No Digits? This CAN'T work!

Try J J Olsen's amazing Thermodiamonds sudoku here: app.crackingth...
Normal sudoku rules apply, and digits either increase or stay the same along the thermometers, starting at the bulb, which is at one end of the line, to be discovered. Multiplying the digits along one marked diagonal gives the same product as multiplying the other.

[@jesseolsen7316]

Thanks for showing my puzzle! When I was practice solving, I used the center AND corner pencil marks to show the clockwise and anti-clockwise versions of the puzzle respectively. The testers also left out a rule! (at least two thermos ascend clockwise). Use these together and you can solve it without bifurcation.

[@ChrisVenus]

Ah! That's good to know! As I'm sure you saw in the comments many people were curious as to whether there was a trick missed and this would seem to be it! Great puzzle though. :)

[@wren4077]

I had complete faith in this puzzle not having to rely on bifurcation Thank you Jesse Thank you Chris for directing me here

[@LLCCB]

That is so helpful!

[@freyjarin]

This is beautiful, I appreciate the effort to do it the wrong just to explain that there is only one solution.

[@darreljones8645]

The product of the diagonals in the correct solution is 1,360,800.

[@Ardalambdion]

You know exactly where to put those digits? 2x2x2x2x2x3x3x3x3x5x5x7

[@oliverbouris5293]

honestly, I think it would be a better puzzle with a bulb on the outermost thermo since the two versions are just tedium for the sake of it. Edit* The creator has commented that there was a missing rule that solves this issue.

[@Anomaly92]

Yeah. Would have been an awesome design with that little addition.

[@SirCumference31]

Unless there’s a clever way to know where the bulb is that Mark didn’t spot?

[@awilliams1701]

agreed

[@James-rq9qb]

Sudoku is tedium for the sake of it

[@Caroline-oh8lq]

See Jesse Olsen's comment! The testers left out a rule that would have removed this possibility.

[@SapioTV]

I love how the title is "This CAN'T work!" and yet the video is not even forty minutes long...!

[@andrewgrant6516]

How many no digit sudokus have you guys done now? It's reminding me of my final year maths degree when the presence of something as plebian as a number was for lesser students.

[@PleegWat]

Note you can save your game state by right-clicking your browser tab and picking 'duplicate tab'. Name might vary between browsers.

[@sdrawkcab190]

Feed back for the new software. Please make the reset button look significantly different than the undo button? Or at least move the confirmation button elsewhere. I went to spam undo as I was going to undo a chain and double clicked too quickly to realize I was hitting the wrong button. Lost a whole bunch of progress and that's just super demotivating.

[@Raattis]

And make reset undoable? :)

[@chibinecco1981]

I did this myself the other day. Just really frustrating.

[@MitchellD249]

I did the exact same thing with this very puzzle right after making my first big breakthrough in a long time, that was an awful moment.

[@yaqxs]

Implementing a restore point option into the software would be a good idea for a puzzle like this, I think.

[@tremkl]

What I do is I color one of the cells just before I bifurcate, so if I have to backtrack I just keep hitting undo until the coloring goes away. >.>

[@flobiish]

A bifurcate button to copy the current grid into a new window.

[@MitchellD249]

Personally, I think a feature that encourages bifurcation is probably not great. Solvers should be trying to avoid that wherever possible.

[@SKyrim190]

@@MitchellD249 In the case of this one I think one can hardly blame the solver. It was set with this bifurcation in mind, which honestly is not very great design

[@buzzly108]

*1:26** **_Rules_* *3:13** **_Let's get cracking!_*

[@spencersmith3573]

I love that you geared us up for the knowledge bomb of the century

[@douglasplachy4577]

This one was truly a blast. I took a shot and got it on my first try. What was hard to see was the tail of the yellow line going into the center. It was obscured by the blue diagonal. 👍

[@NLTops]

Hey CTC, I just wanted to give a quick tip for at the end. You wanted to see if the polarity of the thermos could be inverted. You don't have to go all the way back. You can just swap 19, 28, 37 and 46. It preserves both the thermos and sudoku requirement. So the only thing left to check is the factors. Which you'd quickly notice don't add up. This is because the central 9 becomes a 1 (irrelevant to both sides) and another 1 previously on the top-left to bottom-right diagonal (so used to be irrelevant to it) becomes a 9 and thus very relevant to its product. The final products for the diagonals after inversion are 56700 and 235200. In other words, the Thermos and Sudoku requirements had two polar opposite transmutations, but the products requirement didn't and is thus used to locate the position of the bulbs.

