The Genius Equation

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** TODAY'S PUZZLE **
ThePedallingPianist is quite quite mad. But also a genius. This 100%-rated 6x6 puzzle is both fascinating and incredible. A complete one-off from one of the most original minds in sudoku.
Play the puzzle at the link below:
sudokupad.app/eep49o4qx6
Rules:
Normal 6x6 sudoku rules apply. (Place the digits 1 to 6, once each, in every row, column and region).
Yin Yang: Shade some cells such that all shaded cells form one orthogonally connected area, as do all unshaded cells, and no 2x2 area is entirely shaded or unshaded.
Counting Yin Yang: A digit in a shaded cell shows how many times that digit appears in shaded cells.
Quadruples: A digit in a circle must appear in the surrounding 4 cells. If a digit appears twice in a circle, it must appear twice in the surrounding 4 cells.
Jane Street's Bug Bytes puzzle is available here:
www.janestreet.com/bug-byte/
(Simon's solve of this puzzle is on Patreon.)
** NEW SUDOKU HUNT ON PATREON **
We're delighted to share with you a brand new sudoku hunt themed around snake egg puzzles by Glum Hippo. If you've never tried snake egg logic puzzles before, prepare for serious fun - these sudokus are outstanding! Finish by May 20 to enter the competition!
Other treats on Patreon include:
- the Sumgeons & Diagrams sudoku by sunnyjum;
- Simon's latest forays into the world of Islands Of Insight;
- Mark's video looking at the new OneUp puzzle from Rodolfo Kurchan;
- his solve of Region Geometry by Emre Kolotoğlu (3hr 36min long...!);
- and Mark's latest solve of The Times Club Monthly cryptic crossword
/ crackingthecryptic
** GET OUR FOG KICKSTARTER DELUXE & OUR BOOKS **
Check out this link for the kickstarter books and Fog Novella we've created over the years:
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▶ SUDOKU PAD - Use Our Software For Your Puzzles ◀
You can input classic sudoku puzzles into our software and help support Sven, the programmer responsible for the wonderful user interface we all use to play these puzzles everyday. The app also comes with 12 handmade puzzles from us:
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Android:
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ALSO on Amazon: Search for “SudokuPad”
▶ Contents Of This Video ◀
0:00 Theme music & puzzle intro
1:34 The Hardest Crossword Of The Year
1:57 Extra content on Patreon
2:13 Happy Birthdays etc
5:54 Rules
8:19 Start of Solve: Let's Get Cracking
▶ Contact Us ◀
Twitter: @Cracking The Cryptic
email: crackingthecryptic@gmail.com
Our PO Box address:
Simon Anthony & Mark Goodliffe
Box 102
56 Gloucester Road
London
SW7 4UB
(Please note to use our real names rather than 'Cracking The Cryptic'.)
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Опубликовано:

15 июн 2024

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Комментарии : 82

@ThePedallingPianist Месяц назад

Thank you for this feature, and to those who sent in a recommendation! To be honest, "counting yin yang" seemed like quite an obvious progression after Marty Sears' excellent development of "counting circles", but maybe that's only obvious to mad people!! I spent ages about half a year ago trying to make the 9x9 version of this puzzle work to no avail, but my dad (ralphwaldo1 on LMD) encouraged me to look at smaller grids, and this fell into place almost instantly. I'd like to revisit the 9x9, but I suppose I can't use the 1-1-9-9 quadruple clue that I had planned for the break-in now! [spoiler alert] Your solution path hit all the important intended points, albeit you could've corner pencil marked 1 and 6 into box 2 much earlier and then considered the implications on the perimeter shading (including the point about the top left being unable to be fully unshaded) so that your thoughts about 5s could've related to a real corner of the grid rather than a hypothetical one. I'm impressed you got all that logic without a real corner in which to visualise it, though! Thanks again for a lovely showcase :)

@JaymanOttawa Месяц назад

A stellar puzzle and solve! Bravo!

