River Crossings (and Alcuin Numbers) - Numberphile
Рет қаралды 394,980
6 жыл бұрынDiscussing vertex covers and Alcuin numbers for graphs - and a famous old puzzle. Filmed at MSRI with Dr Annie Raymond.
More links & stuff in full description below ↓↓↓
Annie Raymond: www.msri.org/people/38568
The Alcuin Number of a Graph: link.springer.com/chapter/10....
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.
Discuss this video on Brady's subreddit: redd.it/7ob1n2
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@Dominikcos7 6 жыл бұрын
that cabbage is a broccoli
@tohopes 6 жыл бұрын
BROCCOLI... is SPY!!!
@edsiefker1301 6 жыл бұрын
Broccoli and cabbage are the same species.
@RubixB0y 6 жыл бұрын
Ed Siefker, so? They're different strains so that doesn't make them interchangeable.
@timseguine2 6 жыл бұрын
They don't have to be interchangeable. The species itself is called cabbage. Broccoli is a cultivar of that species, ergo a type of cabbage.
@RubixB0y 6 жыл бұрын
Tim Seguine I thought they all came from wild mustard way back when.
@johnox2226 6 жыл бұрын
"An Anglo-Saxon really smart dude" That is the best description ever, 10/10
@yungml 6 жыл бұрын
Also not applicable very often
@paulc4629 6 жыл бұрын
That's racist
@stevethecatcouch6532 6 жыл бұрын
Well, Alguin was at least smart enough to copy fro the Arab sources of the problem.
@johnox2226 6 жыл бұрын
Paul C Your name is racist
@yvesivo 6 жыл бұрын
*Anglo-Sachson
@rostfleck79 6 жыл бұрын
I can't believe you missed the opportunity to say "We're gonna need a bigger boat!".
@jmchez 6 жыл бұрын
+1,000
@gorillaau 6 жыл бұрын
Some one has jumped the shark.
@tr3ndkiller 6 жыл бұрын
My jaw's dropped ...
@KasabianFan44 5 жыл бұрын
?
@Triantalex 9 ай бұрын
??.
@Willzp360 6 жыл бұрын
Brady I think your cabbage may, uh, be a broccoli
@numberphile 6 жыл бұрын
I know but there is no cabbage emoji! ;)
@ragnkja 6 жыл бұрын
Will Price It’s the same species, so does it really matter?
@Lauraphoid 6 жыл бұрын
Broccoli is a cabbage.
@imveryangryitsnotbutter 6 жыл бұрын
It's a Parker Cabbage.
@OctagonalSquare 6 жыл бұрын
I'm Very Angry It's Not Butter!! That's it! Somebody tell Matt!
@KungFuBlitzKrieg 6 жыл бұрын
So the moral of the story is, "Keep your friends close and your enemies closer."
@bazoozoo1186 6 жыл бұрын
...And keep the friends of your enimies away from enimies of your friends.
@KungFuBlitzKrieg 6 жыл бұрын
Haha! Yes indeed! :)
@dan_tr4pd00r 6 жыл бұрын
I thought the moral was just get a big enough boat.
@RandomRageDude 6 жыл бұрын
keep your friends close and their enemies closer.
@osotanuki3359 6 жыл бұрын
KungFuBlitzKrieg mmm... not really
@Hello-fb7sp 6 жыл бұрын
I knew about this problem since childhood but had never thought of it in a mathematical way, this was really interesting! The Dr also explained it very well, I hope she appears more on this channel in the future.
@Borednesss 6 жыл бұрын
Dr. Annie Raymond seems pretty cool!
@moviesmaster2399 6 жыл бұрын
where can i attempt to post a proof for this problem ?????????????????? please
@RWBHere 6 жыл бұрын
It's an NP problem.
@EaglePicking 3 жыл бұрын
@@moviesmaster2399 That is probably the nerdiest pick-up line I ever heard :D
@diaz6874 6 жыл бұрын
But what if the farmer can eat the boat?
@reflex5729 6 жыл бұрын
El Díaz in this situations you’ve to take goat on the boat that goat will check him out
@LokiClock 6 жыл бұрын
Who boats the boaters at the boaters' exhibition?
@RWBHere 6 жыл бұрын
LokiClock, the person wearing the boater would do that.
