The Light Switch Problem - Numberphile

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  • Опубліковано 15 лют 2023
  • Featuring Ben Sparks... See brilliant.org/numberphile for Brilliant and get 20% off their premium service and 30-day trial (episode sponsor)... More links & stuff in full description below ↓↓↓
    This is also widely known as The Locker Problem - we liked the light switches better!
    More Ben Sparks on Numberphile: bit.ly/Sparks_Playlist
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  • Наука та технологія

КОМЕНТАРІ • 796

  • @robadkerson
    @robadkerson Рік тому +1443

    I like that Ben treats you like any random novice. Helps us actual novices.

    • @geraldsnodd
      @geraldsnodd Рік тому +4

      True

    • @SirCalculator
      @SirCalculator Рік тому +35

      And he forgot 1 as a devisor at first. Very relatable

    • @AntiChangeling
      @AntiChangeling Рік тому +94

      Brady is like a veteran novice. He's the perfect person to do these.

    • @Pope_Balenciaga
      @Pope_Balenciaga Рік тому +25

      Einstein once said if you can't explain something clear enough to a novice, you don't understand it clearly yourself

    • @Silvar55x
      @Silvar55x Рік тому +4

      @@SirCalculator I think he was doing that intentionally to engage the viewer (and Brady).

  • @goodboi650
    @goodboi650 Рік тому +745

    Ben Sparks is always an absolute delight to watch, and his puzzles are always so satisfying too. Thank you for everything you do!

    • @cyrileo
      @cyrileo Рік тому +4

      👍 I totally agree, Ben Sparks' puzzles are fun and rewarding to solve!

    • @pear7777
      @pear7777 Рік тому +1

      Love these puzzles, subbed!

  • @Kaisharga
    @Kaisharga Рік тому +25

    This video gave me the realization that a square times a square is also a square. Which, now that I think about it and why that's true, seems obvious and clear, but I very much did not expect it until I saw it.

  • @ZachGatesHere
    @ZachGatesHere Рік тому +448

    Ben is the MVP when it comes to breaking concepts down to make them easy to understand.

    • @bencrossley647
      @bencrossley647 Рік тому +7

      Thanks ;)
      - I think he's also a school teacher / did a stint of school teaching so he will have had plenty of practice!

    • @cyrileo
      @cyrileo Рік тому +2

      ⭐️ I'm glad you think so! Let's solve the remaining puzzle together! 🤓

    • @xl000
      @xl000 Рік тому +1

      Mvp?

    • @SirNobleIZH
      @SirNobleIZH Рік тому +1

      Grant from 3b1b too

    • @MichaelMoore99
      @MichaelMoore99 18 днів тому

      Breaking them down? Does that mean that the concepts are composite? 😀

  • @QuantumHistorian
    @QuantumHistorian Рік тому +539

    The connection to primes is actually very very close. Take the same problem, but once a light is off you can never turn it back on. You now have an algorithm called _The Sieve of Eratosthenes_ which is a well known (and efficient!) way of generating the prime numbers. It's cute that a tiny change in the rules is the difference between spitting out primes and squares. Bonus fun fact: Eratosthenes was also the first guy to measure the radius of the Earth.

    • @oscarn-
      @oscarn- Рік тому +21

      That's the one! I had a nagging feeling that this reminds me of something else, thanks!

    • @ke9tv
      @ke9tv Рік тому +84

      Sift the twos and sift the threes
      In the Sieve of Eratosthenes,
      And as the multiples sublime,
      The numbers that remain are prime.

    • @columbus8myhw
      @columbus8myhw Рік тому +49

      Not quite - you also need the nth person to skip the number n itself.

    • @adarshmohapatra5058
      @adarshmohapatra5058 Рік тому +17

      ​@@ke9tvI love your rhyme!
      You are quite sublime
      You made my time
      I'd give you a dime

    • @EconAtheist
      @EconAtheist Рік тому +22

      "Don't believe everything you read on the internet."
      ~ Eratosthenes, Second Emperor of the Sixteen Kingdoms

  • @bryantfuehrer2095
    @bryantfuehrer2095 Рік тому +151

    One of my favorite things about this video is that, through their conjecture, I discovered it before they said it and I felt like a genius even though I needed to lean on them leaving bread crumbs to lead me.