[@jsun223]

the Monica Geller joke lol

[@WillyBotson]

And so subtle and quick about it too! Loved it, Mark!

[@Coyotek4]

58:42 ... Yeesh! I juggled the two polarities for as long as I could ... but eventually, I opened a second window up to try the 'alternate' path. That quickly dried up, allowing me to focus on the 'true' path; even then, it took a while to get to the end. But ... I did. (Which is more than how I did on today's 'Simon' puzzle.) Tough puzzle!

[@stevieinselby]

At 20:00, you've moved into the realms of bifurcation rather than simply working on a reverse polarity puzzle. Once you use the rule the diagonals having equal products to say that _this_ diagonal has a 7 and so _that_ diagonal must also have a 7, you can no longer just flip the polarity to make it work if it turns out you've taken the wrong path ... because that first 7 is no longer a 7, it's now a 3 and so _doesn't_ need to be matched by a 3 on the other diagonal, as there are other ways of making the same product. I'm not saying that that's the wrong way to go about the puzzle, I wouldn't have the first idea of what else to do!, but it might have been worth noting in your explanation that it isn't now just a case of subtracting everything from 10.

[@ChanSoloCup]

He talks about it at 17:45, and then again at 19:50 when he places the 7. He stops mid-sentence short of stating it explicitly but he does mention that he's past the point of reversal.

[@tremkl]

I think the easiest way to articulate the final flourish on the diagonals is that the main diagonal needed to be either 8x8 or 8x4. If you put an 8 in r2c2, it would force an 8 into r8c3, so you couldn't put an 8 in both spots on the diagonal, therefore it was 4x8 and your other diagonal needed 6x2, which was resolvable.

[@johngassmann9581]

I was truly fascinated by this puzzle. Excellent solution!

[@srwapo]

I don't like the try-and-see method used in the video, but my method took almost 3 hours, so I guess I can't fault it too much. I ended up with a Schrödinger's thermo with two values in every cell, then coloring them if they are on the one side of the 5 or the other, which let me narrow down to two numbers the majority of the cells. Then I got stuck. After "peaking" at the video, used the number of 7's on the diagonals to force a 7 in r4c5. But, yeah, needed help to clue me into using the prime factors on the diagonals to limit the options.

[@aliaungst1174]

Beautiful puzzle. Love the maths and the visual.

[@kelseyredford219]

I took forever to realize that the 1 in box 5 did not have to be at the end of a thermo. It kept breaking on me and I couldn't figure out why.

[@efa666]

Just finished Simon's puzzle. Great timing again.

[@flobiish]

Same thing happens to me almost every day.

[@JohnWalker-hk5pg]

Why has Mark moved to the land of yellow?

[@PH34RB]

Looks like the lighting. I posit that he's hiding from rampant construction in someone's basement with an old yellow lightbulb.

[@Rangsk]

Just in case anyone wants a serious answer, it looks like the white balance is off on his camera.

[@MarkPermyakov]

He is in Breaking Bad's Mexico

[@Nyarlah]

Bifurcation by definition is kind of frustrating. Is it the way this puzzle was aiming at ? I stopped rather soon after the overflow of pencil marks.

[@t71024]

On these types of puzzles I can "technically" avoid bifurcation by going quantum: center pencil marks for the case that the cat is alive, and corner pencil marks for the case that the dog is alive. (Corner marks are a dog anyway because you can't do them with the numpad. Is that a hardware limitation on how PC keyboards are wired?) But logically, it's still bifurcation.

[@Zer0ji]

Not hardware, but a limitation of how your OS interprets what your keyboard sends to it: Shift+Numpad7 sends "Home" on my keyboard, with 2468 being arrows, 1 is End, and 39 are PgUp / PgDown. The CTC app does some weird things with input handling on top of it, which is why Shift+Numpad7 still writes a (non-corner) 7 in the grid, I have no clue why tbh.

[@FirstLast-gw5mg]

@@Zer0ji The app is looking at the physical key code value, "Numpad7", and since the OS converted that to "Home" it suppressed the state of the Shift key modifier. The app could be programmed that if "Numpad7" produces something other than "7" it should know that the shift key was pressed, and then it would be able to correctly tell which keys were pressed, but it's not that smart.

[@Justin-TPG]

3:40 Accidental(?) brilliant pun.

