The River-Crossing Puzzle (Dino + Santa edition) 

Santa should fly on his sleigh across the river

Loved the generalizing of the solution at the end there, but I wonder, what if we adjust the number of people rather raft can carry? That expands the number of movement vectors we get so I can imagine that we would get different solutions. Is there any point at which we would need more rafts, or does that stop once one extra person can get on?

omg this is such an interesting way to visualise the puzzle! i wonder what other similar puzzles look like on a similar graph

I’ll keep this in mind next time I’m visiting the North Pole in the Cretaceous period

As a Yoshi, I’m glad carykh is finally giving us some representation.

8:20 no way!!!!! Jokes aside, this is a really cool visualization of this problem that I never would’ve thought of. Great video as always!

8:58 Cary's getting too real :P Love the video!!

Pretty neat visualisation, would be a fun project (for me, or someone else) to write a solver using these heuristics, given an 'n' input, output an array of vectors of each step Also, I guess you chose this version of the puzzle (or, TED-Ed) because its the easier one to visualize and reason about, while the other versions are more nuanced, like the one with the farmer, wolf, goat, and cabbage, or the one with a whole family that is super weird

Love this new style of video editing, Cary! I can tell you had fun with little bits like the "so wasteful" voice in the background lol

i love the visualization, i never would have thought about it this way. your videos are the best

So great! I feel like I'm actually understanding the world in extra dimensions. P.S. I still show your scale of the universe to my students every term.

I love your algorithm videos and how you explore the concepts visually, so glad to see them return!

I like how it shows these visualizations can offer insights that are hard to see by just thinking through it.

8:56 dang that got deep really quick... Had to solve this problem in college using PROLOG. Never fully understood how that worked.

1:32 Ha, I knew you would slip and call em Yoshi's at least once! Cool Yoshi models btw, honestly clicked for the Yoshi, wondering what it was doing here in a puzzle video

Love this visualization, that it generalizes to an arbitrary number of dinos, santas, and rafts, and that you can be confident you didn't miss any alternate solutions! :) Fantastic video!

1:30 He got tired of saying dinosaur and finally saved our souls

I am really loving this method of visualization, it’s just one of the simplest

Yoshis: flutterjump across the river Santas: use their sleigh to fly over the river Raft: :(

1:17 “-in their journey, the Dinosaurs can’t help but eat the Santa, killing him.” (Childhood Memories of Winter plays)

0:42 “None of these creatures can swim.” (Childhood Memories of Winter plays)

this is really satisfying to watch! seeing how you dissected the graph to show the solution was cool

I've been working on a similar thing, making data visualizations for the puzzle "signpost". the terminology of graph types that you mentioned will definitely be useful to me. thanks!

I would really love to see this with other bridge crossing problems like the lamp and torch one!

That is a very cool way to find the solution! And you mentioned the graphics library you used, thanks for that either! Thanks for the quality content!

This is amazing! Especially the generalization part.

I was thinking about the river puzzle quite recently. Nice to see a mathematical explanation behind it. I love math (except when I was taking soul-crushing classes in college)! Also, it's nice to be early for a video.

would never think to see so many tautologies of the river-crossing puzzle being fleshed out in one comfortable niche since this interpretation of the experiment would agree in every aspect

Insane visualization !! Great work !

Yeah this video makes it so much easier to understand than the ted ed video especially with the higher level crossings

Excellent video about an excellent solution 👍. I hope you will keep making videos like this!

Happy 2023, Cary. That one is a nice puzzle there.

the whole of the universe tends towards entropy, and this is just one example. you're welcome. 10 points to me.

hey cary! im going into highschool soon and ive been watching your videos all throughout middle school! your videos got me interested in programming and ive been learning python! thanks for inspiring me so much and I want wait for the next upload!

Yoshi: how do we get across this river Santa: I know graph theory Yoshi: why? Santa: I've solved the traveling salesman problem

Very nice visualization and generalization!

I realized the Hazbin Hotel reference with Angeldust!

3:51 This bit reminds me of the part of jan Misali's video on regular polyhedra, specifically the part about zig-zag/skew polygons

There's a variation on this puzzle I saw a while back that is probably easier. You are a farmer with a Wolf, Chicken, and bag of corn. You must cross a river with a boat that only you may paddle and may only hold one item. If the Wolf is ever left alone with the Chicken you die and if the Chicken is left with the Corn you die. The Wolf may never eat the Corn however. [Solution Below] The solution would be to row the chicken over first then come back with nothing, then to row the wolf over and come back with the chicken (the wolf doesn't eat the chicken since you are there) then take the corn immediately back to the wolf and go back then take the chicken across.

0:39 FIREY UNDERWEAR!? That’s my kidnapper!

