A riddle of ice and fire dragons - Henri Picciotto
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- čas přidán 28. 03. 2022
- Practice more problem-solving at brilliant.org/TedEd
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It’s your first day as Center Realm’s official cartographer, and you’ve already got a big problem. Center Realm is home to three elder dragons: two ice, one fire, and they’ve lived in harmony for centuries. But scouts have sighted three fire dragons and five ice dragons flying towards the region. Can you figure out where to place the new dragons? Henri Picciotto shows how.
Lesson by Henri Picciotto, directed by Igor Coric, Artrake Studio.
Try your hand at drawing the new dragon regions with these downloadable (and drawable!) maps: bit.ly/TEDEdMaps
Henri Picciotto is a math educator, retired from teaching after 42 years in K-12 classrooms. He maintains a website (www.mathed.page) and a blog (blog.mathed.page) for math teachers, including many online and downloadable puzzles.
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sure thing
I already know I can’t solve this lol
Wow
Heads up Ted-Ed, the second riddle's rules still says you can create 3 new regions when it is meant to only be 2 in that one.
Marvelous!
Man, first he risks his head on a jousting competition. Then he risks his head polling for votes. Now he risks his head arranging dragons? Give him a break!
He'll probably risk his head again, someday...
Why does he keep taking such high -risk jobs?? Don't forget when he was the giant's baker and could've been eaten
@@TheAlps36 different elf
Yare yare daze (or yare yare dawa if you're female)
ozo
This character feels like an anime protagonist, underqualified yet still does everything right
I am actually interested in how fast this character is doing the math to save his head🤔
No... it feels like a one-armed person from a game where they have 3 siblings.
Mary Sue
Unrivaled
Unequaled
Me: Does everything wrong. Starts the age of the Dragon Wars. Is the reason for the protagonist.
If only there was a fourth type of dragon, that way every map is solvable!
Is that 4-colour map problem mate ?
Unless you are limited on quantities of each one, which is a case here.
but then of maybe yes idk but eh prolly ngl
@@garin6482 I... Uh, what are u trying to say lol.😅
They would probably live in a kingdom that has five regions all touching each other
We now have a ted-ed universe with recurring characters
The TCU has been around for a while now
We had a crossover episode with the demon of reason one time
The multi-dimensional riddle also had the unstoppable blob
@@noahmasoodi1035 And the eggs feature in multiple riddles
The demon of reason has also been around for a while now.
Our little buddy is really failing his way up the ladder of success.
Wouldn't be surprised if he's the one getting elected in one of these puzzles one day!
He's really starting to breakout in this series, isn't he?
@@adamsiq4851 I think so. So far, I’ve seen him in a total of 3 Ted-Ed riddles, including this one.
Ted-Ed puzzles have lore now, no denying it
Wow they actually acknowledge this
@@dannyluo2077 yep. dragon jousting, fantasy election and this one
Score keeper, professional polling agent, and now cartographer... we must be the best user of a quill in all the land for us to keep landing these jobs
Life was way much simpler when the only ice, lightning, and fire elder dragons I know are Articuno, Zapdos, and Moltres.
None of those are dragon types though.
You could have said kyurem reshiram and zekrom!
@@xavierbegerow6402 When i knew kyurem reshiram and zekrom life wasnt that simple anymore :( .
Yup
@@BonScott1995But then, there was Dragonite, Charizard, and Dragapult.
Honestly, it seems like getting your head cut off is a common form of punishment in the realm and doing anything warrants it.
"What did this man do?"
"He stole a piece of candy!"
"Off with his head!"
That really is VERY True
The subtle Trogdor reference is so top tier. Thank you TED-ed!!!!
Right? I actually laughed out loud at the thatched roof cottages
Thatched roof cottages!
And one of the fire dragons had one big muscle-y arm.
t
e
That second island was surprisingly picky considering they were under constant dragon attacks. Also it's lucky the dragons numbers are never mentioned or this riddle be much harder.
It said on rule 3: 7 ice, 6 fire, 4 lightning dragons
Your boss thinks you did a great job so he exiles you to another continent.
*Correction:*
At 3:17 the rules text mistakenly says add "three" new territories to the kingdom of Westia instead of "two" new territories.
I found this out just after i finished solving with 3 :(
I noticed that too.
@@sean_haz How do you solve with 3? you will end up with 18 total regions instead of 17
@@ThomasEdits yup, I did it with two afterwards. It's easier with three of course since you have more options.
It says Two though
I love people pointing out the little errata in the second problem at 3:10.
But can we talk about the fact that their country is literally burning to the ground, yet they still can't accept more than 2 new regions inside their borders ?