@DouglasZwick 6 жыл бұрын
I knew it was a mistake to leave that farmer unsupervised
@limitingchaos 6 жыл бұрын
Turns out the boat, and everything else, is a spherical cow.
@Faramik2000 6 жыл бұрын
Broccoli can't swim? You haven't seen mine
@whitherwhence 6 жыл бұрын
Faramik2000 Um, they're talking about cabbage
@diek_yt 6 жыл бұрын
Eyyy. Sadnecessary?
@JoshGroach 6 жыл бұрын
They talk about cabbage, but they SHOW broccoli.
@connortremblay1259 3 жыл бұрын
Just built different
@Triantalex 9 ай бұрын
??.
@hellocollegejason198 6 жыл бұрын
Goats can be lawnmowers, not a quote I was expecting on this channel.
@Gold161803 6 жыл бұрын
hellocollegejason198 At least not from anyone other than Cliff.
@ccgarciab 6 жыл бұрын
You can actually hire a pack of goats (how are those called?) to mow your grass. I read somewhere that thats what google does in their googleplex.
@jwrm22 6 жыл бұрын
In the meantime, the wolf ate the cabbage as he was very hungry.
@gorillaau 6 жыл бұрын
jwrm22 The wolf relieved itself on the cabbage.... and smirked "Enjoy your dinner now"
@feliciabarker9210 6 жыл бұрын
I'd really like a follow-up video that dug into how you DO check if a vertex cover is the minimum size
@soulstealer29a 6 жыл бұрын
From the thumbnail I thought we were summoning a really cute demon.
@supersionsupersion 6 жыл бұрын
hahaha
@ObjectsInMotion 6 жыл бұрын
I mean the venn diagram of satanists and graph theorists IS a circle...
@miteshgurav6069 6 жыл бұрын
Anthony Khodanian The math is strong with this one!!
@dreadbaron10 6 жыл бұрын
You can try to summon a demon with any shape you want it will Probably have the same result.
@omikronweapon 5 жыл бұрын
I'd try a penciltangle, to summon a cute nerdy demon.
@MrTheNaboo 6 жыл бұрын
Graph theory seems to pop up everywhere.
@anselmschueler 6 жыл бұрын
Maximilian Wollner it does
@kailomonkey 6 жыл бұрын
Because graph theory says this problem can get too complicated let's just draw it as a network, try our best then declare it too complicated.
@mensaswede4028 4 жыл бұрын
Yeah, graphs are succinct representation of “things” (vertices) and “relationships between things” (edges). And a lot of problems deal with things and the relationships between those things.
@rohansastry 6 жыл бұрын
But... goats eat everything! So... wouldn’t the goat also eat the boat?
@lukasschmidt2478 6 жыл бұрын
For the puzzle to work though, none of the animals must do anything when the farmer is watching.
@josephoduor2358 6 жыл бұрын
Says the one who has a wolf as a pet
@pleasedontwatchthese9593 6 жыл бұрын
The 🐐 ate the 🚜.
@pmcpartlan 6 жыл бұрын
Rohan Sastry If a goat ate a boat, would it float?
@Nemelis0 6 жыл бұрын
@Pete McPartlan: Only in a moat
@Dominikcos7 6 жыл бұрын
*insert the cabbage scene from avatar here*
@serkanmuhcu1270 6 жыл бұрын
My cabbages!
@fossilfighters101 6 жыл бұрын
mY cAbBaGeS
@Greg042869 6 жыл бұрын
I don't remember, did that look like broccoli?
@GeekyNeil 6 жыл бұрын
10:00-10:10 Any vertex cover of this graph needs 4 vertices because there are 4 non-intersecting edges. Cat-Mouse, Goat-Carrot, Rabbit-Cabbage and Wolf-Goose. You need at least one vertex from each of those edges, so you need at least 4 vertices.
@mikewilliams6025 6 жыл бұрын
Wolf would definitely eat the cat. You've broken math, Brady. Stop that.
@StezzerLolz 6 жыл бұрын
The cat would eat the rabbit, too. And the goose would just destroy everything in a psychotic rampage, because geese are bastards.
@gabehennessy-oreilly1177 6 жыл бұрын
Nice callback
@Siggvard 6 жыл бұрын
The cat could climb up a tree.
@Siggvard 6 жыл бұрын
The cat could climb up a tree.
@HappyBeezerStudios 6 жыл бұрын
The cat would climb up the boat.
