordQuake2]

@@davejacob5208 buzzkill

[@davejacob5208]

@@Gakuloni never claimed the opposite.

[@longwaytotipperary]

Yay, Mark!!!! I’m a super fan of Cracking the Cryptic! I’ve learned so much watching Mark and Simon solve puzzles!

[@TheGreatSpanishBaldwin]

Completing the set! I love it! (So glad you’ve teamed up with Mark and Simon, love both these channels!)

[@nestoreleuteriopaivabendo5415]

Simon, Mark... Who's next? Mostafa? Brem Ster? The anticipation will kill me!

[@kpaasial]

Maybe Zetamath, he has is own YT channel with math and sudoku puzzles.

[@matthewgiallourakis7645]

Imagine if they had phistomefel on 😂

[@dikkedorus]

Loving the cross-over. More of this please!

[@mikew6644]

Finally! This was teased in Simon’s video 2 months ago, I’ve been waiting for it to drop!

[@Mujaki]

I had seen the video of Simon explaining the Phistomephel Ring a while back, and there were clips of Mark in the outro. Finally, after the long wait, we get his video in full!

[@aka_Iron]

Was a really fun Sudoku to solve! Thank you for that!

[@nitinunnava6388]

Let's goo!! Was waiting for Marks turn!

[@GeekRedux]

Glad to see Mark getting some Numberphile screen time also!

[@nestoreleuteriopaivabendo5415]

Wait a minute! Where is the link to the puzzle?

[@victorribera5796]

You can go to the video os Simon solving it, they always put the links to the sudokus they solve there

[@CatzHoek]

in the description

[@SeanKennedy]

4:40 - 😮 We count on modulo numbers quite a bit in computer science! 😂

[@wilsonli5642]

Modulo mathematics are also called "clock arithmetics" - quite literally named after an application!

[@rocker223rock]

It took me an hour but I got it! Probably the funnest Sudoku I've ever done, thank you.

[@jarnorajala]

Of course modular arithmetic has practical uses, outside of solving Sudokus. For example, it forms the basis for finite fields, which are used, among other things, in encryption. Another extremely common use of modular arithmetic is in pseudo random number generators.

[@CloudMountainJuror]

Great little video!

[@ScottBroughton-ql3mi]

Solved it in a few hours. Very satisfying.

[@azrobbins01]

I hope you do more from Mark and Simon!

[@bigsarge2085]

Fascinating!

[@ZeroTroubles]

'you may never have realized modulo numbers have an actual application' Programmers: 👀

[@colemanhansen206]

It's Pencil Mark!

[@fleeb]

Quite a bit of software uses modulo to ensure something happens every x number of times in a loop. It absolutely has a practical application outside of puzzles.

[@lynk5902]

Love the crossover!!

[@sHillChannel]

I use modulo to match columns and column headers across multiple rows (when the row has a a multiple entries per column) in computer programs.

[@gibbbon]

i just unsubscribed from cracking the cryptic cause the puzzles were too much for my little brain, and now you make me think about sudoku again, curses!

[@mimialreadyexists8903]

Love this kinda stuff, can’t wait to watch this

[@chadwickhjones]

Modulus is very useful in gis to generalize mapping data at higher or lower scales

[@smylesg]

4:50 ... if this is an actual application. Brady stole my line!

[@Scanlaid]

Yessss, saw some sneaky Mark footage in the last one, was wondering if there'd be a part 2!

[@thatoneginger]

More cracking plz 💗

[@awebmate]

Finally! I have been waiting for this one,

[@douglasrogers3918]

You will note that both Simon and Mark's Numberphile videos are shot in the same room and the same table. So this may be proof that they actual meet each other! Also guessing both videos were made on the same day.

[@azpcox]

Mark flexing his solves by doing them with a sharpie. #SharpieMark

[@IgnDolphin]

I love this

[@blockshift758]

Didn't expect cross over today

[@eu4um]

Oh hey it's Mark from CrackingTheCryptic!

[@johngranahan6102]

Mark! Numberphile! Yes!

[@greggassen5548]

The sound effects from this video really remind me of the old Gamboy game Mario Tennis Power Tour

[@FetchTheCow]

Given the lines & diagonals shown in the Sudoku square, can the same rules be additively overlaid on the square when rotated 90°, 180°, and 270°? Edited for clarity.

[@stephenbeck7222]

Yes, why wouldn’t they?

[@FetchTheCow]

If the rules shown are overlaid on the square in 0°, 90°, 180°, and 270° orientations, there are many more opportunities to calculate unknown values. I don't see any obvious conflicts, but these properties of Sudokus are fairly complex.