@puritan7473 Месяц назад

An excellent puzzle, thank you!

@afrayedknot81 Месяц назад

Truly one of the best 6x6s in existence! Loved it!

@GabyGrecu Месяц назад

Now i want to be on a deserted island with you!

@johnpauladamovsky86 Месяц назад

@@GabyGrecu If there were two people, then it wouldn't be deserted...! Plus, you would also have to contend with Jesus, who is always present whenever two people are gathered together.

@martysears Месяц назад

Thoroughly deserved feature. These kind of 'high concept' puzzles are my absolute fave, and no one is better at setting them than Stu.

@Walrein1106 Месяц назад

OMG IM THE ETHAN FROM SOUTH DAKOTA. I had no idea she sent a shoutout to you, and it was for the sudoku, too. I appreciate you, and I found your channel last year when I was finding new content with a sleepy newborn ❤️❤️❤️

@leppyr64 Месяц назад

It's really impressive the amount of work Simon has put in with this logic with the 5s even before talking about the unshaded 1 and 6 that must be in row 1 of box 2.

@kamilmalach6383 Месяц назад

I always loved smaller puzzles with smaller boxes as they force the creator to come up with more innovations in limited area. I wonder if one can make 3x3 in non-standard grid with unusual rules.

@darreljones8645 Месяц назад

Rare case of a Yin-Yang puzzle in which the shaded cells are different from the unshaded cells (i.e., it matters which set you shade). And following Simon's logic here, I figured the fewest shaded cells you can have in a complete 6x6 puzzle is 13.

@user-kc6yp3gj8w Месяц назад

Today is also my birthday! I forgot all about the birthday celebrations at the start of videos. It's nice to hear that more people share my birthday. Greatly appreciated!

@Amycalledshooter Месяц назад

Happy birthday!

@0Taneb Месяц назад

Impressive solve! I never know where to begin with these variant sudoku. I really enjoyed watching you unspool the logic

@Raven-Creations 6 дней назад

10:24 for me. My logic at the start was this. On the 1166 quad, the 6s must both be shaded or both unshaded. To avoid a 2x2 and a chequerboard, the 1s must be of opposite shading, therefore, there can be no more shaded 1s. Every side must therefore contain an unshaded 1, which makes it impossible for each side to also contain a shaded 6. Therefore, the 1166 contains unshaded 166 and a shaded 1, and there can be no more shaded 1s or 6s in the puzzle. The cells adjacent to the 1166 on the side cannot all be unshaded or you'd isolate the shaded 1, but there must be an unshaded 1 and 6 in R1, C6, and R6, therefore we can unshade the last two cells of R1 and C1, and all of C6 and R6. This puts shaded cells in R2C5, R5C2 and R5C5. Also, because there can be no shaded 6, we know there can be no more than 15 shaded cells. It's not possible for there to be no shaded 5, because there are 9 2x2s, and it's not possible to arrange the one shaded cell in each such that the tenth connects them all. Therefore, we need 5 shaded 5s, and the only unshaded 5 must be in R6C6. There must be a shaded 5 in both R1 and C1, so R1C1 must be shaded. After a bit of sudoku, most of the grid is covered in digits or pairs of digits and the yin yang resolves it all. It was quite painful watching you following the initial logic. You had worked out everything you needed, but applying it was like pulling teeth. It's as if you get so excited to make a deduction that you forget to take advantage of the rules to extend its effect. You got the 16 in R1, but failed to green them. You got the 1 in C5 but failed to green it, which made R5C4, R3C5, and R3C4 shaded to avoid a chequerboard. Now R2C4 is unshaded, so cannot be 4, which resolves the 34s around the grid. You now have a shaded 2, and another in C2, so R4C1 is unshaded, making R3C2 shaded and therefore 1, and it's all over in a matter of seconds.