[@evlredsun]

i missed it, pls explain

[@CosmosSurfer]

@@evlredsun I think that they’re pointing out that “degree of freedom” and “thermo” are both terms from statistical mechanics

[@Wecoc1]

The digits in thermos indicate degrees (Temperature), so if the thermo has one _degree_ of freedom it can be understood as candidates on the cell and what the digits would represent on a real thermo.

[@Justin-TPG]

@@evlredsun Just a degrees/thermo/thermometer thing :)

[@toddbiesel4288]

When will we get a puzzle in which it helps to know that the product of all the digits in any row, column, or box is 362,880?

[@flobiish]

I don't think it's bifurcation. You *had* to check the factors and the only way to do that was to figure out what they could be in either situation.

[@mauer1]

Maybe there is some sudoku wizardry to be able to figure something out in an earlier stage

[@flobiish]

@@mauer1 The base rules of sudoku are completely agnostic towards the values of the numbers. The only reason it was cut down to two options was the thermos. Any way it’s looked at, he had to sudoku to the point of getting the possible values of the diagonals just to check the factor possibilities.

[@notchmath9642]

22:38 why can’t it be a 6 and a 1 against a 2 and an 8?

[@beilkster]

In your example the non highlighted numbers on the diagonal multiply to 6*1*8=24 and 3*8*2=48, which aren't equal. I was not able to justify the assumption at 23:01 which removed the possible 3*2*4=6*1*8=24

[@jsun223]

or 4 and 4

[@BoundlessxArts]

The 1 would have to be in r2c8 which together with the 1 in r1c4 would force the 1 in box 1 into r3c1 which it can't be because of the 1 in r4c1.

[@alvaropallete]

I was wondering the same, but I realized later that if you look into column 3, 1 can already be placed in r2c3 and that rules the 1 in r2c8. btw Mark just got lucky there because he didn't considered that until @24:10

[@chaselausted3679]

@@beilkster 6*1*8=48, not 24

[@buzzly108]

Has anyone tried solving without Mark's "bifurcation?" I, for one, have no problem with his method of solving this, but I'm wondering if it's possible another way...

[@Math.Bandit]

You could use the letters A-I in place of numbers until you get to the point where you can disambiguate the thermos. It would be similar to Simon's puzzle that he did a while back with all the 10-cages where he couldn't disambiguate the dominos until the whole grid was 'solved' in pairs of letters.

[@bodemeister118]

At 23:00 why is 2 ruled out from the main diagonal. If 2 and 8 are placed on the main diagonal, and 1 and 6 on the counter diagonal, the products match.

[@hilcovanbreeschoten720]

@19:35 His conclusion is true, it does take the position of one of the 7s, but from this point forward he's mixing up Schrödinger 7s (the ones that are either 3 or 7, and he assumes as being 3), with actual 7s. For example he then proceeds to conclude from the pencil mark 3s in r8/9c9, that the 7 takes one of those positions, and therefore r8c9 is a 3. But actually that 3 is a Schrödinger 7, and could have been the 7 in r9c9. Solution: Without any additional rules: Let's recode Mark's 3s as red, and his 7s as black. We have: red in r1c1, a 7 in r9c9, a black in r1c2/3 and a black in r9c7/9. Let's look what happens for black in r9c9 and r9c7. - Black in r9c9: This means black is 7, and that means there is only one 7 on this diagonal, so the other diagonal also contains one 7, which is already in r7c3. Therefore r4c6 can never be another 7, which means it isn't black. We conclude r4c5 and r1c6 are black. - Black in r9c7: This means black in c9 must be in r2/r3. But we also have black in c1 in r2/r3. The only position for black in r1 is in r1c6. Conclusion: r1c6 is black, and r4c6 is not black. Now let's look again at the top left to bottom right (TL) diagonal. There are three 1/9 cells. One is at the crossing of both diagonals, the other two have opposite polarity. So regardless of which is which, there is now one additional 9 in the TL diagonal compared to the bottom left to top right (BL) diagonal. Notice that there is a black cell on the BL diagonal at r7c3. If black is 3 then we need another black 3 on this diagonal, but since r4c6 can no longer be black, there are no more possible cells on this diagonal to be black. Therefore black isn't 3 and it's 7.