[@BryanLu0]

​@@FetchTheCowIf you rotate the grid 90 degrees, it has the same solution but rotated 90 degrees

[@ChadTanker]

Crossovers are nice! But let's hope we don't get another "ParkerSquare" situation. xD

[@GenericAnimeBoy]

Modular arithmetic comes up in cryptography, and I'd argue that's infrastructure on a similar level to building a bridge. Maybe more Computerphile territory, though.

[@MaxximillionPerrin]

Where is the link? I’ve looked everywhere for the video

[@DarklordZagarna]

It's Mark!!

[@monnishs9775]

Well RSA is a pretty good application of modulo concepts.

[@guanche011]

I would have liked some more info on why 1-4-7 should be the case. I'm missing something.

[@ScottBroughton-ql3mi]

The total of the diagonal of 4 numbers is given as 25. Three of those numbers are consecutive (any order) so they make up a multiple of 3. If the number where the 25 arrow points equals 1, the remaining 3 digits will add to 24, a multiple of 3 (7, 8, 9). In the same way, if the number is 4, the remaining 3 digits will add to 21 (6, 7, 8). And if the number is 7, the digits will add to 18 (5, 6, 7). This lets you eliminate 1-4 from those 3 consecutive digits.

[@RichSmith77]

Modulo arithmetic has the property that (A+B) mod 3 = (A mod 3) + (B mod 3). The four cells that sum to 25, along the little killer diagonal, can be written as a+b+c+d=25, with 'a' being the digit off the line (r4c1) and b,c,d the three digits on the purple ('renban') line. We therefore know (a+b+c+d) mod 3 is the same as 25 mod 3 = 1 mod 3. Also, (a+b+c+d) mod 3 = a mod 3 + (b+c+d) mod 3. Since b,c,d are three consecutive digits, b+c+d = (x-1)+x+(x+1)=3x (in some order), where x is the middle digit. In other words, (b+c+d) is divisible by 3 and so (b+c+d) mod 3 = 0. Putting all those together gives, a mod 3 = (a+b+c+d) mod 3 - (b+c+d) mod 3 = 25 mod 3 - (b+c+d) mod 3 = 1 mod 3 - 0 mod 3 = (1 - 0) mod 3 = 1 mod 3 Therefore 'a' is 1, 4 or 7.

[@walkingwriter4325]

Another great Numberphile/CTC crossover episode. More please!

[@hoazl.]

Ohh, finally the second part of the crossover! This sudoku was a great choice - I never thought that 3-cell renbans must contain one of each mod 3 numbers! And I really enjoyed the animations on this one as well, fantastic video all around

[@TiagoMorbusSa]

OMG it's Mark!!!!!

[@intrepidmixedmedia7939]

Don't worry Brady, it's a Parker application

[@nathanmays7926]

Two my favorite channels

[@gavinriley5232]

Matt! That secret was meant for only very special friends!!!

[@HamsterFurtif]

I'd love to see how these puzzles are built!

[@iang4662]

There are some videos on Cracking The Cryptic where the constructors describe the process of setting their puzzles

[@Pulsar77]

If you're wondering what software people use, most puzzles are constructed on the website F-Puzzles and posted on Logic Masters Deutschland.

[@SwordQuake2]

"featuring Mark and his off-sider Simon" How did you come up with this... Simon gets way more views.

[@stephenbeck7222]

Same was said but in reverse in the first numberphile with Simon

[@EighteenCharacters]

Sudoku puzzle with no givens and an exact-cover solution... What will they think of next. **waits for Donald Knuth to think of the next thing**

[@JohnSmith-zq9mo]

Suggestion: show how solving a sudoku can be formulated as solving a system of equations.

[@jlivewell]

That was quite fascinating.

[@robertolson7304]

If i could only win the lottery doing that. That means there is a preset value. A complete number. A number that never changes. That number is the mean median mode and range. If i had a value of 3. There would be location, value and function. To have a area of 9x9 you would need Dot, line, area, quad, etc to have function. In this case fuction is a combination of line, area. So its multilayer perceptron. Location is many sets..

[@sulimanalzanki9546]

First time he didn’t crack the cryptic😅

[@loqkLoqkson]

oh, hi mark!

[@arlentuba6446]

1:23 explains the concept of Killer Clues and Renban lines 2:11 explains the math behind the Killer Clues 3:22 explains how to solve the puzzle using the Modulo concept 4:14 talks about the creator of the puzzle Mr Menace 4:22 mentions Simon solving the puzzle on the channel 5:22 talks about Brilliant the sponsor and the courses they offer

[@JamieDenAdel]

Thanks, but are people that short on time that they have to skip around?

[@arlentuba6446]

@@JamieDenAdel 😂 just if someone wants to

[@palfly1864]

Important distinction, they're "Little Killer" clues, Killer is an entirely different thing

[@arlentuba6446]

@@palfly1864 😂

[@BryanLu0]

​@@arlentuba6446Killer refers to cages with given totals

[@tehkokhoe]

Modulos are important in cryptography!

