Audrey was like: I want learn math, why me out? Cute

Brady: [picks 3] Ben: You didn't pick pi, right? Brady: [lies and says no]

@choiie

3 жыл бұрын

Found the engineer

@danielyuan9862

3 жыл бұрын

If he says yes the he'll give the number away. What else could he do?

@SeanCMonahan

3 жыл бұрын

π ≈ e ≈ 3; sin(x) = x

Fun fact: this is not the first time Audrey has been on the show. Audrey appered in the langtons ant episode

@drenz1523

3 жыл бұрын

Audrey had been also at the random Fibonacci sequences with James Grime at Numberphile

@NoriMori1992

3 жыл бұрын

Yes! And I always loved Katie Steckles's reaction! "Hello! Hello, tiny dog! 'It's a different person!'"

@Triantalex

5 ай бұрын

false.

I want more Audrey.

How could you send that cute rat away!

@DROSTraceurADD

2 жыл бұрын

Yeah I didn't get that sudden hate either

@null8507

2 жыл бұрын

The cutest rats give me rabies 😍

@Triantalex

5 ай бұрын

??

awww audrey just wants to be included 🐾

@marcbogonovich3974

3 жыл бұрын

Audrey is my number :(

@HumbleNewMusic

3 жыл бұрын

@@marcbogonovich3974 👊🐾

The least impressive: doing this with a coin

@skulliam4

3 жыл бұрын

Even less impressive: a mobius strip. You don't ask any questions and you can already guess which side they chose.

@tomkerruish2982

3 жыл бұрын

@@skulliam4 There's a company that makes Möbius strip dice.

@Logicallymath

3 жыл бұрын

@@tomkerruish2982 really where?

@tomkerruish2982

3 жыл бұрын

@@Logicallymath Awesome Dice, which makes both plastic and metal versions. Unfortunately, they're currently out of both. I literally have no idea if they'll make more, although their website has a "notify when available" button, so presumably they will.

@Logicallymath

3 жыл бұрын

@@tomkerruish2982 oh cool thanks!

Even knowing the maths, the fine motor skills required to pull the trick off blindfolded are super impressive.

@Kalumbatsch

3 жыл бұрын

Fine motor skills like rotating a cube that you are holding in your hands? Do you have to look at your shoelaces while you're tying them?

@SeanSMST

3 жыл бұрын

@@Kalumbatsch No need to be sarcastic about it. Tying your laces is a skill you learn and practice each day over years alone. The dice trick is harder with it being a party trick that you only use occassionally and have the social pressure to pull it off right first try. As well as that because of the amount of sides, you need to keep a mental note of the orientation changes as well as the maths involved, which gets quite a bit harder the more complicated the die gets. Even with all that, if you could have your eyes open it makes it easier to deal with. You're at least able to have your eyes open for card tricks and tying your laces, even just looking at your hands doing the movements and not the die itself is easier to handle. But having to be blindfolded too, with a party trick in front of others is commendable

@Kalumbatsch

3 жыл бұрын

@@SeanSMST It's really not that impressive.

@Danicker

3 жыл бұрын

I think Kalum has a point. It's not that the trick is easy, but it doesn't require fine motor skills. It requires spacial awareness and memory to jeep track of how the dice is oriented and where the possible faces are

@LouisOnAir

3 жыл бұрын

@@Kalumbatsch you're right, in fact I was just fishing for a like from the channel (and I succeeded)

We absolutely need more Audrey!

Poor Audrey. I'm so sad.

@mathwithjanine

2 жыл бұрын

Me too!

I find the rotation of the die to halve the solution space is more interesting than the binary search itself. That aspect seemed pretty obvious from the onset.

@renecura

3 жыл бұрын

Yes!

That reminds of the card trick with 27 cards Matt Parker showed. With that card trick you could not only find the card, but also put it on any of the 27 places with just three steps.

@vladimirfokow6420

3 жыл бұрын

Yes. Me too!

"I'm supremely confident in mathematics, and my tactile blind handling of a d8." [*GM scrutiny intensifies*] I wondered how you were getting so many critical hits... 🤔

For the d8, if you draw a line from each vertex to the opposing one, you get three perpendicular axes. Each “can you see your number” question has you looking down that axis, and eliminating half the values depending upon whether or not your number is in one of the four octants (like quadrants in 2D, but with 8) closest to you.