    • @piercexlr878
      @piercexlr878 Рік тому +22

      That's one of the best ways to be taught. Leaving you stranded, most people won't make much progress, but with just a little push, you get all the benefits of figuring it out without all the suffering looking for those bread crumbs. Math is all about taking things someone told you and trying to apply it to something they didn't tell you.

  • @BZAD1989
    @BZAD1989 Рік тому +4

    "Told ya!"
    That was so wholesome :))

  • @cramesplays
    @cramesplays Рік тому +41

    Ben's excitement about this problem is contagious and his method of explaining it was excellent. Great video.

    • @cyrileo
      @cyrileo Рік тому

      Wow, awesome! 👍😃

  • @DaTux91
    @DaTux91 Рік тому +8

    I'm stealing this puzzle and adapting it for my D&D game. Instead of lights getting switched, I'm thinking trapdoors over death pits. Stand on a non-square labeled one at your own peril, adventurer!

  • @atharva1509
    @atharva1509 Рік тому +47

    This conversation with cameraman format is really great👍

    • @numberphile
      @numberphile  Рік тому +68

      Cool - maybe I could make something more of it! :)

    • @cyrileo
      @cyrileo Рік тому +6

      🤓 That's a great insight! It really speaks to the creativity of your thought process.

  • @seedmole
    @seedmole Рік тому +148

    The slight segue about anyone beyond the 50th being able to only interact with a single switch would be a wonderful point to go off on a tangent about Nyquist theory in the context of Audio Sampling

    • @ke9tv
      @ke9tv Рік тому +6

      Yeah! Watrch the animation, and you'll see that there's an interesting complementary pattern starting from 100 as you run the light switches in reverse.

    • @cyrileo
      @cyrileo Рік тому

      Neat observation! 😎🤓

    • @TheStoneblogs
      @TheStoneblogs 2 місяці тому

      Can you please explain?

  • @hyfy-tr2jy
    @hyfy-tr2jy Рік тому +196

    Its always nice to see Maximus the Mathematician! We are entertained!

    • @cyrileo
      @cyrileo Рік тому +1

      😊 I too appreciate Maximus and the video was captivating!

    • @WaltTFB
      @WaltTFB Рік тому +6

      'At my signal...unleash maths'.

  • @stathyena
    @stathyena Рік тому +23

    Seeing Ben briefly question himself on some basic multiplication is oddly reassuring.

    • @piercexlr878
      @piercexlr878 Рік тому +5

      The difference between you and a mathematician isn't usually intelligence but time spent learning.

  • @BleachWizz
    @BleachWizz Рік тому +57

    amazing video. I love the fact Brady is clearly improving and participating more. Plus he brings a lot of questions that teachers usually gloss over because they're used to see that question so many times that it has become irrelevant.
    They're usually the ones that brings back connections from the model to the problem and those really help understanding.

    • @jursamaj
      @jursamaj Рік тому

      No, the questions teachers hear the most are where the most learning is, so they *don't* gloss over them.

  • @LeonardChurch33
    @LeonardChurch33 Рік тому +7

    I love when I realize that I can implement a solution to a particular math problem in code. I paused the video at 1:34 and wrote a little Java program to run through all 100 iterations before continuing with the video and was very satisfied when Ben got to the final answer and my result matched his.

    • @cyrileo
      @cyrileo Рік тому +1

      👊🏽 Nice work, MrCharlz! Props for taking immediate action and coding a solution! 😮

    • @Tommy_007
      @Tommy_007 Рік тому +1

      In general, experimenting by hand generates more ideas that can be used in a proof (which is the essential part of the problem).

  • @RavenZahadoom
    @RavenZahadoom Рік тому +21

    I knew it would be something to do with how many factors they have, because only the people with one of their factors would ever touch the switch, but didn't see the square thing coming. Interesting puzzle that one.