[@litigioussociety4249]

I understood almost nothing about how that works, but I feel stupid for not realizing any odd number of positive, consecutive numbers is equal to the middle number times the amount of consecutive numbers. It's so obviously after he said it.

[@steve470]

Also, any even number of positive, consecutive integers is equal to the "middle number" (halfway between the two actual middle numbers) times the count of consecutive numbers.

[@DiamondzFinder_]

Very interesting!

[@invisibledave]

Something doesn't make sense. He said 2 of the cells have to be 3,6,9 but they could also be 2,5,8 or 1,4,7 depending on the side unless the rules of Sudoku are different in this puzzle.

[@WeirdMole]

The common digit of those two diagonals is what restricts them. It creates a situation where those two side digits would either be 0mod3, or they must be simultaneously 1mod3 AND 2mod3 - which is impossible.

[@flikkie72]

3:22 I could follow everything up to this point pretty easily, but what he says here sounds like it doesn't really make sense

[@RichSmith77]

I don't know if this helps, but if we use some variables, we can write the little killer clues from the bottom of the grid as, 15 = A + L1 + B, and 27 = A + L2 + C where, A is the digit common to both diagonal lines in the bottom row (r9c5), L1 and L2 are the respective sums along the diagonal purple 'renban' lines, B and C are the two ends in row 5. If we convert these to mod 3, we get 0 = (A mod 3) + 0 + (B mod 3) 0 = (A mod 3) + 0 + (C mod 3) Combine these, and we get, B mod 3 = C mod 3 In other words, the two digits at either end of row 5 come from the same modulo 3 set, either {147}, {258} or {369}.

[@Trias805]

What is this? A crossover episode? ;)

[@linforcer]

It's weird to see Mark from this angle lol.

[@graduator14]

The meaning of life is 45!

[@LogansVHSChannel]

a very interesting setup indeed. i’m very interested in mathematical conundrums like this.

[@Awkwerp]

Had to do a double take which channel I was on lol

[@kumarsohail]

sudoku final boss.

[@palfly1864]

oh believe me, this is nowhere near the final boss

[@alanclarke4646]

​@@palfly1864certainly isn't, there's SET, German Whisper lines, Equal Sum lines, Nabner lines...

[@xxgn]

If you want a modulo-based final boss, I'd say that Gliperal's Rosette is a candidate.

[@DJejbarros]

that is how you do a crossover... take notes Marvel and DC

[@xyz.ijk.]

"Renban" lines ... that's new!

[@JohnADoe-pg1qk]

In recent years, several types of Sudoku lines have been invented. For example, matching the "Renban" lines, so-called "Nabner" lines later appeared, the digits of which cannot be consecutive.

[@xyz.ijk.]

@@JohnADoe-pg1qk I appreciate this. I was thinking this was an old mathematical concept (not that I think I’ve heard all of them ) and I couldn’t dope out the spelling from the video or the transcript. Took a few tries to find it.

[@JohnADoe-pg1qk]

@@xyz.ijk. "Renban" is a type of Japanese logic puzzle, or at least a term therein. And for "Nabner" someone (probably not Japanese 😁) reversed the word and the meaning.

[@My-Say]

I was once told by someone fairly intelligent that programming code could be used to solve a Sudoku puzzle fast enough to prove P=NP in computer science, and this can somehow lead to the cures for cancers. Since I was diagnosed with cancer several years ago, this has become a topic of interest. I've been a programmer all my life and have developed a solver that works pretty fast, but I am curious just how fast it would need to solve them. It is an enjoyable experiment to be quite honest because it is challenging. Various clues such as in these videos can potentially be very helpful in contests to make the fastest solver. Is there such a contest? I feel there should be.

[@xxgn]

To my knowledge there are no contests for making the fastest sudoku solver. However, there's a $1,000,000 prize for proving P=NP. Creating a "fast enough" Sudoku solver would constitute a constructive proof that P=NP. Specifically, this means creating a sudoku solver that can solve puzzles of any size without relying on bifurcation. This is not as simple as finding better heuristics. By definition, heuristics don't completely work. Every time we abandon heuristics in favor of bifurcation, our solving performance is cut in half. Supposing we found powerful enough heuristics to make our solvers 1,000 times faster, that improvement would instantly vanish as soon as we needed 10 more levels of bifurcation (i.e., because we were working with slightly larger puzzles).

[@kespeth2]

2:48 not to mention that duplicate nubmers in the entire column, row or square violates the soduku rules in general. I presume those are still in effect in this version, too?

[@stephenbeck7222]

Yes regular sudoku still applies in this particular puzzle. Generally with renban lines, you can’t repeat digits on the line even if by sudoku you may have been able to do so. So the diagonal renban lines that go across boxes must have 3 different digits on them - that’s the whole concept which makes the modular arithmetic ‘break in’ of the puzzle work.

