Stephanie the editor is having fun and it is much appreciated. 42
@anlev11
Жыл бұрын
I would like your comment, but you have exactly 42 likes
@Bodyknock
Жыл бұрын
An interesting thing here is you can generalize this out using modular arithmetic. Instead of looking at numbers as "*ab", look at them as numbers "mod 100". Then replace that modulo 100 with some other base and see how it works. For example, for the sake of argument let's keep it at 101 total numbers in a circle. Likewise let's keep the notation Sₙ to be the partial sum from a₁ to aₙ like in the video. Now consider those sums mod 42 (for reasons which are clear in the video). Because there are only 42 remainders mod 42, but 101 total partial sums, there must be two sums Sₙ₊ₖ and Sₙ that both equal some remainder x mod 42. Therefore, similar to the video, Sₙ₊ₖ - Sₙ = 0 mod 42. Since that difference must be >0, that means it can only be some strictly positive multiple of 42 (i.e. 42, 84, 126, etc). And likewise, the complimentary sum with respect to that difference must be whatever the grand total of all the numbers is minus that (so if the grand total was n, for instance, then the complimentary difference is n-42, n-84, etc). So the trick then is to have the grand total of the circle be exactly 3 times the modulo you're using. In the above case, with modulo 42, that means we set the grand total of all the numbers in the circle to be 126 and claim that there is a sequence that adds to 42 and another that adds to 84. With that done, we have that there must exist two subsequences such that Sₙ₊ₖ - Sₙ = 0 mod 42, and thus Sₙ₊ₖ - Sₙ = 42 or Sₙ₊ₖ - Sₙ = 84 (since it can't equal 126 which would be too much). And that proves the claim, since the consecutive sequence corresponding to Sₙ₊ₖ - Sₙ either adds to 42 or 84 and its complimentary consecutive sequence adds to 126 minus that number which is the other result we're looking for. To sum it all up, therefore, you can make versions of this problem by having - the grand total of the natural numbers in the circle be 3n for some natural number n (i.e. in the video n=100) - the size of the circle is >n numbers. (In the video the size is 101, but note that the same proof would have worked for any size larger than 100.) - Claim that there is a consecutive sequence of numbers in the circle that adds to n (and also therefore a complimentary sequence that adds to 2n)
@hunganhnguyen6401
Жыл бұрын
I have done this problem before as homework, but it's nice to see a more easily understandable method than using modular arithmetic
@skylardeslypere9909
Жыл бұрын
This is related to a course about intro to proofs. People taking that course haven't learned about modular arithmetic probably
@wannabeactuary01
Жыл бұрын
if you understand modiulo artihmetic great but it is more accessible the way it is presented. Plus when the next different question comes along you/he will need modulo arithemetic.
@Bodyknock
Жыл бұрын
@@skylardeslypere9909 Actually they have, if you look at video 16 in the Proof Writing course where he talks about relations he uses modular arithmetic as an example without defining what it is, implying he expects the listener to already know who “a mod n” means.
@Bodyknock
Жыл бұрын
@@wannabeactuary01 The basics of “a mod n” is actually taught a bit earlier than this proof writing course. See my above comment about how he uses it as an example of a Relationship without defining what “mod” means.
@MrGyulaBacsi
Жыл бұрын
Here in Hungary we call this the matchbox-principle. Michael, once again you've made a problem look so easy like a walk in the park! Thank you!
@arkaprovodas4920
Жыл бұрын
OMG the secret to life the universe and everyting is in this video I can hardly believe it ! ! !
@enpeacemusic192
Жыл бұрын
Hilarious thumbnail and description as always, really interesting interesting math problem too. By the way, it's quite windy here, and remember 6*9 = 42 in base 13
@UltraMaXAtAXX
Жыл бұрын
Nice.
@klausolekristiansen2960
Жыл бұрын
Covering one of the numbers with the pause sign is not helpful.
@sochjan
Жыл бұрын
In Poland we call it Dirichlet drawer principle instead of pigeon hole principle
@paulanderson5704
Жыл бұрын
Same in Belarus.
@Jonas-gm4my
Жыл бұрын
Here in Germany we call it drawer principle as well.