@pants1337 6 жыл бұрын
Runescape's 'Recruitment Drive' quest.
@ab12345cdf 6 жыл бұрын
always think about this when i see this proble lol
@Devan... 6 жыл бұрын
first think i thought of. lol
@andyrhodes1554 6 жыл бұрын
I wish I had seen this video years ago when I did this quest...
@arejm7304 6 жыл бұрын
hahahhah awesome
@RalphDratman 6 жыл бұрын
Excellent. Annie Raymond is a fantastic explainer and teacher!
@michaelzumpano7318 6 жыл бұрын
I have seen the first problem before but never the generalization to a vertex cover plus one. Nicely done Dr Raymond. I’d like to see more videos on the application of graph theory. Any relationship to Hamiltonian path, partition or Ramsey theory would be fun too.
@jessesantana8408 6 жыл бұрын
I was entranced by Dr. Raymond I could listen to her teach for years.
@dm551 6 жыл бұрын
kzfaq.info/get/bejne/o5OkrMt2vcWwkXk.html
@jessesantana8408 6 жыл бұрын
dm551 thank you wonderful stranger! Hope you have a nice day :)
@jukka-pekkatuominen4540 6 жыл бұрын
The Wolf would definitely eat the Cat.
@SuperSMT 6 жыл бұрын
And the cat would eat the rabbit... My cat has
@MateusSFigueiredo 6 жыл бұрын
it would have to get the cat first
@jukka-pekkatuominen4540 6 жыл бұрын
If the Cat runs away you'll end up losing them both. So in case of riddle it wouldn't work either.
@cyberneticube 6 жыл бұрын
And the goose would definitely eat the carrot and the cabbage, but what does it really matter, it's just en example :)
@seraphimwiththecheese5880 4 жыл бұрын
Cats eat grass. I've seen mine do it.
@johnbouttell5827 6 жыл бұрын
After spending so much time in the boat, the wolf will soon become domesticated. He may end up rowing the boat. Wolf Boat Tours R' Us.
@rockinRrr 6 жыл бұрын
the wolf is the boat.
@BeeryGamer 6 жыл бұрын
Then we won't need the rower/owner of all those vegetables and animals no more, so the number of seats of the boat required will always be the lowest vertex number! Give me those millions now thank you very much!
@RWBHere 6 жыл бұрын
If the farmer rowed badly enough, and the river was rough, then the wolf would soon become too travel sick to eat anything.
@jans1982 6 жыл бұрын
Or maybe ff you do every trip with your wolf, then you'll be friends with the wolf and then leave him with his food on purpose
@elimalinsky7069 6 жыл бұрын
John Bicycle So that's how the wolf became a dog? Being ferried from one bank of the river to the other :D
@LaGuerre19 6 жыл бұрын
My broccoli brings all the goats to the yard
@acbonbe7059 5 жыл бұрын
LaGuerre19 no that’s a carrot
@MateusSFigueiredo 6 жыл бұрын
She's great! Do more videos with her
@hossamel2006 2 жыл бұрын
Somehow this is an amazing video...probably the best one I've ever watched 😃
@ROL4NDpkmnguide 6 жыл бұрын
I like her accent
@paint4pain 6 жыл бұрын
French Canadian, probably from greater Montreal area.
@monkey7431_ 6 жыл бұрын
Sounds Dutch to me mate
@joewhitmore6776 6 жыл бұрын
I was just wondering what kind of accent is that
@timhoheisel8939 4 жыл бұрын
French-Canadian, in fact, Montreal.
@shahbazsheikh3545 6 жыл бұрын
"Blood everywhere or shreds of cabbage".... hahahaha! Great video.
@rohansastry 6 жыл бұрын
Shahbaz Sheikh Sheds of broccoli everywhere
@CharlesTheClumsy 6 жыл бұрын
I don't know any other channel that puts their name in the title of every video.
@azbyn692 6 жыл бұрын
Computerphile also does it
@frozenglobe 6 жыл бұрын
and Sixty Symbols
@JohnDCrafton 6 жыл бұрын
It's for search engine optimization (SEO).