[@JeremyButlerquarterthru]

1,360,800

[@Whatwhat3434]

I like the bifurcation technique for a puzzle like this. I wish the setter made for a more elegant initial state by giving a single digit or one bulb end, because it seems unnecessarily difficult. Kudos to Mark to going back to prove it also!

[@wren4077]

did the setter say that this was only possible to beak in through bifurcation? I'm convinced there might be an actual logic to it... scouring the comments looking for someone else's take on it. I really don't like using bifurcation.

[@ChrisVenus]

@@wren4077 Yeah. I'm thinking that there probably was a more elegant way of solving it and am likewise combing these comments looking to see if anybody has found it. :)

[@wren4077]

@@ChrisVenus man tag me if you find something pls. I have a playlist for puzzles I intend to revisit. Usually its because Ive made a mistake and messed it up really bad and dont want to go over it right away. I just added this video to that playlist and planned on trying it another day. Tell me if you find something.

[@RichSmith77]

Up to 19:35 it's not bifurcation. After 19:35, it becomes bifurcation, but that's no longer the break-in. 🙂

[@ChrisVenus]

@@wren4077 There is now a comment from Jesse Olsen (couldn't work out how to tag you in a reply to that) which explains that there was a rule the testers didn't pass on! So I think maybe as presented it is bifurcation time but the original was slightly different to what we were presented with! I'm interested to know if the testers left this out on purpose or accidentally and if on purpose if they had some clever way of determining the thermos...

[@missioncardiac7599]

Who else heard Alan Rickman's voice when Mark talked about a brain the size of (2) planets?

[@Patterner]

@Robert Cuperus yes, Moore! (RIP)

[@keithtemple8418]

To everyone complaining about bifurcation: it only becomes bifurcation at 19:37, when Mark uses the fact that 7 is prime to place a 7 in the bottom right. Before that point, he was just using a notation where every digit could represent itself or 10 minus itself. In fact, he could've placed a 7 in the same spot using logic (there was a 3 and a 7 in the other diagonal), except it would have been a "true" 7, with the rest of the puzzle still unknown whether it was completely correct or completely "10-x" switched. From there, he could have continued to use logic rather than bifurcation to determine the state of the solution, specifically that the 9s create too many factors of 3.

[@RichSmith77]

Thank-you. Agree completely.

[@notchmath9642]

18:00 You can actually cross off the 5s and the center 9 before you know which end is which, because the 5s stay the same after a flip and the center 9 is on both diagonals no matter what Edit: And that’s what I get for not waiting ten seconds before commenting

[@magicmurloc]

You can solve it more cleanly using colors to avoid guessing where the thermos start/end. I didn't actually managed to solve it since I didn't understand to use factors to deduce the diagonals, but going back to what I had along with that assistance from the video, I could finish it without an early guess.

[@colinfun]

Mark is wrong when he says early on that without the diagonals, the thermos would have to be reversible. Since there is never the same amount of values in the box where the end and/or bulb of each one are never the same as each other. What I mean is take the grey one, the bulb could be reversible, but if counterclockwise, the second value could be the same as the bulb, but that is not valid for the clockwise variation.

[@TomiRantanen]

The new software is great, except could you please use center alignment in the browser window? Now the grid is somewhat annoyingly stuck to the far left side of the screen.

[@justinwhite2725]

@17:17 this would be a great time for that square trick you or Simon showed us a few months ago. I forget exactly how it went though but it was something to do with all the numbers around the outsode of the central box appear in the four squares in each corner of the whole puzzles.

[@mauer1]

Phistomefels ring

[@justinwhite2725]

@@mauer1 that's the one. I frequently start colouring ring areas as they are 'used up' in the corners to help eliminate options one way or the other later.

[@mauer1]

@@leftsheppard5867 yeah it has a reason it was unknown for so long. unless its path is somehow built into the grid its most likely just a logical consequence to the previous used logic. Not a logic to gain new information, more like a logic to verify old information.

[@jochenkeller6102]

It took me more than 3 hours to solve this one, and all the time I was wondering how symmetry would be broken. Very unsatisfying to see two solutions in the end.

[@ericveneto1593]

I knew yellow was a bad choice AS SOON as he made it.

[@madisonking8057]

Hmmm idk if it is even possible to pull information from it, but the yellow and burnt orange thermometers in that middle box are what catch my eye i dont think he will get anywhere with the diagonals just yet

[@yichen6313]

I love this beautiful design! It's not hard at all either, and overall it's very enjoyable.

