Hidden Dice Faces - Numberphile

Featuring Ben Sparks. More links & stuff in full description below ↓↓↓
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This is the first of a trilogy of dice tricks with Ben Sparks... More to come soon...
Martin Gardner called this trick "Hummer's Die Mystery" and attributed it to Bob Hummer in 1952.
More dice videos from Numberphile: bit.ly/Dice_Videos
Ben Sparks: www.bensparks.co.uk
More Ben Sparks on Numberphile: bit.ly/Sparks_Playlist
More Audrey: • Chihuahua Bubbles - So...
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[@hectooooor]

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

[@yamomwasthebomb7159]

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

[@choiie]

Found the engineer

[@danielyuan9862]

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

[@SeanCMonahan]

π ≈ e ≈ 3; sin(x) = x

[@tomtostadioom5593]

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

[@drenz1523]

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

[@NoriMori1992]

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

[@Triantalex]

false.

[@dyhrbergdk9541]

How could you send that cute rat away!

[@DROSTraceurADD]

Yeah I didn't get that sudden hate either

[@null8507]

The cutest rats give me rabies 😍

[@Triantalex]

??

[@frankscontentoutlet573]

I want more Audrey.

[@HumbleNewMusic]

awww audrey just wants to be included 🐾

[@marcbogonovich3974]

Audrey is my number :(

[@HumbleNewMusic]

@@marcbogonovich3974 👊🐾

[@firehawk1293]

The least impressive: doing this with a coin

[@skulliam4]

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

[@tomkerruish2982]

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

[@Logicallymath]

@@tomkerruish2982 really where?

[@tomkerruish2982]

@@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]

@@tomkerruish2982 oh cool thanks!

[@user-pk9qo1gd6r]

We absolutely need more Audrey!

[@LouisOnAir]

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

[@Kalumbatsch]

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]

@@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]

@@SeanSMST It's really not that impressive.

[@Danicker]

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]

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

[@christianrossouw1]

Poor Audrey. I'm so sad.

[@mathwithjanine]

Me too!

[@Jazardly]

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]

Yes!

[@galacticbob1]

"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... 🤔

[@skyscraperfan]

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]

Yes. Me too!

[@PaulFisher]

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.

[@Ishidalover]

More Audrey pls lol

[@nickrees4706]

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

[@dominiclohry1782]

MORE PUPPY SCENES PLEASE

[@aMondia]

What a supremely cute doggo.

[@WAMTAT]

We demand Justice for Audrey, more dogs in Math.

[@ThePurza]

Audrey deserves better treatment

[@drenz1523]

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

[@magicalpencil]

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

[@c.james1]

Would need 6 or 7 questions, and an extremely impressive blindfolded tactile skills lol.

[@hotdogskid]

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]

Finally it has another use other than for wild magic sorcerers

[@MrDowntownjbrown]

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

[@GodIsLoveEternally888]

yes that would be awesome!

[@hyfy-tr2jy]

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

[@OlliWilkman]

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.

[@numberphile]

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]

Zabloing

[@frogz]

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

[@playerscience]

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

[@rubenouwerkerk3288]

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

[@numberphile]

Sure: kzbin.info/www/bejne/qWmXlXWlpdh8m5Y

[@coucoucoucou8321]

@@numberphileHi

[@volodyadykun6490]

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

[@Phriedah]

@@numberphile Now this is the good shit

[@jcespinoza]

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

[@markkoops3614]

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

[@angeldude101]

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

[@AngadSingh-bv7vn]

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

[@miriamrosemary9110]

Nice!

[@mow184]

You mean within the first 2^5 seconds :)

[@capy9846]

@@mow184 That would be 2^5-1

[@vez3834]

@@capy9846 a Mersenne prime!

[@Triantalex]

??

[@IceMetalPunk]

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

[@Robbiebert14]

No, let Audrey back in!! :D

[@landsgevaer]

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

[@KaiseruSoze]

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.

[@tomrivlin7278]

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]

Shut up and take my money!

[@vsm1456]

Ben Sparks is awesome! Please more of him.

[@Veilure]

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

[@headlibrarian1996]

Numberphile needs more Audrey.

[@fluffykitten077]

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

[@rosiefay7283]

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

[@mbakenemdusink9757]

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

[@una_10bananas]

I'm liking these ben sparks videos

[@rmsgrey]

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.

[@DynestiGTI]

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

[@nemeczek67]

This trick would be even more impressive with two dice.

[@galacticbob1]

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.

[@themasqueradingcow91]

We demand more Audrey

[@n20games52]

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

[@davidgustavsson4000]

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.

[@lenpolygon]

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

[@GuidoHaverkort]

:( poor Audrey just wanted to learn about binary searching

[@bbcat-3972]

I love this channel.

[@robinbrowne5419]

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

[@aldena6989]

WE NEED MORE AUDREY CONTENT

[@BeeCeeJay]

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

[@FLS96]

We want you to introduce Audrey on Numberphile2 !

[@numberphile]

instagram.com/adorable_audrey

[@frogz]

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

[@MrPuzzoncello]

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

[@Dalenthas]

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

[@publiconions6313]

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

[@vez3834]

@@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]

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

[@frankharr9466]

That was fun.

[@nicholaswilliams4507]

Poor Audrey didn't understand what she did wrong.

[@crowd3r862]

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

[@digitig]

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

[@mbakenemdusink9757]

Same here. Amazing books written by an amazing person

[@theemissary1313]

Poor Audrey! :(

[@liamnilssonIFS]

Nice i can now flex to my parents

[@Mirvana]

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)

[@talideon]

No, Audrey! Stay! Good girl!

[@mina86]

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).

[@gcewing]

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

[@VincentGroenewold]

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

[@MCLooyverse]

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)).

[@chhayapatel4098]

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

[@AnonimityAssured]

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.

[@claytonsanchez5264]

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

[@MathAdam]

More videos need to feature Audrey

[@GenericInternetter]

"Russell Crowe Goes Gambling"

[@ericmilburn4801]

We need more Audrey

[@martijn3151]

We need more Audrey!

[@aL3891_]

Audrey, stealer of shows

[@renecura]

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

[@FLScrabbler]

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

[@rosiefay7283]

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.

[@kashefmandal6939]

Please recommend some Martin Gardner books!

[@That_One_Gaming_Guy]

That's magic!

[@veggiet2009]

That's a brilliant trick

[@tristanbay]

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.

[@petergreenson]

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.

[@theadamabrams]

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 🤔

[@jcespinoza]

Those 15 dislikes are from frustrated magicians who can no longer use this trick on 3.7 million of us

[@reidflemingworldstoughestm1394]

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.

[@AsBi1]

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.

[@andymcl92]

Once is a trick. Twice is a lesson.

[@WillGame4Beer]

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

[@jesusfigueroa6678]

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.

[@azfarahsan]

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

[@RodelIturalde]

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

[@azfarahsan]

@@RodelIturalde noice

[@tomek3633]

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

[@ericwelsh4853]

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

[@dfmayes]

Great video! Never got to comment this early. 😁

[@talhaqadeerqadeer4533]

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

[@SquirrelASMR]

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

[@diegorodriguesdesouza7389]

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

[@ANunes06]

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

[@pauljonesdemos]

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

[@matthewaustin233]

More Audrey!

[@rickseiden1]

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.

[@rosiefay7283]

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

[@mme725]

Awwww, Audrey