Poor Audrey. Although frequently admonished during maths lessons, i never got sent out. Harsh! 😉

More Audrey pls lol

now I know what to do with my d100 after being useless for so many years

@hotdogskid

3 жыл бұрын

I can just imagine your audience "uhhh hold on lemme find it real quick... n-no its not wait yes ok i can see it"

@jamesbowers5478

2 жыл бұрын

Finally it has another use other than for wild magic sorcerers

MORE PUPPY SCENES PLEASE

Could you do an interview with your animator Pete? He does amazing work and I'm curious how he does it.

@BlessedForever888

2 жыл бұрын

yes that would be awesome!

What a supremely cute doggo.

We demand Justice for Audrey, more dogs in Math.

@ThePurza

3 жыл бұрын

Audrey deserves better treatment

2:24 Audrey: Silly humans talking about dices while I have a proof to the Reimann zeta function

Can we get a video with just the dog? :)

@numberphile

3 жыл бұрын

Sure: kzread.info/dash/bejne/pWxoxqSooNavlZc.html

@coucoucoucou8321

3 жыл бұрын

@@numberphileHi

@volodyadykun6490

3 жыл бұрын

@@numberphile dog's role in today's video is a Parker square of a role

@Phriedah

3 жыл бұрын

@@numberphile Now this is the good shit

@jcespinoza

3 жыл бұрын

@@numberphile woah!! you're prepared for anything aren't you Bady?

Hey...I always love Maths videos by Maximus! We are always entertained!!!!

This is related to information theory: one yes/no question gives you at most one bit of information (if it exactly halves the set of possibilities). You need about 2.58 bits of information (base-2 log of 6) to encode the value of a six-sided die, so two questions (at most 2 bits) is not enough to get the answer, but three questions (at most 3 bits) is. For a nice textbook on this, checkout MacKay's "Information Theory, Inference and Learning Algorithms", especially Chapter 4. You can find it for free online.

if you remember the dice layout you can callout their number which is even more impressive

@angeldude101

3 жыл бұрын

If the numbers are indents, then it'd absolutely be possible to tell which number is which just by touch.

I'm so impressed with myself that I guessed binary search and halving possibilities in the first 31 seconds of the video

@miriamrosemary9110

3 жыл бұрын

Nice!

@mow184

3 жыл бұрын

You mean within the first 2^5 seconds :)

@capy9846

2 жыл бұрын

@@mow184 That would be 2^5-1

@vez3834

11 ай бұрын

@@capy9846 a Mersenne prime!

@Triantalex

5 ай бұрын

??

You definitely need to find a way to include Audrey as the subject of a future video. Some kind of Dog Maths :D

Nice extension for d6: you can also do it in 3 turns, sometimes 2, if you can only show the viewer 2 faces simultaneously...

If you're planning a campus LAN this is a handy way of isolating faulty nodes. In a pre-trouble shooting way. Oct-trees and K-D balanced and unbalanced trees work really well for lots of different apps.

6:00 Mathematical Puzzles and Diversions, the first book collection of Martin Gardner's Mathematical Games articles.

@mbakenemdusink9757

2 жыл бұрын

If ever my house burns down and I could save just one book... it'll definitely be this one

Really cool video, Brady! Gonna try this on my friends later.

Ben Sparks is awesome! Please more of him.

Anyone else watching this video and thinking damn now I really want a dice set with that colour and Numberphile-font numbers on the faces? It's money on the table, Brady!

@turpialito

3 жыл бұрын

Shut up and take my money!

No, let Audrey back in!! :D

This reminds me of the card trick with the three piles, I think you did a video with Matt Parker on it.

I'm liking these ben sparks videos

The biggest magic trick was that i picked the same numbers as Brady. What the hell?

I can't wait to try this one with my friends.

Thanks. I love these magic tricks, to do for my grand-kids.

I was confused about the first one, that's how you say 8 in Swedish sign language. I instinctively thought you were messing with him.

I'm not convinced you can reliably get a d20 in 5 questions - it's not easy to align one so 10 faces are readable.

Would love to see this trick with "dUltimate Dice" !

Main takeaway from this video: Ben plays D&D (or some tabletop RPG). Love it!

This trick would be even more impressive with two dice.