[@dwdei8815]

Extremely gallant of you to do the appendix disproving the beta-version. I was lucky and tried the "right" way out from the start. But it could easily have been the other way round.

[@DWestheim]

Never before have I been as clueless as with this one.

[@sotek2784]

There were a couple pieces of logic still available that Mark didn't get until later - the 4 in box 7 was a hidden single at the point when he actually relied on the identity of the thermos for logic on the factors, for instance. I was able to use a few inferences to go from where Mark did what I'd deem bifurcation (IE, declaring that the number of sevens on the diagonal had to match) to working out that r9c9 had to be 3 or 7 (because either it was 7 in the real solution, or 3-which-was-7 in the inverse land), and a few other pieces to see that there was apparently an assignment for the diagonals that would work (26 or 46 with 48 or 88, just as Mark saw), then ... well, did what I'd deem bifurcation - went for broke since I figured it would either finish or break fast, and it did finish fast from there.

[@SSGranor]

The way to solve this puzzle without bifurcation is use a high/low coloring scheme where you don't know a priori which color is high and which is low - just that everything of the same color is to the same side of 5.

[@bait6652]

Its nice to find these old puzzles, beautifully designed ...the letter solve method would "negate" the "tedious" bifurcation as It would eliminate the relabelling of cells... The only bifurcation would happen when resolving the diagonal products tracing the prime factors. Once C, G is deduced to be 3 or 7 then the letter mapping resolve(only take few steps to see which factors work. Whats very strange w this puzzle if u shift the yellow/oj ring openning b/w B2 and B5...the puzzle solves itself. But the diagonals arenot equal products rather 32* ratio. Whats nifty is the inner two rings change pairty

[@MrXami08]

I initially chose the wrong order by chance, then discarded it accidentally when trying to place equal amount of primes on the diagonals without considering 1*6 = 2*3. Realized after starting the other way round that placing the primes wasn't my intent, but the prime factorizations. Secretly I hoped the new path would be incorrect forcing me to redo the first path, but this one got there

[@dolf370]

Do not understand why Mark doesn't use the new features in the software. Much easier to check switch figures with these as you can select all the 1s and replace them by 0s, and then select all 9s and replace them with 1s, and then change all 0s with 9s, and then do the same 2-0-8, 3-0-7, 4-0-6 switching. Takes just a minute and less likely to introduce errors compared to changing the digits one by one like Mark does.

[@alienrenders]

Great solve! I made two guesses and they both ended up being correct. I couldn't figure out how to start so just tried a 2 at the top since that forces the rest of the thermo. Not sure I would have known to flip the digits.

[@matthiasvancampen3770]

At 23:00 does he make a correct deduction? He says they have to be 8 and 8 OR 8 and 4. However, on that point 8 and 2 would also be possible (8x2x3 = 6x8x1)

[@chewy531]

I started this with the bulb ends reversed from this... the mistake I then made at the end was that I used some logic based on the diagonal products and then replaced those numbers also... I needed to revert the grid to a point prior to using the diagonal product logic prior to changing the polarity of the thermos.

[@mbwun5]

This was a fun solve to watch. Great job.

[@HienNguyenHMN]

Since the logic is the same once reversed (subtracted from 10), wouldn't it be easier to swap the final board and then recalculate the cross product?

[@victoriam6569]

The logic is the same only for the first part, with thermos. From some point when you start using multiplications it differs a lot. (Compare 3 and 7 -- you can't use them the same way)

[@boldBryan]

Fascinating puzzle

[@matthewender3473]

Ha! Thought I'd beaten the expert solve with 26:43, and went to watch in shock to see how. Of course, he solved it partway through and was just playing with the inverse. I did get close! In my opinion, we don't need to consider it bifurcation, you're following a logical thread even if it is a twisted pair of embroidery floss :)

[@stevesebzda570]

"Do give it a go.. on the link below.. the video.." again. Okay, Mark Thanks, Santa Cheerio.. 😂

[@serkanergun0]

23:46 it could be 3 x 4 x 4 on one diagonal and 6 x 8 x 1 on the other?

[@felixbornholdt9371]

If every number became its polar opposite, you just could have checked the opposite of the diagonals and check those products.

[@felixbornholdt9371]

Don't mind, this doesn't work obviously. Because in the second attempt not all numers are the actual opposites.

[@jonathanallan5007]

What a brilliant construction, J J Olsen!