@subinmdr 6 жыл бұрын
Smarter Every Day and almost every singer and band channels
@cyrillamat4888 6 жыл бұрын
I do
@AnastasisGrammenos 6 жыл бұрын
A cool application of this is in chemical storage units. There you have chemicals that shouldn't be close with some (conflict) and chemicals that are ok to be side by side (not conflict). So you need to get a storage unit with the min_vertex_ cover + 1 different rooms
@sweatygenius 6 жыл бұрын
I loved this
@brenthooton3412 3 жыл бұрын
14:15 the interesting question is the balance between efficiency (do it in as few crossings as possible) vs capacity (get away with the smallest boat as possible). 7 crossings for 5 animals seems really inefficient. But maybe the cost of a bigger boat outweighs the cost of the extra crossings. Or maybe the river is really wide and the cost of the extra crossings makes the bigger boat worth it.
@housellama 2 жыл бұрын
Found the engineer!
@kennethgee2004 2 жыл бұрын
@@housellama well probably, but optimization issue are also in mathematics with the equilibrium theory discovered by Nash. The optimization issue has also been extended into law and other areas, so it is an important concept.
@ninogaggi 6 жыл бұрын
Why would a farmer have a wolf?
@wierdalien1 6 жыл бұрын
Alan Murray 4000bc farmer
@numberphile 6 жыл бұрын
kzfaq.info/get/bejne/eqqqh9yAr7nJXY0.html
@ritikchawla8298 6 жыл бұрын
lol
@ninogaggi 6 жыл бұрын
Numberphile yes that was my inspiration
@revjmyoung 6 жыл бұрын
Thank you for this -- I had the same thought from Gareth! ;-)
@sachamm 6 жыл бұрын
Great stuff, I love how your subjects are so enthusiastic. We definitely need more on complexity theory!
@flinkwieeinwiesel5657 2 жыл бұрын
Wow, what an inspiring and cheerful way to present the problem. More please!
@beeeesac 6 жыл бұрын
Always loved problems like these!
@neelparmar6690 6 жыл бұрын
Many years of playing Professor Layton have prepared me for unexpected river crossings...I'm sure it will happen one of these days...
@dragoncurveenthusiast 6 жыл бұрын
As a kid I always wondered how the farmer keeps the wolf from eating the goat and the goat from eating the cabbage if he IS there with them. I never got an answer.
@lucianodebenedictis6014 6 жыл бұрын
He just says: "No, you can't".
@gabehennessy-oreilly1177 6 жыл бұрын
He makes them attempt to prove the collatz conjecture
@liltonyabc 6 жыл бұрын
Swiper no swiping
@Gold161803 6 жыл бұрын
Spray bottle?
@NathanK97 6 жыл бұрын
he has an oar and not a flimsy plastic one... a solid hand carved oak oar
@franktoffel 6 жыл бұрын
Excellent explanation! I really like the way it drives you to the limitation of the initial thought. More of these!!
@macacoman 6 жыл бұрын
One of my favorite videos! Great job you guys.
@JohnDCrafton 6 жыл бұрын
A wolf will definitely eat a cat, if it can catch the cat.
@JohnDCrafton 6 жыл бұрын
So? I have personally seen a mild-mannered dog rip a cat to shreds (the dog just wanted to play, but unfortunately for the cat, he played too rough). Wolves are decidedly less mild-mannered than dogs.
@hart-of-gold 6 жыл бұрын
When I was a kid our cat (a small tom cat) beat a large rottweiler by climbing on to the back of its neck and clawing the eyes and chewing its ears.
@JohnDCrafton 6 жыл бұрын
We can exchange anecdotes until we die, doesn't change the fact that a wolf will at least try to eat a cat, and will have varying levels of success depending on the intelligence and fitness of the cat. But if the cat gets away it's most likely gone up a tree, and then the farmer has a different problem on his hands.
@PuzzleQodec 6 жыл бұрын
At least the wolf and cat will be sufficiently distracted from eating anything else, so the farmer can bring the rest of his stuff to the other side of the river, and his boat can be smaller.
@Frosty-oj6hw 6 жыл бұрын
This channel is like a never ending fountain of attractive, nerdy, maths goddesses.
@camilohiche4475 5 жыл бұрын
Instant platonic crush right from the thumbnail.
@omikronweapon 5 жыл бұрын
How can you have a crush on someone simply by looks, implying attraction, and it being *platonic*?. It's almost the exact opposite of platonic. Your statement is indeed false. Now I'm wondering if you actually ONLY comment falsehoods.
@camilohiche4475 5 жыл бұрын
@@omikronweapon Thank you for making me check this comment so I come back to this video and admire this beautiful professor once again.