"3 ? 4 more regions ? Nah, we'd rather die, thank you tho !"
That is exactly what I was thinking
When you get it after three minutes of intense trying: "Where's my award?"
May we humbly present you with your Riddle Solving Prowess Award: 🏆
yoooooo me too
@@TEDEd Why not conduct it at a ceremony?
this is beautiful
@@TEDEd a core memory
4:50 The four colors theorem also has far reaching applications! We allocate radio frequencies using graph coloring
SPOILERS:
When I realized that a triple intersection meant an impossible solution, all I needed to do was find the total number of triple intersections. There are 6, so I realized each line needed to start and end at an intersection. First option I tried yielded 5 Fire, 6 Ice, so I changed the permutation and got 4 fire, 7 ice!
And that's right.
I never thought I’d hear a Homestar reference in a Ted-Ed video.
BURNINATING THATCH-ROOF COTTAGES 🐉💪
As soon as i heard that i had to look in the comments to see if anyone else heard that lmao
The burninating dragon at the 3:05 mark has a beefy arm sticking outta his neck there.
@@kathrynlynnkipfmiller9110 no consummate v's :(
3:18 - the rules say 3 new regions, but this time it should be 2
Now that I have done these two, I want more puzzles like this to solve and will have to visit the website! There's just one typo in the second puzzle's rules - should say two regions instead of three not to confuse, but a minor issue in yet another brilliant Ted-Ed riddle!
4:01 Technically, there is a 4th such set of 4 regions that all mutually border. You take regions 1, 2, and 4 of the top left cluster, and not only to all 3 of them border the region labeled 3, but they also all border the large green region on the north shore. The big white region just borders it on the right side. But I think any cut that remedies the top left group will remedy this sub-group as well.
Time to try (and fail) to solve another TED-Ed riddle!!
There's a mistake at the rules section of the second part 3:19. It says you can add 3 new regions but it should be 2. Anyway this is a great video! Thanks Ted Ed :)
Actually, I think they should have spoke 3 new regions.
@@Yusuf-ke5iu No its 2 in the 2nd one. Their solution also only provides 2
The solution carves 3 new regions from the original territory using 2 subdivisions
@@IconOfSin no there is only 2 new regions he hade 1 and made 3 out of that one so only 2 new regions was created.
Indeed! I tried to solve it with 3 new regios and found there was an extra region available xD Maybe they want a region free of dragons? They do cause a lot of trouble.
I am very pleasantly surprised that not only did I solve the first puzzle, I came to the exact same solution Ted-Ed did!
Anyways, I think there is a mistake in the video. 3:09 says that only two regions can be created, but the rules in the next slide say three can be created.
There's no mistake. The white region in 4:19 was just 1 part, then u make it into 3 parts. So it's making 1 -> 3, or basically two more regions were created.
One thing so good about this kind of riddles is that there are only few possible answers. And it sounds impossible really...but it is solvable ..that's what makes it more worthy compared to other riddles ...other riddles are so diverse there are so many possible answers to other riddles.
Ted-Ed riddles are...better and more legit
Kings: *allow for only a small number of regions to be created*
Dragons: *start fighting*
Kings: *surprised pikachu face*
Your heart fills with satisfaction when you solve a "ted ed puzzle"..
This guy has fixed so many problems in situations where they'd have his head if he failed... he needs a break... or at this point just let him run things, he clearly gets the job done
We're seeing a story of success here, wonder what new roles will he take on. Cheers to reaching personal goals
The first one I solved in another way, still working and according the rules, sure.
The second one was equal i made! I just changed one of the divisors a little bit. I made kinda a incomplete circumference, still working too.
Im so happy I solved it alone! ♡
Riddles are amazing 👏🏻👏🏻
A fantasy world where there are three elemental dragons, being ice, fire and electricity? Now where have I seen that before...
Edit: this comment is from a year ago, but I want to confirm now that yes, I was thinking of BOTW :)
Elden ring😁
Breath of the Wild?
Pokémon??
@@yartastic Groudon, Kyorge, Rayquaza
@@edyrahman2208 groudon is ground type, kyogre is water and rayquaza is flying/dragon...
Elder dragons : assign our territory and dont make the same element border each other
Lil goblin : i have *GREEN* eyes
Elder dragons : ... thats a good point
TedEd getting real comfortable with these two-part riddles.
I like how goblin is just a proper Ted Ed character at this point
Someone at TED-Ed is very happy to be using their Graph Theory college class into use.