@TedHopp
Жыл бұрын
If 42 is the answer to the ultimate question of life, the universe, and everything, can Michael do a video about what the ultimate question is? I sure hope it's not "What is six times nine?"!
@yuryshimansky6333
11 ай бұрын
Of course not. It’s “What is six time seven?”!
@davidintokyo
Жыл бұрын
42. It's raining cat's and dogs here in Tokyo, so I'm home watching math videos.
@goodplacetostop2973
Жыл бұрын
14:13 Easter egg in the video at the timestamp of a famous constant. I’m not telling when 😂
@senseof_outrage9390
Жыл бұрын
101010
@floretionguru2977
Жыл бұрын
Ah, I remember a long time ago a mathematician told me some of the deepest results in math result from a very easy principle: the pigeon hole principle. Thank you for showing such a cool example.
@alexdemoura9972
Жыл бұрын
42!!! the "Answer to the Ultimate Question of Life, the Universe, and Everything," ... Stephanie - I am glad to know you have a cousin here in Rio... I believe he told you this summer was hot as hell😁😁😁
@thesecondderivative8967
Жыл бұрын
Square root of 1764! What an interesting number. Hey Stephanie.
@wannabeactuary01
Жыл бұрын
I watched the whole 42 seconds - to be fair keeping attention matters more when you are being entertained rather than infomed. I recalled a simiar proof from previous time.
@whatelseison8970
Жыл бұрын
42. Haha That gives me an excuse for why I didn't get the solution in that time. You were distracting me Stephanie!
@lexinwonderland5741
Жыл бұрын
42 ;) (keep up the great work, Stephanie! And Dr. Penn! And all y'all!)
@charlessmith1931
Жыл бұрын
42! The answer to life, the universe, and everything.
@LucaIlarioCarbonini
Жыл бұрын
42 because... Stephanie knows best!
@Ch1pp007
Жыл бұрын
"42" for the algorithm's sake if nothing else.
@tonyhaddad1394
4 ай бұрын
great problem , thanks michael
@tonyhaddad1394
4 ай бұрын
42
@hunganhnguyen6401
Жыл бұрын
42. Elegant one.
@holidayeveryday3121
Жыл бұрын
Got you Stephanie "The answer to the Ultimate Question of Life, the Universe, and Everything"
@IngvarMattsson
Жыл бұрын
In Hitchhiker's Guid to the Galaxy. the number 42 is quite important, but no actual proof for that is given.
@CM63_France
Жыл бұрын
Hi, 14:13 : good place to check out, 14:14 : good place to stop.
@veselindimov307
Жыл бұрын
There are no less than 42 reasons to like this video!❤
@cierokilpatrick6034
Жыл бұрын
42 😆 (but also, that Built to Spill shirt)
@bentationfunkiloglio
Жыл бұрын
Lol, 42 reasons for a good laughs
@zoltanposfai3451
Жыл бұрын
If the weather is nice, and you have two white mice, then I shall not bore you, as the answer is forty-two.
@01binaryboy
Жыл бұрын
Thanks!
@tobyfitzpatrick3914
Жыл бұрын
...and that's a good place to Pause
@llchan
Жыл бұрын
I tried to skip during pause but it doesn’t matter. KZitem decided I wanted to watch their ads😂
@ralfbodemann1542
Жыл бұрын
42, dear Stephanie. I know, 42 is the answer. But I haven't figured out the question yet.
@dentonyoung4314
Жыл бұрын
42... and that gave me a good laugh.
@tomkerruish2982
Жыл бұрын
"42"
@stevenwilson5556
Жыл бұрын
42, got it before you said to "pause the video", was pretty easy
@liltimshady
Жыл бұрын
42. Editor's just playing with us now. 😂
@trevorreynolds9272
Жыл бұрын
42 love it
@joaovictorreis434
12 күн бұрын
42, really nice one
@kentgauen
Жыл бұрын
What a fun proof!
@neilwoller
Жыл бұрын
the Answer to the Ultimate Question of Life, The Universe, and Everything; 42
@NickKravitz
Жыл бұрын
Stephanie, What is the answer to Life, the Universe and Everything?
@QuantumHistorian
Жыл бұрын
I find it very curious that such an elegant proof completely falls apart just by replacing "positive integers" with "non-negative integers" (obvious counter example: 1 number is 300, all the others are 200). It feels like a small change but the whole edifice comes crashing down.