[@yichen6313]

At 20:33, we can already know that the other polarity won't work. We haven't really used the product constraint (other than the 5) so far. There is no need to check the other afterwards. 3 maps to 7, so the other polarity would have two 7 factors on one diagonal and one 7 on the other.

[@Nighthound]

We have already used the product constraint. At 19:44, 7 was placed in R9C9 because in that is the only place for 7 in this polarity. However, in the other polarity when 3 maps to 7, R9C9 would contain the 7, so this does not break the other polarity yet. So R9C9 is 3 or 7 in this polarity.

[@yichen6313]

@@Nighthound Ah yes I missed it. Though in my solve I remembered concluding that this is the only working polarity around this point, but I forgot the details.

[@flash24g]

Around 10:32 you make a mistake. The yellow corner (directly above the 9) could at this point potentially be a 3. In the end it's no consequence as the eliminations around 12:15 rule it out, but still the mistake is there.

[@AussieJohnny]

To make all the numbers 10's complement: Double-click 1 change to all zero Double-click 9 change to all 1 Double-click 0 change to all 9 Repeat for 2/8 then 3/7 then 4/6

[@ceejaydoesstuff9944]

I kept on hearing some weird loud echo during this video.

[@conexant51]

I don't consider this solve as bifurcation, but by choosing one solve path from one of two possibilities. Well done Mark, I enjoyed this!

[@nomore6167]

Choosing one solve path from one of two possibilities is the literal definition of bifurcation.

[@conexant51]

@@nomore6167 Fair enough, let me put it differently then. It seems to me that bifurcation was part of this construction because it lacked a bulb or a digit.

[@BaldorfBreakdowns]

I got stuck after solving the thermos.

[@Tiger21us]

In the new software / web app on ios mobile you cannot highlight squares that are not touching each other orthogonally at the same time :/ Very difficult to input things into more than one cell at the time. Unless I am missing something in the settings?

[@jonathanbredehoft6961]

It appears you can actually solve the puzzle completely in the wrong thermo direction but the diagonals dont equal each other in the end--maddening but super clever.

[@bristolrovers27]

Loved this clever puzzle

[@capistro5]

Killer App is GREAT! Thanks!

[@dextersmith526]

The new software needs a mobile friendly version, it tends to zoom when I’m tapping the squares to add numbers

[@mostman]

This drives me mad.

[@antoniozumpano826]

You are supposing the sequence to be constant along de thermo, but it may be not constante, it can increase at any point, there no hint where it is constant or increase. The conjunction "or" is not exclusive. We can have increase, constant, constant, increase, increase, increase, and so on. The rule says that the sequence is "non decreasing" along the thermo.

[@hapyotaku]

Rules of sudoku

[@glennmelven3414]

When the thermo has more than one cell in a box, it must increase in that box. Otherwise you would have 2 of the same digit in the box.

[@RichSmith77]

To add to Glenn's reply. When Mark assumes a thermo stays constant, as he's pencilmarking the options, he's looking at either the minimum or maximum values that can be placed in the cells. If he's started at the assumed bulb end, he wants to only increase as he moves along the thermometer when he's forced to, so that he can work out what the minimum value has to be at the non-bulb end. The thermo can stay constant when it crosses diagonally into another box, but has to increase if the thermo moves to a cell in the same box.

[@jeremyclitheroe1683]

Beautiful thumbnail. Can't wait to watch!

[@GirGir183]

3:34 What is the Monica Geller moment referred to here?

[@jochenkeller6102]

Oops, no solution shown in the video. I always wondered about the diagonals, but didnt notice it really broke as I chose the right one by chance at the start.

[@Trandhal]

I personally have no problem with bifurcation puzzle. Sure they're not as elegant as "pure logic" puzzles, but they're still very fascinating

[@libra_v3]

you forgot to paste the misc links into the description

[@Jack-vm1kp]

Interesting layout!

[@arifleischer8285]

Why couldn’t it be 6 1 and then the others being 8 and 2 on the diagonal

[@justanotherman1114]

6 and 1 causes problem in box 1.

[@mikkelsvendsen]

For anyone wondering, the product is 1.360.800

[@Jodawo]

As it says in the beginning, he was a Sudoku Champion. When you do competition Sudoku one of the techniques is bifurcation. It works or it would not be used by many of the fastest solvers. I would have liked to see if adding the pencil marks would have done its elimination and gotten you to the same point. It's possible the way the puzzle was created that a lot of the terms would fall out just because of the geometry. If you look, there is a lot of numbers close enough to each other to possibly affect each other. I do believe it should have been looked at before going to a method that is not exactly the most logical solve.