[@mav3818]

Test it

[@PULLABHATLAMEDHA]

can you make a video on ramanujan's near misses to fermats last theorem for n=3

[@TheCosmicGuy0111]

Nice

[@ultralightjay7793]

🖤

[@TsarHare]

dmt am that purple color. cool. i do love Bella Hadid

[@petrospaulos7736]

You want an actual application of modular numbers? Just ask someone the time...

[@pierreabbat6157]

What is that word? "Renvan"?

[@Pulsar77]

Renban. It's a Japanese word that means 'consecutive number'.

[@iteerrex8166]

You gotta be nutz about sudoku to go to these levels. Su.kudos 😁👍

[@palfly1864]

This is only the start of the rabbit hole :p

[@iteerrex8166]

@@palfly1864 I’m still a noob so even this looks advanced.

[@tiarkrezar]

@@iteerrex8166 If you're interested about these kind of sudoku variants with extra rules, go to their channel (cracking the cryptic), and look for shorter videos (

[@Tfin]

@@iteerrex8166 When you go to the CtC KZbin channel (linked in the description), look for the videos with "gas" in the title, uploaded roughly weekly by Mark. These are the easiest (genuinely approachable sudoku) puzzles on the channel, and can often serve as introductions to various... variants. Mark generally solves these in 3 to 12 minutes, doing several in each of the videos. The links to the puzzles are always there in their descriptions, so you can try them yourself, or follow along with the video and try to see what Mark is doing before he does it.

[@cheeseburgermonkey7104]

Interesting I was watching one of his videos earlier...

[@martysears]

Cool video Mark 😊 I don’t remember seeing this puzzle but it’s a very cool break-in

[@leandrogulrt]

The face of the person trying to solve the puzzle is the same as the puzzle itself. 😑

[@jwolfe01234]

Didn't expect to see Mark in a new video this early in the morning (in the USA).

[@justsignmeup911]

Modular arithmetic is used all the time in cryptography.

[@verydryrifle]

why do numberphile videos look like they're shot by Lars Von Trier?

[@xxMrPHDxx]

4:10 Harry Potter? 😮

[@JohnADoe-pg1qk]

👍🤣

[@Cuuniyevo]

I may be missing something here, but I think the example Sudoku given is impossible. The Bottom Row, Center Column (BR-CC) that is at the focus of the diagonals labeled "27" and "15" cannot be a 1,2,3,4,5,6,7,8, or 9 without causing a conflict. Be warned of a large wall'o'text. I tried to be succinct. Can't be a 1 because: Center Row-Far Right Column (CR-FRC) must be one of 3,4,6,7 and none of those add up to a multiple of 3 when 1 is added to them. Can't be a 2 because: Center Row-Far Left Column (CR-FLC) must be one of 2,3,5,6,8 and none of those add up to a multiple of 3 when 2 is added to them. Can't be a 3 because: If CR-FLC were a 3, the squares immediately above and below must be 4,2, and either option interferes with the diagonal between Far Left and BR-CC being the 2,3,4. If instead of using the 2,3,4 diagonal, you used 1,2,3, the CR-FLC would have to be a 6 and the square immediately above must be a 7. The CR-FRC must then be a 3, and the square immediately above that must be a 2. Because there are 2x sequences of numbers between them on that row, and only 1 "wild" square, you cannot account for the 1,8,9 in that row. Can't be a 4 because: CR-FRC must be one of 3,4,6,7 and none of those add up to a multiple of 3 when 4 is added to them. Can't be a 5 because: CR-FLC cannot be 4. Can't be a 6 because: CR-FRC cannot be a 3 or 6 at the same time BR-CC is 6, and CR-FRC also cannot be a 9. Can't be a 7 because: CR-FRC must be one of 3,4,6,7 and none of those add up to a multiple of 3 when 7 is added to them. Can't be an 8 because: CR-FLC cannot be a 1. Can't be a 9 because: The diagonal line to the CR-FLC would equal greater than 15.

[@Pulsar77]

You must have made a mistake somewhere. The solution video (by Simon) to the puzzle is linked in the description, have a look at it.

[@Cuuniyevo]

@@Pulsar77 Ah, I see where the disconnect is. When Mark in this video said the numbers on one of those lines had to be consecutive, I understood it to mean that they had to be, for example, 4,5,6 or 6,5,4 (crossword rules) and that they could NOT be 4,6,5 or 5,4,6, etc. That completely changes the conditions of the puzzle. Edit: Yes, looking back and watching again, he does mention that they may be in any order, so this misunderstanding's all on me.

[@RJSRdg]

"not necessarily in the right order...." ;-)

[@miff227]

the 33 downvoters need to go in the corner

[@dhruvchitroda]

First