@Paolo_De_Leva Месяц назад

Thank you for the structured ruleset 😏👍 The title for each paragraph is quite helpful❗ I hope it will become a CTC standard style.

@Salman-os7pr Месяц назад

Simon missed that 1s and 6s are always unshaded for so long, could have been completed in half the time, also the avoiding 2x2 in the bottom left! Regardless it was a beautiful puzzle! Loved it

@deepanshushukla116 Месяц назад

When you see 6x6 puzzle now, you know you are in for a treat. Constructors are making sure you have to use all your grey brain cells in order to solve them.

@emilywilliams3237 Месяц назад

Totally fun and fascinating to watch - thanks so much, Simon!!

@debrabowen4276 Месяц назад

Watching Simon think is a highlight of my day.

@angec9908 Месяц назад

Simon: starts recording Maverick: 🚁 😈

@anaayoung9142 Месяц назад

Big chain of toughts in this one. Great solve!

@jakejarvis6683 Месяц назад

31:56 is one of the most satisfying moments in any CTC video for me because I saw it in the same moment that Simon was speaking it. An aboslutely gorgeous deduction that I would never have found myself, but I was so surprised to have immediately understood. Simon's reaction of closing his eyes and throwing his hands behind his head in disbelief of the beauty.... Well, I felt that.

@ronjohnson6916 Месяц назад

A puzzle that makes you feel clever but isn't brutal. Loved it.

@johnpauladamovsky86 Месяц назад

These artwork puzzles remind me of what it felt like to discover the Pythagorean theorem, so many, many years ago. They said it couldn't be done...!

@davidhughes7174 Месяц назад

Maddest thing I have seen in a while. Thank you Simon and pedallingpianist

@jdyerjdyer Месяц назад

You can also conclude 6 is unshaded because if it is shaded, then you have to have all six 6s in the shaded region. You can't have a checkerboard pattern, so there would have to be one of the 1s in the 4 cell 16 region shaded. Now you can't "wrap" the perimeter of the puzzle to hit the four 6s (or two 6s in opposite corners) without cutting the grid in half/quarters, or shading another 1 on the border along the way.

@jdyerjdyer Месяц назад

My bad, you said basically the same thing, just in a different order.

@blobz-1 Месяц назад

An amazing construction PedallingPianist - but not surprising, after learning some Yin-Yang secrets from a couple of your "solution videos" on RU-vid. ;P

@gabriels3706 Месяц назад

what a brilliant puzzle, every step is just pure genius, in such a small grid

@Paolo_De_Leva Месяц назад

Excellent innovative puzzle and masterful solve 👏👏👏👏👏

@JohnGottschalk Месяц назад

I got a bunch of cells I knew couldn't be shaded, and then was able to only find 1 solution of the shading, except I overlooked 1 pair of cells that had to be determined later (the 3 & 2 at the end) and then rectified at that point.

@leefisher6366 Месяц назад

I saw a different opening when I tried this (and failed to make progress). One of the 1's in that 1-1-6-6 quad HAS to get shaded. If neither does, then (a) if 6's are shaded, you have a checkerboard, and (b) if they aren't, you have a 2x2 square. [either all 6s are shaded or all are unshaded]. Also, clearly, you can't have two shaded ones. Therefore exactly 1 of the 1s in that area is shaded, and none of the others in the entire puzzle are shaded.

@leefisher6366 Месяц назад

You joined me here at 20:15, except that you also knew 6s were unshaded at that point.

@TheClawNinja Месяц назад

Great puzzle!

@piarittersporn Месяц назад

Lovely puzzle.

@patrickgass787 Месяц назад

There is simply no one better at setting a 6x6 grid than ThePedallingPianist. Always brilliant, always maddening, always a joy to solve.

@martysears Месяц назад

I'm inclined to agree. 4x4s too, and a marbly 5x5 springs to mind too. Stu is the master at taking an idea and making a pure, bitesize version of it that does away with all the fluff and trappings

@MAUOMBO Месяц назад

Great puzzle

@tdbraun6837 Месяц назад

Beautiful. We'll see more of that rule, I suppose.