@galacticbob1

3 жыл бұрын

Now you got me thinking of a version where a person would roll (unseen) two dice, and then the blindfolded magician would roll two dice, and ask how far off the total is from what was rolled. Example: You roll a six and a four. I roll two dice and get a four and three. I ask how far off your roll is from mine, and you answer "three". I flip the four upside down, now I have a total of six, and your answer is "four". Since the total has only changed by one, I know that I must have changed a four to a three, since that's the only possibility for decreasing the total of two dice by only one. I also know that your number is 4+x+3, so I just need to work out the second dice in a similar way. Let's say I can only change one of my dice at a time. Knowing that opposite sides of a six-sided die add up to seven, how many iterations would I need, and what kind of algorithm, in order to correctly guess your number? That would be an impressive party trick, if someone could consistently do it in 3 or so attempts.

I love this channel.

I love how he's got a dice set readily available

I have that Martin Gardner book! But then, I probably have most Martin Gardner books.

@mbakenemdusink9757

2 жыл бұрын

Same here. Amazing books written by an amazing person

Figured out it was a binary search before he explained it. Finally, that computer science degree is paying off!

@publiconions6313

3 жыл бұрын

Of course binary search... just feels like these vids have gotten a lot less challenging recently

@vez3834

11 ай бұрын

@@publiconions6313 Maybe the videos are getting easier or you could be getting better! Or you aren't being realistic about how much easy stuff there was or how much hard stuff there is now.

@publiconions6313

11 ай бұрын

@@vez3834 I regret that statement .. heh, I think many of us don't recognize parts of ourselves a year ago sometimes

Hey, I have a question. Say I had someone’s property with a word on it, can I ask for the sum or product of all the letters in the word to verify the owners legitimacy? I.e. if it had “avenge” written on it, the sum is 54. The product is 53900. Which one is less likely to be guessed? Only 1 number would be provided.

We demand more Audrey

You must realize that you got a bunch of people a free beer at the pub lol

OH ..... i understand now that the opposite sides has the digits whose addition is 7 . means 6 & 1 2 & 5 3 & 4 . very interesting .

Numberphile needs more Audrey.

I really like the elegance of the d8 in this problem.

:( poor Audrey just wanted to learn about binary searching

Please recommend some Martin Gardner books!

Just yesterday I came across a puzzle that some people may enjoy trying. It goes something like this: I'm thinking of a whole number between 1 and 2000. Asking me no more than fifteen yes/no questions, determine the number I have in mind. Note, though, that you must provide me with _all_ of the questions before I give you _any_ of the answers, and I _may lie_ in response to _one_ of the questions.

And in the Extra Footage video, Ben plays 20 Questions with a million-sided die.

So any dice with X-sides needs at most N moves where N is the exponent of the lowest power of 2 that produces a number greater than X (D6 takes 3 since 2^3 = 8. 8 > 6)

We want you to introduce Audrey on Numberphile2 !

@numberphile

3 жыл бұрын

instagram.com/adorable_audrey

@frogz

3 жыл бұрын

@@numberphile we know, we all want videos dedicated to audrey!!!

That was fun.

WE NEED MORE AUDREY CONTENT

Poor Audrey didn't understand what she did wrong.

Related puzzle: In a town live 12 men. 11 of them are exactly the same weight. There is a seesaw in the town which can be used to reliably compare weights but it’s seen better days and it has only three uses left. Using that seesaw, determine which one of the men has different weight and whether is he higher or lighter than the rest of the people in the group. Why related? Minor spoiler: Because log(6) ≤ 3log(2) just like log(24) ≤ 3log(3).

Will it be enough to rotate around one of its axes? What is the minimum number of axes to rotate about, in order to arrive at the solution? Greetings from Venezuela.

More videos need to feature Audrey

We need more Audrey!

A lot of dice with this one ...at least he's not playing pool -- pool, that starts with 'p', that rhymes with 't', that stands for trouble.

That's magic!

Sending that cute doggo out of the room ruined my evening!

Check out Brilliant (get 20% off their premium service): brilliant.org/numberphile (sponsor) More dice videos from Numberphile: bit.ly/Dice_Videos More Ben Sparks on Numberphile: bit.ly/Sparks_Playlist

@user-ik2yi4fm1u

3 жыл бұрын

Zabloing

@frogz

3 жыл бұрын

we need a video of ONLY audrey!!! doggo video please!!!!