@TheEternalVortex42
Жыл бұрын
Did you mean to say all the others are 0?
@QuantumHistorian
Жыл бұрын
@@TheEternalVortex42 ... yep ...
@xAndy1003x
Жыл бұрын
Nice video. Random fact: 42 is a sphenic number (a number that is the product of three distinct prime numbers).
@TheTriggor
Жыл бұрын
The number is 42, the city is Boston MA and the weather is not great, which is a shame because I'm only here over the weekend
@simoneantoniocarretta1048
Жыл бұрын
42 😂😂
@SweDennis
Жыл бұрын
42 😀
@sunritpal1037
Жыл бұрын
This is an amazing application of pigeonhole principle. Also the editing of Stephanie is amazing. Keep up the great work 👍
@bndrcr82a08e349g
Жыл бұрын
Let's see if I understand: Professor, are you saying that if I randomly pick 101 positive integers whose sum is 300, and I always arrange them randomly on a circle, will I always be able to find a sequence of consecutive numbers whose sum gives 200?
@bungaIowbill
Жыл бұрын
Yeah
@shrajalkushwaha282
Жыл бұрын
Consecutive on that circle.
@bscutajar
Жыл бұрын
This is interesting to generalise, can be generalised beyond the base 10 nature or this one.
@mevnesldau8408
Жыл бұрын
Stephanie, you are the Magician. I can barely understand what You write in the description box but I'm fully fascinated! 42
@IlTrojo
Жыл бұрын
42.
@anlev11
Жыл бұрын
This was very genious
@tomholroyd7519
Жыл бұрын
Well I was gonna but the text scroll made it impossible and now for something completely different
@headlibrarian1996
Жыл бұрын
Since the problem doesn’t specify an ordering around the circle I assume that implies no matter how you order them you will always be able to find a sequence that sums to 200. That is certainly not what I would have expected.
@nevoitzhak2092
Жыл бұрын
42 W stephanie
@Toto-cm5ux
Жыл бұрын
Nice!
@MushookieMan
Жыл бұрын
This is reminiscent of the intermediate value theorem but a very discrete version of it
@dentonyoung4314
Жыл бұрын
Bolzano's theorem is one of my favorites. It can be used to prove the ham sandwich theorem, which has one of the greatest names in all of mathematics.
@TymexComputing
Жыл бұрын
"42" Steph ;)
@ezequielangelucci1263
Жыл бұрын
42
@davidbrisbane7206
Жыл бұрын
This proof also shows that there must be a consecutive arc of numbers that add to100 also as a corollary.
@luisfelipe7270
Жыл бұрын
42 😂
@runnow2655
Жыл бұрын
I like how he just ignores that it's possible there are less than two numbers that end in 00, there could be more ending in other numbers. There could be one hundred threes and one one?
@ethandavis7310
Жыл бұрын
That's not what he proved. He proved that there are guaranteed to be at least two sums along the sequence that end in the same two digits. From there you can subtract the sums to result in a sum ending in 00.
@karl131058
Жыл бұрын
for tea, too! 😇
@Nikolas_Davis
Жыл бұрын
The most concise way to state this result & proof would probably be this: there aren't enough distinct sums of consecutive numbers in the sequence for them *not* to sum to 200 at least once.
@bobh6728
Жыл бұрын
The sums don’t have to be distinct. You could have a sum of 50 in numerous ways. So looking at the pigeon hole principle, you could have pigeon holes that are empty and some that have a lot of sequences that have that sum. The principle in this case is that at least one of the holes has two sequences in it.
@ethandavis7310
Жыл бұрын
not necessarily. There are 101! sums and 299 boxes. This guarantees at least two of the sums are the same, but none of them are necessarily 200 based on that fact alone. You actually need the entire proof to show that two of them from the same partial sum sequence end in the same 2 digits and can thus be subtracted to generate a sum ending in 00.