@TymexComputing 5 жыл бұрын
You omitted the pentagram, the goat and the blood :)
@Triantalex 9 ай бұрын
false.
@bidaubadeadieu 6 жыл бұрын
Really nice video, one of my favorites from recent Numberphile. I love the introduction of a simple problem followed by the general case, much like the Josephus video.
@alvkarthik2018 4 жыл бұрын
i have heard this problem a hundred times but never thought that people are actually serious about these kind of problems. and that;s why i love numberphile .
@ndavid42 6 жыл бұрын
"the rabbit and the goat together are fine. there won't be *too much* violence there" TOO MUCH??!
@theendofit 6 жыл бұрын
Pffft....sence when can cabages not swim.
@SolitaryCZ 6 жыл бұрын
theendofit It's common knowledge. No vegetable can swim... the wheelchair is too heavy.
@Superphilipp 6 жыл бұрын
SolitaryCZ, I lol'ed
@SUPAAH_ 6 жыл бұрын
how heavy is the cabbage that you cannot hold it?
@stapler942 4 жыл бұрын
A cabbage would sink in water, otherwise it would be a witch.
@mikeybud3501 6 жыл бұрын
Very interesting mathematical take on this ancient riddle. Love it as always! 😛
@ajtheown 6 жыл бұрын
As a Tim, I appreciate your use of emojis from a variety of platforms :)
@SmileyMPV 6 жыл бұрын
But finding the minimum vertex cover was NP hard already :p
@yero 6 жыл бұрын
I think I fell in love ❤ also I think that the wolf would eat the cat if it was really hungry
@jiggely_spears 6 жыл бұрын
A wolf is basically a dog - it would eat ALL the things...
@vimalk78 4 жыл бұрын
This is perhaps my favorite numberphile video.
@mraBJJ33 6 жыл бұрын
I'm not smart enough to know the practical application of this but it was still really cool to learn about it in a way that was easy for me to follow along.
@delve_ 6 жыл бұрын
Roses are red Violets are fine You see this here hyphen ~ It's a Parker Line
@kye4840 6 жыл бұрын
~~~~~Tilde not hyphen~~~~~
@delve_ 6 жыл бұрын
+Ky E [thatstheidea]
@thexavier666 6 жыл бұрын
That's a Parker Square of a poem
@Triantalex 9 ай бұрын
false.
@swaiii 6 жыл бұрын
This is some anti wolf propaganda. From my point of view the cabbage is the evil one
@pavphone2616 6 жыл бұрын
Well then you are lost!
@omikronweapon 4 жыл бұрын
how about that sadistic farmer that keeps messing with everybody.
@purplewine7362 3 жыл бұрын
only a wolf deals in absolutes
@iamalexkempton 6 жыл бұрын
This is some classic numberphile right here!
@EdithKFrost Жыл бұрын
Cats are so badass that even the wolf is too afraid to eat them.
@bongjoobrianlee 6 жыл бұрын
Cabbage looks like a Broccoli
@ragnkja 6 жыл бұрын
Bong Joo Brian Lee Whatever, it’s the same species.
@isaacbankart 6 жыл бұрын
0:45 i'm glad the cabbage can't swim that would be really worrying
@mihaitmf 5 жыл бұрын
Really cool stuff behind an apparently easy problem. Plus, I love how mathematicians write so neatly on thoes big paper sheets.
@enemdisk6628 6 жыл бұрын
That was super interesting! Thanks for the video!
@olliestone5549 6 жыл бұрын
They should invite Big Shaq here... His math skills are mind boggling.
@OEpistimon 6 жыл бұрын
The mathematicians working with numberphile wouldn't be able to comprehend his quick mafs...
@philipsneck3571 6 жыл бұрын
Agreed, his mafs are just too dang quick
@neelparmar6690 6 жыл бұрын
Mathememagics ting
@cosmicjenny4508 6 жыл бұрын
+Purposely Mistaken Nah, man was decent at maffs. Man got... D...
@alandouglas2789 6 жыл бұрын
Purposely Mistaken lol, seriously?
@将軍九八.彁 6 жыл бұрын
wolf can't eat the cat, lol
@piotrarturklos 6 жыл бұрын
The cat would be way too annoying as prey, scratching the eyes and running between the legs.
