Understanding The Four Colour Theorem

*** TODAY'S PUZZLE ***
A heavily touted puzzle (not sudoku!) today in the form of Spectrum by MicroStudy. This is one of the smoothest pencil puzzles we've seen - an absolute blast to solve and not monstrously hard. Definitely one to have a go at if you can find a few minutes spare.

Play the puzzle at the link below:

Rules:
Fillomino: Divide the grid into regions of orthogonally-connected cells such that no two regions of the same size (ie with the same number of cells) share an edge. Enter a number into each cell equal to the size of its region. Four Colour Theorem: Each region must be shaded entirely in one colour. There are a total of four different colours in the grid. Regions of the same colour cannot touch orthogonally. Additionally, regions of the same colour must be of different sizes. Arrows: Digits on arrows indicate the distance to the nearest cell of the same colour in the indicated direction (Adjacent cells are a distance of 1 from each other). Not all arrows are necessarily given.

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▶ Contents Of This Video ◀

0:00 Theme music & puzzle intro
2:20 Happy Anniversary
3:10 Kraken The Cryptic - a NEW sudoku hunt on Patreon!
4:22 Rules
9:38 Start Of Solve - Let's Get Cracking!

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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:

iOS:

Android:

ALSO on Amazon: Search for “SudokuPad”

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[microstudy_]

Wow, this was quite a pleasant surprise to cap off my day! Thank you so much, Simon, for featuring this puzzle. I'm also glad that some guest stars (Maverick and the Poltergeist) have decided to make an appearance as well! (although I'm sure you're not as glad hahaha)

You pretty much nailed every single intended deduction, and I was super impressed by how smooth you solved it. You even got a record-breaking time of 00:00! Outstanding stuff.

Jokes aside, I'm very happy you enjoyed this, and I hope the rest of the community does as well! Thank you again.

[tobbgoblin]

I like how Maverick and the creaky window kicked off the descent into madness early this time.

[davidrattner]

Congrats microstudy for 1st Simon feature!! Well deserved!

[MrWaffles]

On the topic of the four color theorem and computers, it was the first major proof to be published that was based on computer calculations. It caused a generational split among mathematicians: the older generation couldn't believe in a proof done by computer, because it couldn't be verified by human hands. The younger generation couldn't believe in a proof with that much computation if it HAD been done by human hands, because they didn't believe a person could do that much calculation without human error.

There's an interesting book about it called Four Colors Suffice, if anyone's interested in further reading.

[spacelem]

Can I just say that I find these colouring puzzles to be immensely satisfying to watch!

[stevesebzda]

That door, Simon.
Two things.
"The squeaky wheel/hinge gets the oil" comes to mind (so "oil" it)
And Two ;
Put a block or brick in front of it, simply pinning it to the wall.
Simple fix.

If you want, I have two of them (crafts done by my aunts and grandmother – a brick inside a nice cross-stitching and lattice-work), and another one (brick inside again) covered to make it look like a couch (lounge) pillows and back and armrests included.

Brick that door.
You're welcome 😂

[johnpauladamovsky]

This is another spectacular puzzle of artwork quality. There are only just a few clues dusted around a 10x10 grid, and somehow the logical-solution follows a delightful single-file bread-crumb trail of steps into yet another sublime and colorful finish. Watching this channel for several years has been quite the adventure... Every single day we get to witness an English Poet and his balding-sidekick temp fate and double-down their bets that there will be an even better puzzle to work on tomorrow. Watching Simon, you might think that there's nothing this man can't do, but it turns out there's just this one thing... He can't LOSE...!

[annek]

The Four Color Theorem was conjectured by a school-boy in 1852:
"As far as is known, [6] the conjecture was first proposed on October 23, 1852, [7] when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. At the time, Guthrie's brother, Frederick, was a student of Augustus De Morgan (the former advisor of Francis) at University College London. Francis inquired with Frederick regarding it, who then took it to De Morgan (Francis Guthrie graduated later in 1852, and later became a professor of mathematics in South Africa). According to De Morgan:

" "A student of mine [Guthrie] asked me to day to give him a reason for a fact which I did not know was a fact—and do not yet. He says that if a figure be any how divided and the compartments differently colored so that figures with any portion of common boundary line are differently colored—four colors may be wanted but not more—the following is his case in which four colors are wanted. Query cannot a necessity for five or more be invented… (Wilson 2014, p. 18)" ". [from Wikipedia]

In 1976 Appel and Haken broke down the number of cases to be checked to 1834, which required computers to do the checking. If any one comes up with a simple proof, fame is theirs!