    • @alexandertownsend3291
      @alexandertownsend3291 Рік тому

      I think this is one of my favorite numberphile videos. I like how approachable it is. This is a problem you could reasonably give as extra credit on a math test for high schoolers.

  • @zacprunty
    @zacprunty Рік тому +10

    7:19 is exactly what makes this guy a mathematician. Loved this one.

  • @jucom756
    @jucom756 Рік тому +5

    i think this was an olympiad problem once because i instantly remembered how to do the solution: the amount of times a lightswitch is flicked is the amount of numbers of which the lightswitch is a multiple AKA the amount of divisors of the lightswitch, then because every divisor has an inverse divisor (d*m=K so d and m are both divisors) the total amount of divisors will always be even if those 2 are different for every divisor, so only the numbers that have a divisor equal to itself will be flicked an odd amount of times, divisor equal to itself means a square number so it will be all the squares that are on!

  • @joshuastucky
    @joshuastucky Рік тому +15

    Absolutely stellar video. Interesting, surprising, yet accessible math, coupled with a phenomenal presentation by Ben Sparks. Honestly, this is peak Numberphile content.

  • @DeceptiveSS
    @DeceptiveSS Рік тому +2

    "Drawing" this one out in a spreadsheet was very satisfying. Just for the sake of seeing what it would look like in the end, all 100 manipulations side by side.

    • @TheStoneblogs
      @TheStoneblogs 2 місяці тому

      Would you be willing to share?

  • @localidiot4078
    @localidiot4078 Рік тому +2

    I vaguely remember this puzzle years ago. I never guessed the answer. I completely forgot about it until i watched this video. It took me 5 seconds to go through the primes -> Squares logic. Its crazy what a few years and some programming will do to your neurons.

  • @ysquaredyobozo
    @ysquaredyobozo Рік тому +3

    i love the ending "and that seems like a pleasing outcome to a potentially contrived problem", cuz, aint those the best puzzles

  • @alexbennie
    @alexbennie Рік тому +3

    The best feeling ever, after seeing the obvious 'Answer', without seeing the not-so-obvious-at-first 'Why'; then seeing it after many hours!
    I had this problem in an assessment years ago and ended up spending hours on excel simulating the problem...
    I saw that the pattern was *spoiler*. I then spent a ridiculous amount of time to try and figure out why only the *spoiler* stayed lit...
    One of the most fun/cool and fundamental ideas crop up in solving this problem.

  • @nekogod
    @nekogod Рік тому +55

    James Grime did this with Othello pieces! Also sometimes demonstrated with school lockers. All about perfect squares because they have an odd number of factors!

    • @watcherfox9698
      @watcherfox9698 Рік тому +9

      I knew I seen this before. I thought it was an old Numberphile video, but it turns out it was on his own 'singing banana' channel.

    • @phiefer3
      @phiefer3 Рік тому +6

      James also did a video on Numberphile about highly composite numbers, which was brought up at the end. The episode '5040 and other anti-primes'

    • @davidgillies620
      @davidgillies620 Рік тому +4

      I've seen it with a corridor with 100 doors and 100 (suspiciously well-trained) monkeys.

    • @davidlohmann5098
      @davidlohmann5098 Рік тому +2

      It appears to be a common math or programming question. Other channels like ted-ed have videos on the problem calling it "the locker riddle".

  • @Sevenigma777
    @Sevenigma777 Рік тому +1

    This is the only channel on UA-cam where in every single video i have watched there is a moment where i have no clue whats going on or being said but yet i keep on watching lol

  • @bigpopakap
    @bigpopakap Рік тому +24

    Wow, this little puzzle ended up touching on some really profound topics! So cool!!

    • @numberphile
      @numberphile  Рік тому +8

      So glad you liked it

    • @Einyen
      @Einyen Рік тому +5

      @@numberphile Hey you forgot to call the highly-composite numbers for "Anti-Prime numbers" like you did to annoy Dr. James Grime "5040 and other Anti-Prime Numbers" 😁😂

  • @professorpoke
    @professorpoke Місяць тому +1

    I once read this question in a math magazine when I was in the 7th grade. I tried to solve it but couldn't. Then I almost forgot about this question. After more than a year (now I am in the 9th grade) it suddenly hit me, and I solved it. That made me realize that I never had forgotten about this question. It was there all the time, in my brain waiting for me to learn the right tools, waiting for me to become worthy to solve it.