Beautiful!

It is really interesting to see these type of videos after a semester in college full of classes with stuff like this

I remember learning something like this in class one actually.

1:23 the echo🤩🤩

0:40 this is the most cursed firey i have ever seen. Fire boiii

Me and my homies when we have 30 santas 30 dinosaurs but only 27 rafts: :(

Happy birthday Cary!

6:54 “There’s ZERO Santas.” (Surprised trombone sound)

Ted-ed is exactly why I know this! One of the first riddles I’ve learned AND solved actually!

*Yoshi is eating Santa* DEATH P.A.C.T. (Both Past and Present): Not on our watch

no santas were harmed in the making of this

1:30 as a fellow yoshi im glad he showed us some respect

another day of carykh beating TED-Ed at problem solving :)

Happy late birthday Cary!!!!

Really cool visualization. I remember playing a game like that as a kid, except it was with sticks, wolves, goats and cabbages. I don't think it would be possible to make it into a similar graph if there are more than 2 kinds of creatures

thanks for the 3 am upload while I'm awake with covid, appreciate it my man

Happy 26th birthday Cary Huang!

1:31 Cary accidentally said Yoshi

This video was pretty interesting as I stuggled with the puzzle before, this video help me though. Very cool graphing from the origin

You are the very last person I would expect a hazbin hotel reference from. Not complaining though

I am so stupid I didn’t understand this but it was very entertaining to see you figure everything out!

0:39 Firey's Underware

I love the visualization

Never seen this version of the puzzle before. Think the only one I heard of was about a fox, a chicken, and some grain 🤔

Very glad the santa eating dinosaurs are extinct by now would have been disastrous for christmas.

1:08 "The dinosaurs still have this biological urge to eat humans." -> Sorry, they don't. They had never the opportunity to develop such an urge 😉

I didn't expect this to be coded in Processing . I knew it was capable but not that capable!+

wtf? kary KH science video again? finally!

from the thumbnail i somehow thought this was a veritasium video until i was like “wait that sounds like cary!” lmao anyways that’s a pretty (and) elegant solution ngl, cool work!

i love how you expanded the problem

im just happy to see that you also use processing

move #1. move 2 dinos | move #2. move 2 santas | move #3. move the remaining santa and dino

Omg, Cary is a Hazbin fan?! 8:22

900 IQ way to tackle the problem

Oh look it’s yoshi! Hi yoshi! Anywho, this is a great visualization of the river crossing puzzle!

You just had to throw in the brief has Hazben Hotel referencesI love it

0:41 cary reveals the actual reason why i stopped using cyshi

Teacher: please concrentrate during the test Me trying to figure out how to get Dinosaurs and Santas on the other side of the lake

Easy solution. Get trees from the forest (on fire so be careful!) and build a second raft. 2 rafts that can carry 3 people. 2 X 3 is 6 so everyone goes free!

i really love the “comin to getcha moves”

your videos are always so cool i don't know what else to say

Noo!!! Now no one will have Christmas presents!

i love how hes just referend to the purple yellow and light blue yoshis as dinos even though if you look into yoshis they arent dinosaurs so cary your wrong I WIN

Love the video, nice use of visualization!

Hey! These are three YOSHIS! Not dinosaurs!

I like this MetaPerspective solving

This is such a good way to visualize

Clicked for the Yoshi, stayed for the graph theory.

I am always exited when he uploads

The puzzle i heard of as a kid had a farmer, fox, chicken and a bag of corn. For some reason he wants to take the fox with him. And no it's not a pet trained fox it does want to eat the chicken. And oh boy the chicken eats fast so not leaving it with the corn. Also. The farmer needs to be on every trip, the fox is also not trained to control the raft.

This is a fantastic visualization! Cheers

"n Santas and n dinosaurs can cross iff we have n-2 rafts" ...that would imply 2 Santas and 2 dinosaurs can cross without any raft at all

The Yoshi’s Are Looking for a Meal Let’s Protect the Santa’s While Also Saving the Yoshis

Yes dinosaurs are my favorite mario character

8:20 every state that can be explored hazbin. (Bottom left)

Out of everything, you did Santas and dinosaurs.

I’m happy Yoshi’s In this :D. Also Cool Puzzle!

I was playing with nice sounding chord progressions and I went to hooktheory to find if mine was already used. I proceeded to get distracted and I went to see what is the most common chord progression in A minor. I then found your more lasers and thought to myself that your profile picture was familiar. It seems I have seen some of your videos before and now I am here.

I'm quite sure that, if Santas out number the dinosaurs, they will f up the dinosaurs for what they are. They are old and wise men.

Graph theory gets a bad rap; this approach feels a lot more "right" than the guess-and-check method of searching. Also haha love the allegory