The Genius Equation

** 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:
coffeebean.games/product-cate...
▶ 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:
iOS:
apps.apple.com/us/app/svens-s...
Steam: store.steampowered.com/app/17...
Android:
play.google.com/store/apps/de...
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: [e-mail]
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'.)
**************************************************************
▶ CTC FAN DISCORD SERVER◀
/ discord
▶ OUR BACK CATALOGUE - ALL CATEGORISED WITH LINKS!◀
tinyurl.com/CTCCatalogue
▶ NEW CRACKING THE CRYPTIC MERCHANDISE◀
teespring.com/en-GB/stores/cr...
▶SEND US PUZZLES TO SOLVE/CONTACT US◀
[e-mail]
▶FOLLOW US◀
Twitter: @crypticcracking
Instagram (for how to solve daily clues from The Times): crackingthe...
We also post the Wordle In A Minute videos on TikTok.

[@ThePedallingPianist]

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]

A stellar puzzle and solve! Bravo!

[@puritan7473]

An excellent puzzle, thank you!

[@afrayedknot81]

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

[@GabyGrecu]

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

[@johnpauladamovsky86]

​@@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]

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

[@Walrein1106]

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]

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]

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]

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]

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]

Happy birthday!

[@0Taneb]

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

[@angec9908]

Simon: starts recording Maverick: 🚁 😈

[@Salman-os7pr]

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

[@jakejarvis6683]

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.

[@debrabowen4276]

Watching Simon think is a highlight of my day.

[@deepanshushukla116]

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]

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

[@johnpauladamovsky86]

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...!

[@ronjohnson6916]

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

[@Paolo_De_Leva]

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

[@anaayoung9142]

Big chain of toughts in this one. Great solve!

[@blobz-1]

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

[@JohnGottschalk]

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.

[@markp7262]

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

[@jdyerjdyer]

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]

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

[@tiemen9095]

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.

[@davidhughes7174]

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

[@aaronfuzion]

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

[@gabriels3706]

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

[@darcyboese5943]

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

[@Darkstar2342]

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

[@murrayty]

33:37, Simon.exe has stopped working.

[@leefisher6366]

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]

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

[@ericpraline1302]

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.

[@Paolo_De_Leva]

Excellent innovative puzzle and masterful solve 👏👏👏👏👏

[@patrickgass787]

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

[@martysears]

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

[@TheClawNinja]

Great puzzle!

[@MattYDdraig]

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

[@Gonzalo_Garcia_]

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

[@srwapo]

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.

[@piarittersporn]

Lovely puzzle.

[@tdbraun6837]

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

[@CauchyIntegralFormula]

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

[@Rach881101]

35:17 for me. Nice puzzle!

[@MAUOMBO]

Great puzzle

[@LednacekZ]

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

[@leefisher6366]

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

[@shawncarter7188]

❤️ Ian ❤️. So sorry for your loss... I read something on a sign the other day in the pet section,: "Your wings were ready but my heart was not" 🥹

[@chitraagarwal8259]

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

[@fulltimeslackerii8229]

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?

[@davidhughes7174]

Thank you for the birthday shout out from the tragic David

[@xfayzlucky7408]

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

[@warheads9676]

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]

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

[@TurquoizeGoldscraper]

41:55 for me.

[@LyuboRyuk]

This puzzle proves that the aliens exist

[@theredstoneengineer6934]

46:27 for me

[@vikingslayer34]

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]

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

[@vikingslayer34]

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

[@riluna3695]

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]

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]

@@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]

​@@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]

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

[@hrbattenfeld]

Kind

[@Pritchie45]

35 minutes

[@gi0nbecell]

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…

[@deathpigeon2]

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.

[@rubenverg]

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

[@transrightsbaybee]

bro needs a new mic holy shit