I just took a combinatorics course and it served me well in solving this puzzle. The first puzzle is relatively easy, it just need to add to lines to make the dual graph bipartite. The theorem said a graph is bipartite if and only if there is no odd cycle. A odd cycle in dual graph means exactly an intersection with odd number of edges, so removing those solved the problem. The second puzzle is a bit more challenging though. It need to make the dual graph 3-colorable, which means it must not contain subgraph of K4 by Hadwiger conjecture. With these principles, the problem is not too difficult solve.
Glad to have riddles back!
Ah yes, the plight of the medival days. I love learned about the lives of those before me.
I heard a TROGDOR joke. You made My day and you made me feel old thank you.
Love the Trogdor reference!
That was a really fun problem to try solving & the explanation was greatly amusing to watch/listen to :D
I’m glad I left my old job, I wasn’t good at that scorekeeping gig
There's two errors regarding the second puzzle:
- the recap says three new areas may be added although the introduction and solution ask for two new areas;
- the solution states three configurations of 4 areas all bordering each other exist, although I was able to find at least four such configurations (the two top right areas, the great center area and the top leftmost area all touch as well).
I missed ur riddles so much
This is first of these riddle videos that I actually solved on my own. Yes, both of them.
I love the VeggieTales version of Lord of the Rings, especially the Eagle.
"Ow! What was that? 'Oh, there's a bird! Let's jump on him! He'll fly us anywhere we want! Maybe he'll give us drinks and those little bags of peanuts!' GET YOUR OWN RIDE!"
love every one of their riddles
I like these compound riddles. Keep it up!
Ted-Ed: "Connect the meeting points together to separate the dragons."
My Gerrymandering A--: Let us draw two circles in the Northern region, not connected to any other territory, and just divide the south so it goes Ice-Fire-Ice at the very bottom.
3:15 there is an error in the second riddle, the narrator says that you can only create new 2 regions but the image says 3.
You need to go with the image's rules to solve it
When I saw ice and fire, I immediately clicked the video thinking to find a riddle of A Song of Ice and Fire.
Tough, yet marvelous.
I actually managed to found one- making a map but with squares and use the side dragon as a base. Start with the possibility of the smalles amount of dragon(fire) and work with the existing line to find where the last fire dragon should be (the 2 first fire dragon will be next the ice dragon in the side so) and after that the answer will reveal itself. For the second the way is also the same but with a little twist, start with drawing the map then put an initial in one of the box and work your way out, if there's no possibility you just need to divide it and you'll find the answer eventually
Ahh i love you these riddles 🤩🤩😁❤️
Love your riddles
I've been waiting so long for a new riddle
From a poller to a dragon hunter. Wow.
i like this riddle because you can just do it by guessing and checking, whereas some of the other ted-ed riddles i just stare at the rules stuck forever.
Ted Ed should make a another series like "Think like a coder" Man I loved that
First ted ed riddle solved :) I feel so proud
The TED-Ed Riddle Cinematic Universe is starting to form, hopefully better than the DCEU and the MCU
I spent more than two hours figuring this thing out.
I accomplished BOTH correct.
The more important thing is, I still did it.
I went drawing broders along rivers, mountains and other logical geographic landmarks.
And then remembered I was supposed to house dragons in a magical land where people draw circles as regions...
thatch-roofed
NOBODY ASKED FOR THIS MUCH LEVEL OF DETAIL, BUT HERE WE ARE.
THATCH-ROOFED!
Love many riddles provided by Ted . They help me improve my critical thinking so as to solve the problem and therefore becoming one of my advantages for another progresses
2:40 F in the chat for the ice dragons with those rly small landmasses-
i got this one! thanks vi-hart and your doodle games, somehow those helped me :)
Nice voice it mixs well with the whole channels
2:35 pretty sad for 2 of the ice dragons
these 2 got a very small region
ted ed riddles have been tricking me into doing math for too long
with this series of riddles where I am this little troll, i would've lost my head the first day
This thing lost me at “the matching dragons will go on a rampage” at the beginning 💀 I can’t process that fast 😭
Oh wait. I rewatched it 💀💀💀 I get it now
What if you subdivide right region 2 into 2, use the fire ice method and surround them with lightning? Wouldn't that be another way?
This was *cool.* Thank you
This place seems to really love chopping heads, makes you wonder what they’re planning
This guy's kingdom is literally on the break of COLLAPSE and he is like "um you can only change our borders a little bit"
{ وكأين من دآبة لا تحمل رزقها الله يرزقها }
ملايين الكائنات بلا جيوب ولا خزائن ولا أرصدة تنام الآن دون أن تشعر بالقلق لرزق غدها ." ❤
د. عبدالله بلقاسم
If I were him, I’d contemplate fleeing to a place where I won’t be decapitated for trivial things!