@soberhippie 6 жыл бұрын
Given half a chance, a cat might eat the wolf.
@RWBHere 6 жыл бұрын
Or run up a tree.
@mensaswede4028 4 жыл бұрын
I love how there is always a line in these videos where the guest says “I’ll need another piece of paper...”
@CesarDainezi 6 жыл бұрын
"If you were able come up with a polynomial time algorithm to determine it for any graph what it is, then you would prove that P = NP." That plot twist!
@beeble2003 3 жыл бұрын
Not much of a plot twist, really. It's extremely common for problems in graph theory to be NP-hard. Once you've seen a hundred of them, the only reason this one is interesting is because the problem is "Is the answer x or x+1?" Another similar one is that, but the four-colour theorem, every planar graph can be coloured with four colours, but it turns out to be NP-complete to determine whether a planar graph is 3-colourable.
@ProgresistTaliban 6 жыл бұрын
But...Why she has a Wolf in the first place?
@Derpster2493 6 жыл бұрын
Mittens.
@Gumshoesamurai 6 жыл бұрын
Protection from other wolves. Camouflage? An "apex predator" makes your party a danger to aggress (attack).
@jakubpekarek6400 6 жыл бұрын
So the wolf doesn't attack goats the farmer has at home. Remember? You need to take the troublemaker with you everywhere, every time. Duh.
@LinkEX 6 жыл бұрын
I guess that's one reason why mathematicians are sometimes perceived as aloof, living in surreal imaginary world; and why exploring math is actually far more creative and far from dry and formulaic, as some would argue.
@OriginalPiMan 6 жыл бұрын
Guard dog.
@althaz 6 жыл бұрын
Well I *was* going to go to bed, Brady, but I guess I'll watch this first instead :).
@allwinaugustine 6 жыл бұрын
i was waiting for this!
@moorentje 6 жыл бұрын
At the end you see a penguin and a bee emoji fade in. A cheeky nod for us Tims :)
@Luxalpa 6 жыл бұрын
The cat would definitely eat the rabbit and it would probably try the goose too.
@ethanpfeiffer7403 6 жыл бұрын
I prefer the Professor Layton river crossings.
@neelparmar6690 6 жыл бұрын
One of these days solving all of those Layton puzzles will come in handy in real life...one day soon I'm sure...
@jcortese3300 6 жыл бұрын
I had to laugh at the conclusion to keep the wolf with you at all times, because it occurred to me that any kindergarten teacher who has to herd around kids during a field trip, one of whom is a troublemaker, has already figured this out: you have to keep the troublemaker kid right next to you all day.
@mothman.industries 6 жыл бұрын
Geese having Teeths is the most terrifying thing I'll ever learn from this channel, tbh.
@saras8166 6 жыл бұрын
I've not seen a single comment about the problem itself yet.
@yvesivo 6 жыл бұрын
Sara S Me neither. I hoped for some comments on the P NP topic
@andrewl5267 6 жыл бұрын
Then you haven't seen mine yet ( ͡° ͜ʖ ͡°)
@laptop006 6 жыл бұрын
Rabbit's can't cut through steel beams
@ragnkja 6 жыл бұрын
LapTop006 [citation needed]
@stevethecatcouch6532 6 жыл бұрын
A farmer is trying to cross a river with a wolf, a rabbit, and a steel beam ...
@jiggely_spears 6 жыл бұрын
Neither can burning aviation fuel....
@atom1496 6 жыл бұрын
Very cool, Annie!
@anteconfig5391 6 жыл бұрын
You just gave me an easy problem to see if p = np thanks. Now I know which puzzle to do when I get bored.
@danieltaber4924 6 жыл бұрын
That's not a cabbage. That's a Broccoli.
@Aoltooliol 6 жыл бұрын
Daniel Taber same species
@RWBHere 6 жыл бұрын
One word for that: Brassica!
@TigruArdavi 3 жыл бұрын
@@RWBHere Wrong, two words for this: _Brassica oleracea_
@rollstuhlmeister 6 жыл бұрын
What if the wolf eats the farmer???
@yingo4098 3 жыл бұрын
I like how the 'cabbage', the carrot and the grass can get on and off the boat by itself
@CaptainHandsome 6 жыл бұрын
Why does the Farmer have a wolf?
@menturinai1387 6 жыл бұрын
What is the smallest number of trips required?
