วีดีโอ

subbed for random french

16:32 😂😂😂

The number of digits (or bits) in a number is actually log n, so, by that argument, the linear implementation should be O(n log n) rather than O(n^2). However, the nth fibonacci number is proportional to φ^n, therefore, the number of digits is in fact O(n log φ), which means O(n^2) is correct.

is the knave/knight solving question really the solution though? if i asked the knave that, and he *was* giarding the castle, would he not just lie and say no? i thought the solution involves asking one of the guards about the other guards.

5:30 “hawk tuah”

6:40 lol

Hey, great video, just one thing I'd be interested in (I'll prob try it myself), how long does the final algorithm take to calculate the (2^25-1)th fibonacci number? Edit: just watched the last part. F, now I have the urge to use a custom complex class or sth to test it

For the challenge 3 should be possible. I’ll take another look at it tomorrow :)

The answer of lower bound is 4. I have discovered a truly remarkable proof which this margin is too small to contain.

Sheeeeesh! This problem ALWAYS eluded me, no more!!!

give 'em the 5:30

i understood less than 5% of what you were up to, how do you go from "add two numbas, get fibonacci" to whatever happened at 18:04? enjoyed the video, stayed for the sass. will be back.

Man, I am stupid

I haven't watched the video yet, trying to work through the puzzle myself. And I think I've found a problem. Suppose I ask A "If I were to ask B <question>, would they answer foo?" If A would be the random person, they would respond with foo or bar. If B would be the random person, then A couldn't respond with foo or bar, because doing so would imply that A can predict the randomness of B.

really nice video.

simple, ask what is the value of pi. If they say 3, they are engineerings. If they say 3.14... to 14 decimal places then is a physicist because "the result will work for the radius of the universe". If they write an infinite series, they are mathematicians

Well, you are limited only by the output speed of the medium you want to output result to. You can precompute maximum supported number and output it,

I wish I could hit the subscribe button twice :( anyways I'm going to try beat the hard mode high score!

“is foo yes” also gets you the answer in the easy problem

In reality you can only guess Charlie because communication between Alice and Bob is always encrypted.

My hype moments where when you revealed that the -1 makes the sequence always converge, and when I realized the very definition of ordinals force every decreasing sequence to converge

You really had me at “lookup table”

I would love to see an information theory video or article on the tiktok challenge thingy with the 5 colored balls and you guess the color of each ball and then they tell you how many correct you have. (PLEASE)

Great video(since im a hs student i understood close to nothing, but yea xD)

Hamburger

limitless puns i’m dying

My question for the simple form was to ask Alice "Will Bob say Foo if I ask Bob whether Alice studies Mathematics", I think it works the same in that Foo/Bar become irrelevant

I think I can prove it at least confidently say that 6 is the lower bound for the challenge (i do not have an example for it). That is because by knowing who the philosopher is we will (most likely) know what is the word for idk, therefore we already need to be able to tell 72 cases apart instead of 24. Moreover we can divide by 3 only once bc in one assumption we know what means idk and then only yes/no answers are meaningful, and in the other assumption we know what doesn't mean idk and then even learning what idk means would bring uncertainty about answers from 4 to 2. Sadly i can't do it rigourously

this was amazing! i want more high-level math like this always. keep up the amazing quality, i know i will be seeing the next one!

Huh?

Please can you make the bit at 16:35 ish a short/separate clip. There may come a time i need to send it to someone…

There's an issue with the PR update-scoreboard action btw!

Another way to think about xor is identity, like if a implies b and b implies a, they might as well be the same thing, meaning we could ask "is the knight guarding the castle" Knight/castle: yes Knave/castle: yes Knight/dungeon: no Knave/dungeon: no And, likewise, "is the mathematician a Foo Truther?" Math/Foo: Foo Math/Bar: Foo Phys/Foo: Bar Phys/Bar: Bar

10:30 why would asking politely change the result? Holding a Red Flag up and asking the Knave "would you say this is red?" should never result in a "Yes" (feels like the words receive some extra portion of logic operators) isn't the usual way to "solve" this to ask: "would the other guy say Left leads to the Castle?" -> if Left leads to the Castle, asking the Knight would result in "No" (as the Knave asked directly would lie to you) -> if Left leads to the Castle, asking the Knave would result in "No" (as the Knight would tell you Yes, but the Knave lies about that result) -> Right Castle, asking Knight results in "Yes" (as the Knave asked directly would tell you "yes, left leads to the castle" which is a lie) -> Right Castle, asking Knave results in "Yes" (as the Knight would tell you No, but the Knave lies about that result ) So, Yes -> Right Castle, No -> Left Castle this way you use the negation in the behavior to streamline the results and not interpret a politely asked question differently than a normally asked one. Edit after writing the comment below this one, the key is not the "Would you" the key is to map the "true/false" result into the question: So instead of "would *you* say Left leads to the Castle?" we have to ask "would you answer 'Left leads to the Castle' with True". this makes the asked person evaluate "left leads to the castle" first and then compare that to "True" -> Left Castle, asked Knave -> LLTTC would be answered with False, False==True? -> Result: True (as he lies about it) -> Left Castle, asked Knight -> LLTTC would be answered with True, True==True? -> Result: True -> Right Castle, asked Knave -> LLTTC would be answered with True, True==True? -> Result: False (as he lies about it) -> Right Castle, asked Knight -> LLTTC would be answered with False, False==True? -> Result: False

I love you

Just wanted to say this is extremely well made, in particular the hints and pushes to solve the problem for yourself and spend time thinking about it - looking at easier analogous problems and showing how someone solving the problem might come across a solution all make this a really well made video!

God I fucking love this channel

6:51 I think I found a way to get the correct answer by asking two questions Question 1: Determines is he a Knight or a Knave? The question which I will ask is something which is a universal fact and everybody agrees upon. Just for the sake of argument let the question be "Is water a universal solvent?" The Knight will say Yes while the Knave will say No. Now, that we know who we are dealing with could be a Knight or a Knave we can Easily determine which gate leads to which. My thinking was to ask a question on which both of them don't agree on!

Can't believe watching this made me understand a chess video more lol

thanks for yelling, i was cutting my cuticles instead of paying full attention to the screen, im sorry, it will happen again

The question wasn't "how to solve" It was how many questions you need And I paid attention to the lecture 24<2^5

Something a little interesting. You said your solution to the challenge uses 7 questions and fully determines the system. There are 4!*3! = 144 possible configurations of the fields and responses, and 7 bits would have 2^7 = 128 possibilities. So your 7 question solution actually gets a little more than 1 bit worth of information per question. Which can make sense given that there are up to 3 possible responses per question.