  • @MTulak
    @MTulak Рік тому +5

    I figured out the squares would be the only lights on fairly quickly, but then I spent a while convincing myself they were the only integers with an odd number of factors. I'm glad they proved it!

    • @iCarus_A
      @iCarus_A Рік тому

      Yup, I arrived at the conclusion that odd-number factor numbers will be the ones left on, then drew the connection to squares -- as factors must always come in pairs but in the case (and only in the case) of a square, they can pair with themselves

    • @RunstarHomer
      @RunstarHomer 4 дні тому

      I think intuition is actually clearer than the proof here. Since factors come in pairs, the only way to have an odd number of them is for two factors to be equal. And it's not possible to have two pairs of equal factors totalling the same number. You cannot have a²=b² without a=b in the natural numbers.

  • @ruferd
    @ruferd Рік тому +8

    One of my favorite puzzles to give students. A surprising answer, but when you stop and actually experiment and play around with it, it's almost obvious. Such a wonderful "ah-ha" moment for everyone when they experience it!

    • @alexandertownsend3291
      @alexandertownsend3291 Рік тому +1

      I actually tried it before watching the video. I solved it on my own after having my aha moment. I then watched the video and was happy to see I got it right. A lot of math puzzles that youtubers throw out are quite above my level, but I loved this one. It was a little bit tough, but not too tough.

    • @R3plicant
      @R3plicant Рік тому +1

      A "lightbulb" moment, if you will

    • @cyrileo
      @cyrileo Рік тому

      👍 Experimenting and problem-solving often leads to those special "ah-ha" moments. It's one of the magical sparks of mathematics that I love!

  • @rudodejong
    @rudodejong Рік тому +16

    Very enjoyable video! The part at the end about 60, 180 and 360 blew my mind a little bit. 😉

    • @kindlin
      @kindlin Рік тому +2

      The Babylonian counting systems used 60 as the base, so they had 60 unique digits in their numbering system. This was useful for fractioning things. With 10 we can only do 1x10 and 2x5 and that's it. We just happen to have 10 fingers, is my guess.

    • @lyrimetacurl0
      @lyrimetacurl0 Рік тому

      😯

    • @liamriddy358
      @liamriddy358 Рік тому

      @@kindlin The Mesopotamians / Babylonians used the three sections of each of their four fingers to count to 12 just as easily 🙂

    • @thomasdupont1346
      @thomasdupont1346 Рік тому

      @@kindlin The Babylonians were my first thought as well when the 60, 180 and 360 were mentioned. They are the ones who first used 60 seconds in a minute and 360 degrees in a circle.

  • @OwlRTA
    @OwlRTA Рік тому +7

    I remember doing this type of problem as something fun the teacher gave us in one of my high school math courses. I was so proud when I figured out that the square numbers would be different from the rest. I don't think I proved it rigorously though

    • @alexandertownsend3291
      @alexandertownsend3291 Рік тому

      There a few different ways to prove it. He showed one of them. Maybe you can find one of the others.

    • @cyrileo
      @cyrileo Рік тому

      👍 That's awesome, OwlRTA! Impressive deduction skills!

  • @Ghou1Lord
    @Ghou1Lord Рік тому +6

    "Told ya!" :) Again a very nice video about math. I can imagine a world where teachers like you make many many students love math instead of being afraid of it.

    • @cyrileo
      @cyrileo Рік тому +1

      👏🏻 Amazing insight! Math can be so much fun with the right person teaching it. 😆

  • @nekkowe
    @nekkowe Рік тому +26

    The initial description reminded me of the prime sieve, which then got me thinking about how many times each switch would get flipped total = how many factors it has, which led pretty directly to "all non-square-number lights will be off at the end" - since that's the only case in which a switch would get flicked an odd number of times, with all other pairs of factors cancelling out.