@markp7262 Месяц назад

27:04 finish. Such a fun puzzle with some amazing logic paths. Excellent, as always!

@chitraagarwal8259 Месяц назад

Loved this.. Wondering if there is a meta constraint on the minimum shaded cells required in a counting yin yang

@Darkstar2342 Месяц назад

To me, that the one shaded 1 is in the 2x2 was immediately clear, because if they were both unshaded, you couldn't put the 6's in there anymore (they have to be the same shadedness, so they either create a checkerboard or a 2x2). Not that it helps much on its own without realizing that the 6s cannot be shaded, which I didn't realize as quickly as Simon did

@tiemen9095 Месяц назад

Your deduction of the unshaded bottom-right was so complicated. I figured the 16 pair in col-1, but also a 1 and 6 in any of 3 cells of box 2. And those would also have to be unshaded. Connecting the unshaded 16 bottom-left to the unshaded 16 top right doesnt work through the top left corner for logic shown with the 1166 clue, so it has to connect through the bottom-right.

@aaronfuzion Месяц назад

16:33 Simon says "six six six" !!

@srwapo Месяц назад

39:30 with a lot of looks at the video. Needed help to show 6 isn't shaded and that I needed to count how many cells need to be shaded to see that 5 has to be. Just didn't see how to start, then it flowed fast once I was taught that.

@CauchyIntegralFormula Месяц назад

33m35s. About half of that time was me convincing myself that there had to be at least 13 shaded cells

@Gonzalo_Garcia_ Месяц назад

13:58 for me. Very interesting puzzle, really enjoyed it!!

@MattYDdraig Месяц назад

26:17 A lot squeezed into a small package. Very nice

@leefisher6366 Месяц назад

Let's not forget that the 6s and 3s in the Unshaded area are also counted!!!

@murrayty Месяц назад

33:37, Simon.exe has stopped working.

@darcyboese5943 Месяц назад

Time flies by so fast! Was it only yesterday That I felt younger? Friends singing off-key The room aglow with candles What more could I wish? My Sweet Sixteenth Prime, A fun way to celebrate Trips around the Sun

@ericpraline1302 Месяц назад

Shady indeed, made a dog's dinner of this one at the start, switched brains and then managed to conjure up some logical thinking which certainly helped. And I agree with Simon about setters in general. Every day I am baffled by how they do what they do. I have no comprehension whatsoever of how one can create such puzzles.

@fulltimeslackerii8229 Месяц назад

15:47 because of this 16 deadly pattern, isn’t it now impossible to shade any 6 since that would make every 6 shaded and create a checkerboard?

@Rach881101 Месяц назад

35:17 for me. Nice puzzle!

@LednacekZ Месяц назад

29:02 for me. the solve felt more like intuition than logic.

@davidhughes7174 Месяц назад

Thank you for the birthday shout out from the tragic David

@xfayzlucky7408 Месяц назад

why couldn't we have the two six shaded in top left with 1 one shaded between them

@warheads9676 Месяц назад

I think the first. Thing the rules tell you in my head is there is at most the digit shaded, so 1 -1 and it irritated me no end it took that long

@grahamania Месяц назад

00:26:04 for me. Great puzzle! Looked like it should have been easier AND harder than it was :) Kind comment.

@vikingslayer34 Месяц назад

I see that the finished puzzle has 15 shaded cells and 21 unshaded cells. Since it’s a yin yang, shouldn’t there be an equal number of shaded and unshaded cells?

@pR0stYp3 Месяц назад

No, this is not a part of the rules :)

@vikingslayer34 Месяц назад

@@pR0stYp3Yes i know but in my head yin yang means equality, balance, and harmony. Great puzzle either way!!

