The Josephus Problem - Numberphile 

What about the unpleasant scratching of his marker on the paper? What does that deserve?

ive watched this vid so many times JUST to hear that sound effect

Man scream have to admit i laugh on movies with man screams

It's like an Android button click sound effect

Satisfying

...gnarly

Attention to detail!

finish your sentence

Hilarious!

@@screamsinrussian5773 you had to do it yourself

nothing remains morbid when put in front of a mathematician . . . or on a platter~

Nick Hadfield To be fair, people were pretty enthusiastic when the math for the atomic and nuclear bombs were created For some reason

hm when you say that I asume you Like seeing people get killed^^

Nick Hadfield ha ha yep

Welcome to the history of my people, basically.

Qui?poobLikaz?

@@steveclem7873 indeed my friend

lol

Ok now after spending 30 mins here I know the solution for this problem and now all I need to do is wait till a army of roman soldiers catch me with 41 others

But before you can decide where to sit, you have to know which seat will be “1”. What if you’re not in on that decision? That’s life.

blood oath

"how to weasel out of your suicide pact"

well, i sort of doubt 40 people would care for the sole man's wish to live.

For the first time I can really recommend this; do not do this at home....its just to messy and too much to explain.

😂😂😂😂😂

👍

I tried the problem and got the pattern, but man was it useless. Still fun though.

that is far from irrelevant.

villanelo1987 : Il like your avatar ! baldur's gate \o/ and this char was my favorite because of bouh ^^

Luiz Henrique elaborate

Underrated comment

Hahaha Golden

Exactly, the justification he didn't give is merely what happens when you shift by one digit an entire number in a given base, then add a single unit.

Thanks!

Here sir, take my upvote. I came here for this

So obviously, if n = 2^a - 1 then W(n) = n, and is the only case where W(n) = n. Eg. 3, 7, 15, 31, 63, etc.

I was also wondering why they did not point this trivial bit out, but then I am a programmer so maybe manipulation of binary numbers seem more obvious to me and my kind.

True. Funniest guy in ancient history. What about the "dream" that Traiano would be emperor? LOL Got him his "Flavius". Excellent stories.

Don't you love replaying movies its like we learn how people feel when we have to walk in thier shoes and experiance life through there shoes

His name was Jimmy.

@@ricardocima what

@@commenturthegreat2915 he prophesized to the romans that Tito would become emperor. Trajan died soon after and he became Tito's favorite, hence his name Flavius (Tito's family) Josephus. If i recall it well, I mean...

@@NotAlshami I paused the video to figure it out cuz I had to know.

11:25 makes up for it. Kind of

Winning seat is 101 btw

178=10110010->1100101=101

@@masterspark9880 ye

Thank you

Bravo

Fakjbf I was thinking the same thing. Demystifying is one of the great steps to understanding.

Yep! I also wondered why he didn't explain it in the video as it is a very simple explanation for people understanding base 2, which, I guess is the case of most numberphile viewer

That was genius

Always sit in an odd

@@jovianguyen you always have to be the odd one.

don't sit at 2l+1 number

Josephus: "Um, excuse me Matthias, mind if I stand here instead? It's a, uh, better view."

Tim Thomason Better try it the flattering way: "Let me stand next to you. You are so precise with your sword."

Mangocraft you just find an odd position each turn

Instead of picking a seat, pick who is no. 1 such that you are no. 19

Mangocraft

as one does

They had all agreed to die beforehand

You do it like civilized humans, you force the least liked member to sit there, tie them up, then you explain the game

They were all meant to have been suicidal. Josephus just secretly didn't want to die.

Most people aren't paying attention...

Seriously, considering we are all about to die, I’d rather be #2 then some #22, anticipating my turn while watching the carnage going on around.

Michelle Tabisz you’ve read every other comment section?

Oh so you like this videos comment section, name every person who commented in this comment section

-Not quite correct. You're shifting all bits including the highest bit. You'd need to first remove the highest bit using a bit of math trickery.- Can take this one step further and create a single equation to model the Josephus problem for all positive integers. Note: P is the number of people in the ring, a^b indicates a to the power of b, _log2_ is log base 2, and _floor_ is the function to round down to the nearest integer. To get the highest bit, you need to shift a one bit left _floor( log2(P) )_ times. Doing so is the same as: 2^( _floor_( _log2_(P) ) ) Once you have the highest bit, you need to remove it, which is as simple as subtracting P by the previous equation: P - 2^( _floor_( _log2_(P) ) ) After that, the rest is the same. Shift the remaining lower bits to the left one place, which is the same as multiplying by two, then add one: 2 * (P - 2^( _floor_( _log2_(P) ) ) ) + 1 Thus, you have a single variable equation which produces the answer to the Josephus problem for any positive integer P.