    • @tspander
      @tspander Рік тому

      It was a similar thing for me, but even more basic- I remembered that if you do naïve exhaustive prime checking, you only have to go up to the root of the number because of the factor pairs they show later on in the video. That led me to the same even/odd factors idea and that square numbers would be the only ones where there is a number without a counterpart.

  • @darkdudironaji
    @darkdudironaji Рік тому +12

    I'm putting my guess to the problem down before watching the video.
    My first thought was that it would be easy to work out 1 at a time. Because you don't have to keep track of any numbers you've already passed. That was much harder to keep track of than I thought.
    But then I realized a switch only gets flipped when one of its factors comes up. So you just have to figure out if it has an odd number of factors, which would keep the light on, or an even number of factors, which would flip it off.
    After working on that for a few numbers, I realized factors ALWAYS come in pairs unless the number is a perfect square.
    In conclusion: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 should be on. Everything else should be off.

  • @Ms19754
    @Ms19754 Рік тому +2

    Such a great video! The conversational presentation, the clear explanations, the interesting but not too complicated problem. Just top of the top!

  • @PJSproductions97
    @PJSproductions97 Рік тому +1

    This is the first time in a long time I figured out the answer to a problem during the "pause and solve it" section.

  • @felixmerz6229
    @felixmerz6229 Рік тому +1

    Oh, I liked that detail of the light switch sound at the end.

  • @radonato
    @radonato Рік тому +3

    Short of Mr. Grimes, Mr. Sparks is by far the superlative expositor of these great topics.

  • @codediporpal
    @codediporpal Рік тому

    I love that you guys are still doing these videos. It's been so long! This is one of the first youtube channels I subscribed to!

  • @racecarrik
    @racecarrik Рік тому +7

    I love how Ben knows Brady's favorite square number lol they've got a great working relationship

  • @laurendoe168
    @laurendoe168 Рік тому +7

    What I was wondering was 36 - this is 2 squared time 3 squared, and not writing it out I wondered if having a PAIR of duplications would cause it to have PAIRS of factors once again. Obviously not, but I found this interesting.

    • @cryptoooooooo
      @cryptoooooooo Рік тому +1

      I agree, but for the sake of writing it out:
      1x36 = 1 x (2 x 2 x 3 x 3)
      2x18 = 2 x (2 x 3 x 3)
      3x12 = 3 x (2 x 2 x 3)
      4x9 = (2 x 2) x (3 x 3)
      6x6 = (2 x 3) x (2 x 3)
      5 pairs of factors for 36, while one pair is a duplicate = 9 factors.

    • @laurendoe168
      @laurendoe168 Рік тому

      @@cryptoooooooo I realized long after I posted it that there was only one true duplicate... and didn't bother to delete the comment

    • @cyrileo
      @cyrileo Рік тому

      👍 Brilliant question! Even with 3 sets of duplicated factors, there are still an even number of factors!

  • @deyfuck
    @deyfuck Рік тому +2

    Been watching this channel since the start and this is the best video.

  • @marklonergan3898
    @marklonergan3898 Рік тому +4

    To answer the question, i have heard this before long ago, but in trying to remember it, i did jump to Prime numbers, but then i figured primes still have an even number of factors so i had to figure the answer again from scratch. 😀

  • @guyedwards22
    @guyedwards22 Рік тому +3

    I started this video before having to go to work and didn't get past the initial explanation of the problem. Just worked it out biking home afterwards, and I arrived at the conclusion about the square numbers via the parity of the product of the powers of the prime factors. Nearly crashed into the curb when I had the 'aha' moment 😵

  • @jameslapslie1995
    @jameslapslie1995 Рік тому +1

    Had this question come up for a computer science interview at a London university literally yesterday. Hadn’t seen the video yet so ended up having to work it out in a similar way. A good reminder to watch your videos as soon as they come out rather then a week later 😂

  • @artswri
    @artswri Рік тому +2

    Another fun puzzle, so simple to perform but with interesting non obvious analysis. Thanks ever!