@theredstoneengineer6934 Месяц назад

46:27 for me

@LyuboRyuk Месяц назад

This puzzle proves that the aliens exist

@TurquoizeGoldscraper Месяц назад

41:55 for me.

@hrbattenfeld Месяц назад

Kind

@riluna3695 Месяц назад

Any math or logic nerds able to answer a question for me? Is Simon's illustration around the 27 minute mark sufficient to show beyond a shadow of a doubt that 10 shaded cells is not enough? It feels intuitive enough, but I know intuition can sometimes be faulty, and something about the way I did the same logic just felt like it was missing potential possibilities. I'd love to hear like...a more formal formation of this same argument that leaves absolutely no room for doubt that 10 shaded cells is too few to properly break up all potential 2x2s in a valid Yin/Yang pattern. I know it's right, it's just...nagging at me really bad.

@PsychoSoldierPrometheus Месяц назад

I can't prove it mathematically, but I tried the most efficient way to avoid creating 2x2s of unshaded cells, and in a 6x6 grid, you need at least 9 cells to break all possible 2x2 patterns. Any less than 9 allows at least one unshaded 2x2 area. Now, since all shaded cells have to be connected to each other, you need at least 5 cells in between them. This results in the absolute minimum of 13 shaded cells in the grid. Now, you have to understand that if we have a shaded 1, that will be the only 1 that's shaded, and by the 1166 square, we know we have a shaded 1. We also know that 6s can't be shaded due to the same exact square. Additionally, every shaded number must repeat as shaded as many times as its value shows (so, if you see a shaded 3, there must be three shaded 3s) Since you have to come up with at least 13 shaded squares using the numbers 1 to 5, you must include 5, since the triangular number of 4 is 10, and that's too low. So, you must at least include one (and therefore 5) fives. 5 has to be shaded

@riluna3695 Месяц назад

@@PsychoSoldierPrometheus "Now, since all shaded cells have to be connected to each other, you need at least 5 cells in between them." Where are you seeing this? This seems to be the crucial part of the logic, but I couldn't prove outside of trial and error that we needed more than one connecting square. So all I had was 9 confirmed spaces and a need to prove that I needed at least two more than that, no matter how I arranged the 9.

@PsychoSoldierPrometheus Месяц назад

@@riluna3695ok, so, forget the placement of the shaded cells for a minute. You know you have a 6x6 grid, and you place 9 shaded cells, to break any 2x2 patterns. This means that no matter how you place them, the shaded cells will be one cell apart. Even if you had as little as 3 shaded cells you needed to connect, there would be at least 2 cells between them, to connect them. For 4 cells, you need 3 "connections" and so on. No matter what, you need more than 2 cells to connect the 9 mandatory ones. As I said, I can't prove it mathematically or geometrically, but to connect 3 rows (the minimum of rows you need partially shaded to avoid 2x2s), you need 2 squares, while to connect 2 lines you need 2 more. In any case, you need 2 or more connecting squares, resulting in a shaded cell number greater than 10

@riluna3695 Месяц назад

@@PsychoSoldierPrometheus Apologies, I can't follow that. It might just be me. Either way, I appreciate the attempt. Thank you.

@deathpigeon2 Месяц назад

You could've completed the shading with logic on 2s just as with logic on 3s by noting there was a 2-5 in box 1 both of which were shaded and a shaded 2 you had already found, so the 2-5 in box 5 needed one shaded and one unshaded, and there was already a shaded, so the other needed to be unshaded and the 3 needed to be shaded for connectivity.

@Pritchie45 Месяц назад

35 minutes

@rubenverg Месяц назад

simon missing that avoid a 2x2 in the bottom left corner was quite frustrating

@gi0nbecell Месяц назад

It‘s remarkable how stubbornly Simon ignores the forced unshading of One’s (outside the quadruple in boxes 1 & 3) and Sixes, which would have had immediate and rather important implications rather early on for the YinYang aspect of the puzzle…