[aishwaryaiyer]

can't stress enough how much i just love these fillominos (and other non-sudoku logic puzzles)!! <3

[emilywilliams]

What a fascinating puzzle - I loved watching you solve this, Simon. And yes, I could clearly hear the poltergeist's activities, but it was amusing and not distracting to. Thanks for all that you do to bring two videos a day to this wonderful channel.

[wv]

"And that's too naughty for words" I'd like to start using this phrase on minor inconveniences, almost as brilliant as the solve, cheers

[MarkBennet]

Purple and blue in those shades are really bad for this colour-blind viewer - I am Red/Green mainly and the Red/Green option was better (tonal distinction) and orange/yellow was the best of the tested pairs. I tend to use dark grey these days as one of my colours - dark grey/blue/yellow/red tends to work well for me. Others will have different options.

[Sam_weiqi]

33:26 for me. One of my favourite puzzles for months (amid stiff competition)!

[leighd]

26:33 Love the new ‘Simon is thinking’ sound effects 😂

Great puzzle. Fun solve!

[shteevuk]

Fabulous puzzle. Lost track of the number of times I made a mistake so catastrophic I had to restart but I always had fun solving it ❤

[christophercoleman]

Very beautiful solve! Thank you and Simon for the dedication in entertaining us in solving these puzzles Daily. Please keep up the Great work you guys do everyday!

[kylefullerton]

I loved this puzzle - it's the first CtC puzzle I've finished on my own in less time than the length of the video! (I wasn't quite faster than Simon took to solve it, since I didn't take the time to announce birthdays and read the rules during my solve, but it's a start!) I loved how the end of the puzzle used a new insight that we hadn't used before!

[inspiringsand]

Rules: 02:19
Let's Get Cracking: 09:43

What about this video's Top Tier Simarkisms?!
Maverick: 4x (05:25, 05:25, 05:33, 13:12)
Three In the Corner: 3x (36:51, 36:55, 36:59)
Goodliffing: 1x (10:16)
Knowledge Bomb: 1x (26:14)
Cooking with Gas: 1x (14:34)
You Rotten Thing: 1x (17:44)

And how about this video's Simarkisms?!
Ah: 15x (10:54, 15:31, 15:59, 15:59, 22:04, 22:40, 23:33, 32:03, 32:56, 33:17, 34:14, 44:26, 46:03, 46:06, 47:28)
Sorry: 8x (07:34, 13:35, 21:41, 25:40, 37:58, 37:58, 47:33, 50:25)
In Fact: 7x (17:32, 19:23, 35:32, 35:32, 51:32, 52:14, 52:14)
Brilliant: 5x (03:03, 23:18, 23:21, 29:46, 44:42)
Gorgeous: 5x (22:45, 28:04, 42:52, 51:43, 53:31)
Hang On: 5x (26:05, 32:59, 42:50, 50:35, 51:56)
Stuck: 4x (25:40, 37:14, 37:23, 46:19)
Beautiful: 4x (26:35, 26:39, 48:25, 53:33)
That's Huge: 3x (38:39, 41:30, 41:30)
Out of Nowhere: 2x (24:07, 45:03)
Clever: 2x (16:08, 29:07)
I Have no Clue: 2x (37:33)
Surely: 2x (41:14, 41:33)
Eyes are Drawn: 1x (14:59)
Nonsense: 1x (21:01)
Naughty: 1x (15:27)
Lovely: 1x (54:10)
Fascinating: 1x (01:40)
Hypothecate: 1x (50:19)
Discombobulating: 1x (07:46)
Irritating: 1x (06:59)
Masterpiece: 1x (01:06)
Corollary: 1x (13:38)
Obviously: 1x (34:08)
Whoopsie: 1x (46:03)
Let's Take Stock: 1x (48:15)
What Does This Mean?: 1x (49:27)
Cake!: 1x (03:04)

Most popular number(>9), digit and colour this video:
Ten (5 mentions)
One (101 mentions)
Green (82 mentions)

Antithesis Battles:
Even (7) - Odd (0)
Row (4) - Column (4)

FAQ:
Q1: You missed something!
A1: That could very well be the case! Human speech can be hard to understand for computers like me! Point out the ones that I missed and maybe I'll learn!
Q2: Can you do this for another channel?
A2: I've been thinking about that and wrote some code to make that possible. Let me know which channel you think would be a good fit!

[Coyotek]

37:11 ... I had a bit of a false-start and restarted a couple times before seeing my error; otherwise, I thought I did well.

I *loved* working on this puzzle! Would love to see another like it!

[BevanArps]

29:30 Simon says "Never talk to me at parties"
I must register my objection!
If more people at parties talked about worthwhile things like Sudoku or Fillomino puzzles, rather than competing to see who gets sozzled the fastest, parties would be much more interesting activities.