  • @kevinn1158
    @kevinn1158 Рік тому +4

    This is a great experiment. I'm going to show this to my 14 yr old daughter.

  • @macronencer
    @macronencer Рік тому +1

    Wonderful! I've seen the puzzle before but I'd never seen the proof, and it was pleasingly easy and elegant.

  • @palpytine
    @palpytine Рік тому +1

    My first thought was "This sounds a bit like the sieve of Eratosthenes", which is why I suspect many people first consider primes

  • @5eurosenelsuelo
    @5eurosenelsuelo Рік тому +1

    Videos with Ben are by far the best of this channel

  • @kamikaze2613
    @kamikaze2613 Рік тому +2

    Thank you for making math for novices fun and forever entertaining and engaging.

  • @TheStatisticalPizza
    @TheStatisticalPizza Рік тому

    I actually figured this one out at the beginning without needing help! Kind of spooky because once he walked through it I realized I had the same train of thought by starting with the primes.
    I didn't make the connection beforehand that only perfect squares would have an odd number of factors so I learned something new.

  • @GuusJanssen
    @GuusJanssen Рік тому +2

    *First time in forever I found out the answer before the video was finished!* Yeah! Right after Ben told what the problem was I opened the console and typed this:
    let lights = new Array();
    for ( let x = 1; x

    • @GuusJanssen
      @GuusJanssen Рік тому

      To see the switched on lights, just run:
      for ( let x = 1; x

  • @coreyburton8
    @coreyburton8 Рік тому +3

    loved this episode! thanks. cool association with the squares. and with the number of factors.
    60, 72, 84, 90, 96 have 12 factors they are the highest up to 100

  • @Kanareika2001
    @Kanareika2001 Рік тому

    Great show!
    Thanks for your labour, that's really exciting.

  • @pacefactor
    @pacefactor Рік тому +1

    Man - this was so enlightening. I was messing with this stuff when designing card games, and my mind is just blown. I have so many more ideas.

  • @unvergebeneid
    @unvergebeneid Рік тому +2

    I figured it out up to the point that it depends on whether the number of factors is odd or even but I didn't figure out that the squares are the only numbers with an odd number of factors. I also don't think I ever would've figured that out, maybe with a lot of help by the interviewer... 🤔

  • @FandangoJepZ
    @FandangoJepZ Рік тому +2

    Had a similar problem in 8th grade where marbles were dropped in the nth bucket, and you had to reason about which buckets had such and such many marbles, was quite fun working out but also had 19 other problems to answer in those 90 minutes…

  • @lynk5902
    @lynk5902 Рік тому

    I got to the answer quickly, but not why. Thank you for the breakdown!

  • @GlassDeviant
    @GlassDeviant Рік тому

    Brilliant! I knew the answer by 5 minutes in, and I've never considered this problem before. Excellent presentation.

  • @alienmoonstalker
    @alienmoonstalker Рік тому

    Very nice problem and graphics. More please!

  • @yaduk7710
    @yaduk7710 Рік тому

    This video aligned with my thought process perfectly. That's awsome

  • @marcusklaas4088
    @marcusklaas4088 Рік тому

    Interesting problem wonderfully explained. Thank you!

  • @jonathansperry7974
    @jonathansperry7974 Рік тому +2

    Imagine the lights all in a row (instead of the grid shown in the animation), then view all the successive steps together, and some pleasant patterns emerge. Say the room numbers are n, then there’s a wedge of light between steps 1/2 * n and n, and fainter wedge of light between steps 1/3 * n and 1/2 * n, and so on.

  • @justakiwi
    @justakiwi Рік тому +3

    I love how they keep on using the large piece of paper

  • @JohannaMueller57
    @JohannaMueller57 21 день тому

    that was so much fun! man i love ben sparks videos

  • @suan22
    @suan22 Рік тому +1

    Thank YOU for making such cool stuff on the internet!