***** What I said was completely correct, read it again.

Binyamin Tsadik Sorry about that. I mistakenly thought L was supposed to be the input variable (i.e. 41); I see now you meant it to be the lower bits and 2^a to be the highest bit. Either way, it was fun coming up with an equation to solve the Josephus problem.

This is the first time where a bitwise Left Rotate No Carry could save a life.

XalphYT in a math problem maybe, but moving bits in hardware is pretty useful just for info handling.

Was wondering if someone in comments had enough brainpower... Understood that right away before he managed to move the 1 on the end haha ;) I prefer C# tho :P C++ comes second for me ;)

Xeverous yea I figured it out too. removing the most significant bit removes the 2 ^n bit leaving behind l. Adding a 0 to the least significant bit is the same as multiplying by 2. And then adding 1 is like 0+1 =1. So it actually turns out to be 2*l+1. I couldn't understand it until the end of the video though. 😅 We had to learn this during dsp class learning fixed point arithmetic.

least significant bit position *

3 141 592 subscribers

Joseefus joestar

Every scholar or educated historian I've ever heard pronounce it as you do. He most likely just knows the numbers problem since this is his expertise.

Yosef is how you pronounce his name, though Josephus is I-o-se-phus in Latin (Latin transliteration of Hebrew names) it is Latinized, Ph is F. Though unless we are using Greek which it is pronounced i-o-si-fos Ιωσήφοσ.

It IS pronounced Jo-See-Fus. 😂

amogus

underrated joke

Where are the ratings published?

11:31 THAT sword throw tho

totally unexpected.

Top 10 most overpowered anime characters

11:52

So what is the body count?

In math thousands die and the last guy eats 15 apples

Death of 1 = great tregedy. Death of millions = just a statistic :P

thanks buddy

You can get the result of this problem with just one little operator in code.

One must move to the right so that one ain't on da left of any one that is killing from the right and no witnesses no worries is all besides the fact I still hate math

@@Dr.FeelsGood Which one is that? Rotate left in languages I’m familiar with uses the leading zeroes, so you end up with 82, not the correct answer. Maybe there is another function I’m not aware of.

wow noice

Just came here to say this same thing. Also, you have to remember to drop any leading zeroes if you are using a fixed length binary number to represent your integers.

Danke!

I mean, all your doing is rotating the bits left. It really is a cool and simple solution.

Came here to say this. Thank you.

always happy to help!

wonderful explanation, thanks

If Final_person = Understanding(Calculations) then Killing = true

Fancy seeing a lovely here

Ooh it’s the official GGC didn’t think I’d see you here 😂

I am waiting for the proof of your beautiful theorem.

Game Grumps Compilations Hidden Assumption: If there is a problem, then violence is the solution. Maybe you should have a professional look into it for you?

Thanks Jupiter someone remember that!

Biggus Dickus

All of that existed before the Romans and the Romans just stole it from others

@@arealhuman4127 No, a lot of this was Roman invented

Brought Peace?

fucken nerd

msfattytroll I know!

Ast A. Moore fantastic. Beautiful. Bravo.

Wouldn't just 'rl nr_of_soldiers' be quicker?

Giles Bathgate Hold on. Found a fault. Working on a better solution.

Lol!

I thought you were going to say that the most significant bit should be the least significant and so you missed it

How many?

Shouldn't it be a lot of "hypothetical" soldiers from long ago "hypothetically" died? In real terms, I'm much more concerned about the cost of butcher block paper this guy is going through on a daily basis. Ha! Have a great day everyone.

@@johnburke3693 you're fun at parties aren't you

@@ministerc9513 (2^n)-1 of course

@@johnburke3693 I wonder if there are videos which contained topics about infinity soldiers killing each others, and at least one people watch each day...

Boolean algebra X-D

And if he does it wrong he'll have a alge-bruh moment

He's stoopid

@@jwm6314 He didn't fight to the death. He surrendered and became the right hand man to the general who later became Roman Caesar.

XD

Brandon Lemon 🍋 😂

but its in reverse

Negan should try this

Brandon Lemon eeny meeny miny moe, stab a tiger in his toe

I thought about playing tag, put our feet in. Bubble gum bubble gum in A dish how many pieces do you wish? This was cool.

Lol

SumENazViruleCowO&ootRojaz!

He just gonna pick 35 and he is gonna be safe with his math professor after a truce

spoiler alert bro 😭

@@Shinrakaichu i

The Australians had actual boomerangs. Didn't work out too well for them.