[@rmahu]

19:41 When he put the 7 in r9c9, there are two three in a diagonal and one in the other that are the 7 of the other version which forces a 7 in r9c9 in both versions. r2c2 cannot be a 1 because it forces r4c6 and r8c8 to be 8 so 1 is needed in r2c8 and r8c2 In the other version the 9 in r2c2 and r6c6 force 9 in r2c8 and r8c2 that collide with r8c5. If 1 is not in r2c2 it is in r2c3 which solves a 3 in r9c3 and a 7 in r9c9 which proves that it is the correct version and the rest of the solution is logical

[@Ruddigore]

A cracking solve. 👍

[@antoniozumpano826]

You are supposing that the sequence increase only on the corners. Thar is not what the rules say.

[@hapyotaku]

But there are rules of sudoku

[@PH34RB]

Given the length of the thing, if you increase anywhere else, you eat up your progress. Thermos *have* to increase at the corners because obviously they're within the boxes. But if you lay out the candidates for a minimal and a maximal thermo on the outside 2, you quickly find out that you need all but maybe 1 of the sides to remain constant.

[@philm5872]

I forst read the rule set "or stay the same" as meaning 1,1,1,1,1,1,1,1,1..I thought.. how can this be??!! Turns out I have no clue haha

[@esajpsasipes2822]

this step is applied inviidually to each cell, not the whole thermo, meaning you can go 1, 1, 2, 3, 8, 8, 8, 9

[@philm5872]

I know. Thats what I was saying. :)

[@victoriam6569]

I didn't use bifurcation, and it took me 4,5 hours to solve, and I feel like wasted time.

[@davidhughes7174]

By subtracting from 10 All numbers on the two diagonals would have shown the puzzle breaks

[@ChrisVenus]

This wouldn't actually help. The problem is that when solving the first way some assumptions were made in the grid that didn't apply to the inverted version. eg sevens on a diagonal placed sevens on the other diagonal - in the inverted version these sevens would be threes which couldn't be placed in the same way (since they could also pair into sixes or nines) which means that the solve on the inverted version would take a different path and lead to a contradiction in a different place.

[@asaenco]

Facinating isthe word I thought of too.

[@mamakittea]

was I the only one that paused it and calculated the diagonal products?

[@evlredsun]

only if you didn't read the other comments.

[@Xelger]

Honestly, I think bifurcation is a perfectly legitimate way to solve these puzzles. I'm not picky enough to demand different methods of solving. I enjoy it all the same.

[@nomore6167]

I don't think any reasonable person would argue that there is any right way or wrong way to solve a puzzle (as long as there's no cheating, of course). However, if bifurcation is required in order to solve a puzzle, then it cannot be considered a logic puzzle.

[@stephenbeck7222]

No More the problem is that ‘bifurcation’ is in the eye of the beholder. How long of a chain do you have to have before a ‘coloring technique’ or some other method becomes bifurcation.

[@Math.Bandit]

@@nomore6167 This one can be done the same way without bifurcation if you used the letters A-I in place of numbers for most of the puzzle, and then substituted them once you needed to make use of the diagonals; same as Simon did in that one puzzle with the 10-cages that were only disambiguated at the end with a single thermo.

[@RichSmith77]

@@Math.Bandit You can always view the digits placed in the grid up to 19:40 as the equivalent of letters. They don't represent the actual digit n in the final solution, instead they represent both n and 10-n, the same way a letter would. (With the added bonus that I personally find it more convenient to work with digits than letters, due to familiarity). However, from this point on in Mark's solve, I feel it is bifurcation, because you have to pick one of the two solutions represented by the grid at this point, and follow it through until either a solution is reached or a contradiction. I'm not criticising this approach, as it's the method I used (just executed better and faster).

[@tnk4me4]

22:49 those unfilled sevens have been staring at me for so long.

[@LednacekZ]

I approve the solve after you have done also the other side of the thermo. I really dont like this type of sudoku, though. It forces bifurcation solve in stead of logic.

[@dolf370]

I do not think it is bifurcation when you go ahead and solve it and then do a simple substitution afterwards it comes out wrong. Simon has done similar solves where he assumes a certain permutation and then just substitutes when it runs aground, and he detests all kinds of bifurcations.