  • @bsharpmajorscale
    @bsharpmajorscale Рік тому

    I'm proud that I thought about prime numbers a second before he brought them up. This definitely reminds me of stuff from the discrete mathematics class I took last year. Is there a connection to the method for working the sum-of-divisors function backwards? They both use (a+1)(b+1) form numbers.

  • @galaxy_brain
    @galaxy_brain Рік тому +5

    Holy Lord, Ben's closing comment about the practical usefulness of highly composite numbers like 60/180/360 absolutely shook me. I've always questioned why these numbers were used to define our measurement scales. Phenomenal.

    • @FelineBlender
      @FelineBlender Рік тому +2

      I wish he'd called out 12 as being part of this set. 1,2,3,4,6,12 is just as impressive as 60's 12 divisors, and it explains clocks and rulers.

    • @docastrov9013
      @docastrov9013 Рік тому

      ​@@FelineBlenderPounds, Shillings and Pence.

    • @ExaltedDuck
      @ExaltedDuck Рік тому

      When people complain about pre-metric measurement systems I like to point out that the 12, 60, and 360 bases made great works of architecture possible in the pre-industrial ages. Base 10 and thousands prefixes don't actually mean a whole lot. The prefixes introduce opportunities for conversion errors and are unnecessary due to scientific notation and - in a lot of cases - get a bit unwieldy without helper electronics.

  • @xdjrockstar
    @xdjrockstar Рік тому +1

    What a lovely puzzle and video

  • @twoblink
    @twoblink Рік тому

    I didn't need to know this; but I watched the entire video and was better for it! Thank you! Quite interesting!

  • @jaopredoramires
    @jaopredoramires Рік тому +4

    I like how Ben is like a master in GeoGebra

  • @RUBINHO12321
    @RUBINHO12321 Рік тому +1

    Great video!
    I would love to see a video teaching how to build this problem in geogebra

  • @The_JS_Camper
    @The_JS_Camper Рік тому

    I liked the start of an additional pattern showing on the final shot. If you tally the columns with squares you get 2,0,0,2,1,2,0,0,2,1
    Which you need to go up to 400 in order to see it double. Then I saw different pattern on the rows of 2,2,2,2,1,1,2,2,2,2,1,1. I saw this by starting from the number 1, and going across, you pass 2 squares going right before heading back to the left on the placement of the number line. This one is harder to put into words, but you can see it starting to emerge in the first 100.
    Dig the channel. 👍

  • @gunnarliljas8459
    @gunnarliljas8459 Рік тому

    What a nice guy. Nicely presented and interviewed.

  • @Chelm9
    @Chelm9 Рік тому +1

    729 is an interesting one that would be switched on because it has 7 factors, because it’s 3^6, which has two “duplicate factors”, 3^2 and 3^4

  • @richardl6751
    @richardl6751 Рік тому +2

    About a 20 years ago I wrote a QBASIC program to solve this. It used 100 lockers instead of lights. I wanted to check for higher numbers and expanded the program to 400, then 1600. It was on an old 8086 4 MHz machine so it took a while to run.

    • @philipshell5494
      @philipshell5494 Рік тому

      I made a comment of an observation I saw on this problem basically using addition (or subtraction) to solve this problem. See if you can find my comment and write a program using my more simple logic to solve the problem.

    • @richardl6751
      @richardl6751 Рік тому

      @@philipshell5494 Sorry, couldn't find it. Can you copy and paste it here?

  • @AliGhorbani_a
    @AliGhorbani_a Рік тому

    This is such a refreshing video. Thank you

  • @MrMas9
    @MrMas9 Рік тому

    Great video as always !

  • @NoriMori1992
    @NoriMori1992 11 місяців тому

    I love how over the years you can see Brady's math knowledge and understanding growing and his astuteness improving. I thought he'd be tripped up by 16 seeming to only have one duplication, but he pointed out right away that 4 x 4 can also be expressed as 2 x 2 x 2 x 2.

  • @wiscadams
    @wiscadams Рік тому

    This problem was presented to me in an interview decades ago, except it was a hallway of lockers that you would open and shut, instead of lights. The next level is to figure out what happens if you alternate directions you toggle each number.