@BleuSquid
Жыл бұрын
101010 (base 2)
@matheusjahnke8643
Жыл бұрын
2:53, for your information, I paused the video and found the arc *before* I added the numbers till I got over 20.... then took out a number on the top and added the number below; Like: 1, 5, 2, 4, 3, 2, 5 adds to 22 I take the 1 at the start... and add the 1which is next.... doesn't help me 5,2,4,3,2,5,1 adds to 22 remove the 5 at the star and add the 3... the net difference is -2... so it should add to 20 2,4,3,2,5,1,3 adds to 20 if I'm not mistaken;
@matheusjahnke8643
Жыл бұрын
btw... 42
@TheLopsidedobject
Жыл бұрын
420 / 10
@Atul_Thakur97
Жыл бұрын
42🎉
@yevgeno
Жыл бұрын
6*7
@marsgal42
Жыл бұрын
13. Oh, sorry, wrong video. 42. Sunny, BTW.
@jadduajones
Жыл бұрын
42 ❤
@joseluishablutzelaceijas928
Жыл бұрын
42! =)
@martinkausoh1386
Жыл бұрын
42😊
@alessandrocaia1270
Жыл бұрын
42 lol
@Samsaptaka
Жыл бұрын
Oh, what the heck. 42
@vinceguemat3751
Жыл бұрын
you have forgotten “strictly” before positive integers because as this the numbers 0 0 0 0 0 0 0 0 0 0 30 are allowed on the circle (i do it with the smaller example) and with this it’s obvious that no sum add up to 20
@ethandavis7310
Жыл бұрын
0 is never considered a positive integer. It is a non-negative integer. The word strictly makes no difference if it's modifying "positive"
@vinceguemat3751
Жыл бұрын
@@ethandavis7310 0 is the only integer that is positive and negative
@ethandavis7310
Жыл бұрын
@@vinceguemat3751 Dead wrong. Do a Google search :)
@vinceguemat3751
Жыл бұрын
@@ethandavis7310 Do a google search too. I've done it, and this is a point (as many other) where definition change with the country: In France (and in most French country as Belgium, Quebec, and others) we define positive numbers as IR+ = {x | x ≥ 0} so 0 is positive. So I’m right in my country (I’m French) and you are right if you are not French. In order to have no ambiguity we should never say just "positive" but "strictly positive" or "positive or null" so everyone understand the same.
@yuseifudo6075
8 ай бұрын
@@vinceguemat3751positive integers are well known in English to not include 0. We shouldn't change some convinius for you
@cameronspalding9792
Жыл бұрын
For 20, I had 3+1+5+2+4+3+2=20
@QuantumHistorian
Жыл бұрын
So, where do I send the beer / chocolate / flowers for them to get to Stephanie as a prize for most ridiculous mid video interlude? Number 42 math street?
@xavierwainwright8799
Жыл бұрын
But of course, 42 is the answer!
@adogonasidecar1262
Жыл бұрын
What's the answer to everything? 42?
@GregWeidman
Жыл бұрын
42😂
@senseof_outrage9390
Жыл бұрын
101010.
@Mystery_Biscuits
Жыл бұрын
42 :)
@TomatoBreadOrgasm
Жыл бұрын
Yeah well I'm stuck in a Time Trap.
@memesThatDank
Жыл бұрын
the titles and descriptions never dissapoints lol
@charleyhoward4594
Жыл бұрын
is this ALLWAYS TRUE ??
@sarithasaritha.t.r147
Жыл бұрын
The editor is getting too playful
@asdbsajbdasdbsjdbasd
Жыл бұрын
You got cousins in Brasília, Brazil!? This is 42 times nonsense!
@lisandro73
Жыл бұрын
Almost 42, got bored 😂
@Mustif
Жыл бұрын
A
@Hyo9000
Жыл бұрын
Forty-one
@msdmathssousdopamine8630
Жыл бұрын
42. But these titles weren't helping.
@paolonicolacerea
Жыл бұрын
The real question here is: how many cousins does Stephanie have???
@MichaelPennMath
Жыл бұрын
Very few actually. -Stephanie MP Editor
@paolonicolacerea
Жыл бұрын
@@MichaelPennMath the weather here is beautiful today! Say hello to your few cousins! :-)
@anuragkar8895
Жыл бұрын
Sus😳😳😳
@Hiltok
Жыл бұрын
101010 |base2
@mobatyoutube
Жыл бұрын
Would someone please clue me in to the references to "Stephanie" in the comments?
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