[@wren4077]

@@dolf370 Isn't that the definition of bifurcation. I learned about it in the channel itself here. THrough the videos and comments. You assume a solution and proceed to solve the puzzle with it and if it doesn't contradict anything, great, you solved the puzzle, but if it does contradict something, then you assume one of the other solutions.

[@dolf370]

@@wren4077 Actually no, it's not. An example of a bifurcation is when you have two (or more) alternative for a square, you just choose one alternative randomly, or at a hunch, then proceed from there, if you then break, you know that your choice was the wrong one and you have to pick the other one instead and redo the solve from that point. Say, you have 1 and 2 to chose from, so you pick 1 and go ahead. Then it breaks, you have to go back and start over from that point with 2 instead. That's a bifurcation. But that was not what Mark did here. Because using a similar example. Mark saw that it should be 1 or 9 in a square. He doesn't know which one, but he knows that if he solves it using 1, and then it turns out to be wrong, he does not have to go back to that point and start a new path, but what he has to do is to swap all 1s and all the 9s in the solve. (And in this particular case here, you then swap all the 2s with 8s, all the 3s with 7s and all the 4s with 6s). It's all based on that there are 2 solutions to the sudoku without the constraint that both the diagonal products should be equal. And the 2 solutions are interchangeable by just swapping the digits. So you solve it, and if the solution doesn't satisfy the diagonal products constraint, you just swap to the other solution that does. A smooth and clean why of solving the whole puzzle. Simon demonstrated a similar technique once with a very difficult sudoku where he assumed three digits and solved it towards the end, got a solution that didn't work, but just swapped the three digits with each other to get the correct solution. Unfortunately I do not remember which video it was, so do not really know how to find it. Hope I manage to clarify what the difference is.

[@wren4077]

@@dolf370 I mean you're still trying out solutions, regardless of how easy it is to swap to the other solution I don't think knowing that the 1s will be replaced by a 9 if the 1s turned out to be wrong, has any bearing on whether or not your solve required trial and error. That's the basis of bifurcation isn't it? Knowing what the other possible solution is while assuming one to be correct. I asked about this in an earlier video as well. We use trial and error all the time but its usually in a very limited sense. We only see the projected solution upto 2 or 3 subsequent cells. "If I have a 1 here that will put a 1 there, and there it will clash" etc. That's accepted but as soon as you start doing it with long projected paths people start having a problem with it. My comment was to find out what the magic number was, that if you start projecting your assumption beyond these many cells, you're in bifurcation territory. When does it go from being acceptable to being "cheating". Didn't really get a good response on that. I don't think there is one tbh.

[@dolf370]

@@wren4077 The difference is that when you bifurcate, you BACK UP to the point where you did bifurcate if and when you break, and you have to find a new solution. That's not what is done here. Because you know that if it breaks, you just switch 1-9, 2-8, 3-7, 4-6, and you have the right solution. There is no need to back up and start over from some point and you do not have to find a new solution path. The solution is exactly the same, you just switch digits.

[@AnomAnomMTG]

Wish the CTC apps were free, would love to get them

[@wren4077]

No I'm pretty sure the earlier puzzle with unknown bulb ends had a solve without using bifurcation Man i was struggling with this puzzle. Disappointing to see it solved with bifurcation

[@joeshonk9715]

So the only way to solve this is through bifurcation? I thought Mark hated completing puzzle via bifurcation and wants a more logical ways of deducing the next steps.

[@dkosmari]

I guess it's not entirely bifurcation because the work in filing out the thermos is not wasted, you just gotta flip the digits. At least the wrong path fails quickly if you focus on the diagonals.

[@9tydegreez]

No that's Simon who hates bifurcation.

[@PH34RB]

@@9tydegreez And even then, it's partly out of respect for the elegance of logical solve, and partly through peer pressure. Early on in the channel's history, Simon was a lot more open to bifurcating, but upped his game to rise up to the 'peer pressure' for logical solves in the comments.

[@asterpw]

It's a recognition the logic is going to be entirely symmetric until some point near the end of the puzzle. All of the steps between the beginning and that point he's really doing both paths at once. The real bifurcation started when he started on the diagonals.

[@dolf370]

@@9tydegreez Yeah, but Simon would probably have solved it the same way. He has done similar things in the past, and it isn't really bifurcation.

[@melvintremble4898]

You do the same every time, looking for the complicated, instead of studying the suduko obvious:?