The little guy really gets a job in which he doesn't get fired but gets beheaded if he messed up instead
mom come quick teded just dropped a new riddle
This video is a two-for-one special!
For starters any intersection point that is incident to an odd number of land regions is problematic. On this map we see 6 of those points. Also note that every border you draw will have a start and end that should intersect a border (could also be itself). If between start and end it does not intersect any border, then a single area will be created. So when creating a new region you should make sure to draw a border between unique pairs of those 6 intersection points or you will run out of area's to draw to prevent conflicts.
Drawing borders that go a bit diagonal will quickly make it difficult to get all 3 pairings of the aforementioned 6 points. You could draw 3 horizontal borders, which leave no room for conflict, if there were 5 fire dragons and 6 ice dragons, but that's unfortunately not the case here. The trick is to draw 2 vertical borders and a horizontal border. To be more exact the two vertical borders must start and end on a single border segment (a portion of an existing border between two intersection points) and those border segments must be incident to the same region. The horizontal border will simply connect the remaining pair of points.
This allows for 4 different ways to solve this riddle:
1) Horizontal border through the southmost intersection points in Arnia, two vertical borders through Meddia.
2) Horizontal border through the southmost intersection points in Arnia, one vertical border through Meddia in the east and another vertical border through Sonna in the west.
3) Horizontal border through the northmost intersection points in Meddia, two vertical borders through Arnia.
4) Horizontal border through the northmost intersection points in Meddia, one vertical border through Arnia in the east and another vertical border through Sonna in the west.
The second one is not as obvious. However the larger region adjacent to the tower region is adjacent to a lot of other regions, so that should probably become a lightning region. Because then all those other regions will have to be either fire or ice. If you chose the tower region as ice and keep the large center region unassigned, then there have to be 3 regions ice, 2 fire, and 1 lightning in the regions above the big center region.
The regions below the center have one region that can be assigned differently from all the others, so we make that lightning as well. The region is the one closest to the sea dragon. There are an even number of regions left, 2 will be fire and two will be ice. Just chose the one that does not border the center area as ice in the hopes that the center area will also have ice regions, because those need to be the highest number.
The regions right of the center region will be 1 lightning, 1 fire, and 1 ice, but which will be which is not yet clear. However this does mean that 1 more lightning, fire, and ice dragon could exist somewhere in the center area.
The largest region in the center seems to cause all the conflict so there we should probably create the two new regions. Since we want all types in this area we need to split it such that each can be represented. Only one region above is a fire region adjacent to the center region and it as all the way to the left. This fire region can be sort of separated such that it no longer borders the same center region as the ice and lightning regions. Also note that that below are fire and lightning regions that can border the same piece to create an ice region. However there is also an ice region below that must be separated from this piece to make it work. So we start drawing two borders from intersection points with ice regions so the no ice region is adjacent to the new left center region. The borders should probably end in the right regions intersection points. So only one of those three regions is adjacent to this region. Above this new ice region we also created a region that has to be a fire region. Below this new ice region we created a region that has to be lightning. Now the regions on the right can be assigned in two different ways, which I am sure you can the reader can figure out as well.
Very subtle Trogdor references. 😉
Props to him for not even quitting his job after all the times he have to use his brain or death
Im surprised the two ice dragons werent mad they were given such small territory compared to their neighbor. Still have some manners
for the ending puzzle, its because a fully connected graph with 5 nodes cannot be planar. this also applies to a 3,3 bipartite graph, but thats less relevant
bless you for the trogdor references
Region: We're being devastated because our dragons aren't alotted proper boundaries!
Same Region: We refuse to reshape our territories in any meanigful way and will only allow TWO new territories to be formed >:(
The governments of these islands have an interesting approach to survival.
Anyways, good riddle.
Another riddle back in that cool Fantasy world that looks like something out of lord of the rings
Glad to see one dragon has a beefy arm burninating the peasants and thatched-roof cottages.
Oh yeah, check out all his majesty.
Great introduction to Graph Theory
I did the 2nd one quite differently. I subdivide the big area only in 2 and broke up one of the 3 east districts
Don't you love it when someone calls a math problem a riddle
This little goblin can’t ever catch a break! 😅
My barbarian brain not really wanting to do any math:
I guess we're fighting these dragons then!
first half: ok i got this!
teded: but now there's three types
i'm not equipped for this teded
I finally solved an entire episode of Teded riddles on my own. It’s been a while since I’ve last done that.
this goblin is popping up more and more in these riddles
Is this a metaphor for life??…this is a metaphor for life.
I can’t believe he risked his head on so many things.