@darkfire8008 6 жыл бұрын
7
@johnredberg 6 жыл бұрын
In all fairness: Given the classical result that the minimum vertex cover problem is NP-hard, it is not surprising that the "do I need an extra seat" problem is at least NP-hard as well.
@johnox2226 6 жыл бұрын
Nice Brady!👌
@riccardopratesi7943 6 жыл бұрын
What about the case of one character being at risk of suicide, and it cannot be left alone? or it can be left only with some of the others? I mean, if in the graph there are also lines linking oneself, but only in absence of some other vertex?
@xenialafleur 6 жыл бұрын
The cabbage looks suspiciously like broccoli.
@RWBHere 6 жыл бұрын
Shhh! It's in disguise!
@driziiD 3 жыл бұрын
this was fun and useful for problem solving!
@Krone37Io 6 жыл бұрын
Great video!
@heraok1766 6 жыл бұрын
Please publish a video which the word mathemathics pronounced by everyone who prepared a numberphile video 🙄
@rohansastry 6 жыл бұрын
MatheMATHics?!?!?
@AgentM124 6 жыл бұрын
P=NP? N=1 then. QED
@meh6422 6 жыл бұрын
Wow ya so smart, very intellectual much IQ
@AgentM124 6 жыл бұрын
Horus yas yas. I used to watch Rick and Morty! 🙃
@scottgoodson8295 6 жыл бұрын
Agent M Or P=0
@astamite- 6 жыл бұрын
This is almost 100% correct. The only thing missing is that you forgot to prove P=NP.
@AgentM124 6 жыл бұрын
Astamite true, also wasn't P the variable, so setting it to 0 would mean N could be anything. But meh, I won't ever become a farmer so I don't bother.
@7557adam 6 жыл бұрын
I was actually thinking the other about how one could use math the describe this riddle! And then this video appears!
@gaiaandreacompagni5393 6 жыл бұрын
OMG THIS IS SO COOL AND USEFUL D:
@dbsirius 6 жыл бұрын
VIP cabbage
@tohopes 6 жыл бұрын
*RIP cabbage
@neelparmar6690 6 жыл бұрын
But it was a broccoli in the visuals...
@mikerich32 6 жыл бұрын
Neel Parmar Broccoli is a type of cabbage, so *technically* the visual wasn't wrong lol
@tohopes 6 жыл бұрын
Broccoli is not a type of cabbage. They're different varieties of the same species. Stop.
@antman7673 6 жыл бұрын
AERO BLKHWK32 surely broccoli is made of many small leaves of cabbage.
@shrimatkapoor2200 6 жыл бұрын
The cabbage looks like brocolli
@blazebluebass 6 жыл бұрын
In what universe does a farmer keep a wolf?! Cool video! Always interesting to see these problems being projected by geometry so solve them.
@housellama 2 жыл бұрын
Most farmers keep Canis lupus familiaris. Only the sub-species differ.
@Mrqwerty2109 2 жыл бұрын
Learned about this problem from Professor Layton
@InvadersDie 6 жыл бұрын
A wolf would happily eat a cat.
@wierdalien1 6 жыл бұрын
InvadersDie cat would also be comfortable taking out rabbits
@Theraot 6 жыл бұрын
A wolf would be happy to eat grass ... ... As long as it was in the stomach of its prey
@mikejohnstonbob935 6 жыл бұрын
tis like a graph coloring problem
@doodelay 6 жыл бұрын
I'm convinced that math problems are more fun then physics problems because they can be as playful as the one who imagined them but the generalizations are so profound
@EnginAtik 4 жыл бұрын
Conjecture: Define a measure for the nodes to belong to a vertex cover as: number of loops they are part of plus number edges they have. Remove the node that has the highest measure from the graph by zeroing the row and column that belongs to this node in the incidence matrix. Repeat the process until the rank of the incidence matrix is zero. This will give the minimum vertex cover. Measure = diag(a*a) + a*ones(nodecount,1), where a is the incidence matrix.
@EnginAtik 4 жыл бұрын
Also going to the other side of the river and and coming back is the same thing. It is symmetric: if you film the successful boat crossing and watch it backwards we will note that nobody eats anybody this time either. This symmetry could be useful in figuring out whether boat size should be one more than the minimum vertex cover.
@2supertux 6 жыл бұрын
what if the wolf decide to not eat the mouse ? like chewbacca with the porg
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