@playerscience

3 жыл бұрын

Numberphile, PIN your comment, Or else it will be lost.

id like to know if there is a function f(n) that gives the minimum number of guesses for dice with n sides

@RodelIturalde

2 жыл бұрын

f(n)=2^n n is number of guesses. The function then gives maximum number of sides for that number of guesses.

@azfarahsan

2 жыл бұрын

@@RodelIturalde noice

Now how can you do this trick (d6 version) turning the d6 only 90 degrees about an edge after each answer?

I swear I watched a video about this trick relatively recently, but I can't find where. That one had paper you print out that showed the exact instructions of how to move the D6 at each step based on answers---you don't need to actually remember which faces were visible at which time; you just follow a prescribed set of moves that always works. But now I cannot seem to find the other video 🤔

Audrey, stealer of shows

So in general, the equation for the number of questions in the trick for a die with n sides is ceiling(log_2(n)). So if I tried with my d120, theoretically I should be able to get someone's number in 7 steps.

That's a brilliant trick

At work I do this binary searching all the time. Something is broken, but I don't know which rule is doing it. First, I disable all the rules and see if it went away to make sure I've got the right start. Then I turn on half of them and see if it if the error is there. If not, I know it's one of the ones turned off. And so on.

Nice i can now flex to my parents

Isn't this what they would call a logarithmic complexity in programming? Halving at each step?

@MCLooyverse

3 жыл бұрын

Yeah, the time it takes to "guess" the chosen number on a n-sided die is O(log(n)). More specifically, it's at most ceil(log_2(n)).

Oh, wow! I think I own that book by Martin Gardner. 😃 At least I read it in the 1980s... 😇

@rosiefay7283

3 жыл бұрын

I have that book, and the parallel edition of *More* Mathematical Puzzles and Diversions. I've had 'em since the 1970s and still treasure them as part of my Martin Gardner. collection.

We need more Audrey

This is similar to a trick with numbers on sheets of paper. But, it was done using binary to decimal conversion.

Is that a copy of “Mathematical Puzzles and Diversions” on the table there?

"super confident in my blindhanded tactile of the d8" yeah dude, don't think i wanna you on my table as player.

Can you do it with d4 though?

Poor Audrey! :(

I guarantee audery will be the future mathematician if it remains in company of such a nice guys.😅😅😅

"Russell Crowe Goes Gambling"

I think I can credit the PS1 puzzle game Devil Dice for being able to immediately spot what was happening.

Calling it a "d6" .... I see you, I see you

dice has only 6 sides so not much of an effort to find out a hidden number when you can know even in the first step if its either one of the threes or the other.

Would it be possible with a die that only has dots printed on it as opposed to actual indentations?

@woodfur00

3 жыл бұрын

Obviously? He explained how the trick worked, it has nothing to do with the indentations

@AidanRatnage

3 жыл бұрын

I guess I didn't mean "possible" but "more difficult".

I'm pretty sure I can see the trick instantly lol

No - the reason binary is used in computers is because it is particularly easy and energy efficient to design electric circuits that work with two values - 1 and 0, true and false, but most importantly ON and OFF. A transistor that's all the way off consumes no power, because the current is zero. A transistor that's all the way on consumes VERY LITTLE power, because the voltage is very low. So those are nice states to live in. So that's how we build computers. This is also why computers are so precise and error immune. We define our system so that any voltage from, say, 0 volts to 0.8 volts qualifies as "low," and any voltage above 2.8V or so (back in the old 5 volt days) qualifies as "high." You just don't have any voltages in between in your system, except when a value is changing, and you don't pay attention to it during that transition. So even if your signals are noisy, they have to get at least two volts of noise on them in order for the noise to "flip a value." Honestly, a "trinary search" would be even faster than a binary search, because you'd reduce your options by a factor of THREE every time. But, it would take two comparisons instead of one to identify which bucket to go forward with. Anyway, the choice of binary has to do with what works electronically, nothing to do with our algorithms.

More Audrey!

Do it for all the roleplayers and use a D20 :)

Can someone from Numberphile do a video on Knuth's Mastermind Five Guess Algorithm?

Programmers might not be impressed ^_^ Nice clip about binary search