  • @danielngmoen3901
    @danielngmoen3901 Рік тому +1

    Woah what a cool solution! I thought along side the video, and was thinking of another possible solution:
    If you take all the numbers exponents and remove one, then sum them so
    n = (c1-1) + (c2-1) + . . . + (ck-1),
    the light switch will stay on only if this number is odd, and will stay off if the number is even. Any flaw to my logic?

  • @eugenefullstack7613
    @eugenefullstack7613 Місяць тому

    05:45 broke my brain! THAT WAS AWESOME!!!

  • @U2kheim
    @U2kheim Рік тому

    Great puzzle! I will sure be trying it out on my students sometime in the future!

  • @hughbarton5743
    @hughbarton5743 Рік тому +1

    Hooray for Ben!!!

  • @Unknown-tx5iq
    @Unknown-tx5iq Рік тому +1

    Your channel makes me love maths even more. ❣️

  • @Baritocity
    @Baritocity Рік тому

    I was just thinking about this problem because of a sudoku puzzle I couldn't solve on my own that used this idea. Thanks.

  • @kelqka
    @kelqka Рік тому +1

    In Uni I had a similar question I had to verbally answer on the spot, to cement my grade in a class:
    "If you have 1000 lights. What is the least amount of switches you would need, to turn on Any Number of them"
    Tip: It was for a basic programing class

  • @jamesregovich5244
    @jamesregovich5244 Рік тому

    This problem introduced me to the idea of first differences, in which I “discovered that the first difference of the perfect squares is the series of odd numbers, which makes finding the state of the nth switch easily figured out.

  • @katari8604
    @katari8604 Рік тому

    Amazing old style Numberphile video. I think one specific part deserved more attention. The part at 15:00 where we deem that all square numbers +1 are odd. If we were to use 2^4 * 3^4 we'd get a nice number that satisifes the logic -> that is 1296 but as you might have guessed it's the square another number - 36 as you can evenly split the above multiplication into 2 simetrical groups (2^2 * 3^2) * (2^2 * 3^2) ... or just 36^2 :)

  • @llegaremosalasestrellas3245

    Very interesting!! I love your videos Ben!!

  • @ostimeg
    @ostimeg Рік тому

    That 'click!' at the very end was perfect

  • @user-fp7jz4ot6f
    @user-fp7jz4ot6f Рік тому +2

    heard about this problem a few weeks ago and solved it in a few minutes but very nice

    • @alanredversangel
      @alanredversangel Рік тому

      Me too. Then the Illuminati came and tried to recruit me but I said no thanks I'm quite happy just doing my DJing. They gave me a speedboat though because they respected my answer. I gave it to charity.

  • @pauljones2510
    @pauljones2510 Рік тому +1

    In general, I like math videos. This one was especially nice. Very simple but rather intriguing.

  • @sledgehammer-productions
    @sledgehammer-productions Рік тому +1

    I assigned the on-lights to midi notes sounding and at the end (100, 10^2) I have 2xA, 4xC#, 4xE (that makes A major) and 1xC (A minor). And even when I extend the sequence to 76^2 I only get those 4 notes. This surprised me. So far I haven't been able to assess why this is. I like that it's neither major or minor, just somewhat in the middle.

  • @alexzapf8212
    @alexzapf8212 Рік тому

    Awesome! Very fun and informative.

  • @Greghouse
    @Greghouse Рік тому +6

    Now let's imagine the lights don't switch on and off but rather cycle through 3 states (off-red-blue). Now what colors will the lights be? 😀

    • @PMA_ReginaldBoscoG
      @PMA_ReginaldBoscoG Рік тому +1

      Since there are four possibilities for the state of a light bulb, you have calculate the remainder of the number of factors when divided by 4.

  • @matthewsaulsbury3011
    @matthewsaulsbury3011 Рік тому

    Wow! I didn't know this pattern existed! It's really neat!

  • @mpalin11
    @mpalin11 Рік тому

    Great stuff as always 👌

  • @kushagrapiano9036
    @kushagrapiano9036 Рік тому

    Great explanation