Jb Jaguar Well, Josephus wasn’t caught by an army of emus

@@DavidSavinainen The emus would win anyway

And the boomerang swords...

For the sake of argument I guess.

you are not familiar with the mathematicians employed by the RAF to determine the most efficient way of killing the most people by dropping bombs on them back in the forties..

@@Valchrist1313 SHAD no!

Ever sense how many bombs would bin laden have if 3 terrorists blew themselves up with 4 bombs each and bin laden had 420 bombs in the beginning

After E=MC²

@@Valchrist1313 how 'bout we agree that our original poster meant "math puzzle", in a strictly academic and/or pedagogical (rather than applied maths) context.

Touché

I don't know why I can't stop laughing 😂

Is that a jojo reference ?

@@cloroxman7194 Don't make me remember of jojo, Jojo was my fav character in SC

xD

cool!

It's probably too late, but you should ask him about this problem and see what his response is. Maybe "Hey, I actually helped make a video on that very topic"

I can imagine so. I enjoyed this.

... should learn to iron his shirts though.

@@allasar nobody’s perfect. I’ll accept brilliant in place of pressed laundry. 🧐 😺

Damn bro 😂😂😂

Im 1k like noice

Math to solve pointless problems.

Einstein’s Theory of Relativity was pointless math in the early 1900s. Few people even had the ability to see the need. The problem is you have no crystal ball to have any idea on the applications that may come up in the next 100 or 200 years.

X-D

It cracked me up so hard xD

You just number anticlockwise 🤷🏽‍♀️

@@pranalijoshi4623 but you already sat to where it goes clockwise and you can't switch seats because the killing already started :/ I don't think you got it but ok

@@pranalijoshi4623 imagine not having basic reading comprehension skills

lol 🥲

@@keontedennis7872 That's not entirely fair, while their comment does purposefully ignore the joke of the original comment, the original comment didn't say you were already seated, and so you could reasonably reverse the circle mentally, sitting in the correct seat.

NumBerzDoopkeTaxMainz?

his name is John

that is squid games if u know what i mean

I laughed so hard at that

Laughed out loud at this too 😂🦆🗡

or the most ducked up

wow why is there even 1 like on your comment

playtonz, because at least *2.6K people that read it have a sense of humor. It’s clear that you don’t. And that is just fine. Also, I gave your comment a like. 👍 *Edit: 2.6K (I’m looking at you, playtonz)

If only schools were this interesting.

@@DraconicDuelist idk, back when I was still in school it was pretty much exactly like this. Sometimes a bit faster though, if there wasn't a ton of time

@@Mixu. Then I congratulate you on having a well trained/enthusiastic teacher. I had one who said there are no numbers less than 0 (no, not even negatives), another who spent all of class time on e-bay while flipping through PPT slides, my geometry teacher left only 2 educational memories: proofs and Numb3rs (the tv show)...

@@DraconicDuelist owh. Yeah, guess I got lucky. Had a pretty motivated math teacher who also taught us about how math is applied in every aspect of our daily lives

BECAUSE SIZE MATTERS ,,, ON RU-vid ,,,, VIDEO LENGTH

ah yes, computerspeak

*waits in replies to find the dingus who says “I aCtUaLlY wRiTe My NuMbErS iN bInArY”*

*I aCtUaLlY wRiTe My NuMbErS iN bInArY* (nt rly)

@@haroonq2456 I'm gonna call bs on that one big man

@@majikss yeah it's jokes

-7- man they are all, already, left handed actually 🤷‍♂️

Back then, weaponry training was standardized so everyone could use the same weaponry. It was guaranteed to go to the left.

They'd need to be right handed for a counter clockwise rotation.

or he didnt know what is right and left LULW

The one who takes the napkin first....

because 7-8-9

@@trevormiles5852 You ruined it.

@@trevormiles5852 XDDDD

Trevor Miles r/whoosh

no no no it is why was 6 afraid of 7? because 7 8 9. why so cruel...

what if you sit in an odd seat and someone slides a chair up xD

others will notice that you are odd

well odd and even is relative to how everyone starts counting.If you sit in a circle table practically every sit is even and odd.

Thank you Josephus

odd that you would say that

Noble prize please

What is the answer to the first one? D:

You've purposely left out data on the first you fatlord

Bent

Bent

You'd think that with boomerang words such as that, they could defeat the Roman army.

Soham Kanerkar he did a darth vader

Dsennack - If I would stay alive until the end along with Darth Vader, I would immediately move to the Dark Side and ask Darth Vader for a job interview!

6:33

try 11:25

Amogus