Could you avoid being hit by a laser if you were in a room of mirrors?
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Alright 2 things to add here
1) Be sure to checkout stemerch.com for the new recommended booklist as well as STEM related apparel, the floating globe, and more! Also you'll notice another tab for 'recommended textbooks' which are good for self study, this is a common question I get as well so will keep that updated.
2) Spoilers down below but this is where I want to acknowledge what I mention at the end of the video. I never explained WHY there is repetition after you reflect the midpoint back to the main room and the best explanation I got is quite a mouthful and it involves modular arithmetic. Let's say that the target is at point (x,y) (and we're just going to consider the horizontal reflections). After you reflect it to the right, the reflection lands at (2-x,y) and after another reflection it goes to (2+x,y) then (4-x,y) then (4+x,y) and so on. As you can see, reflected points all land at (2n +- x,y) (as in the x coordinates are just even numbers plus or minus x).
Adding in some modular arithmetic you'll notice these are all congruent to x (mod 1), or -x (mod 1) . That's all that can happen as you reflect a point about the left or ride side of those 1x1 squares actually, the point either stays the same (mod 1), or it becomes negative (mod 1).
Now again, all the x coordinates of the reflected targets can be written as 2n +- x, meaning the midpoints would be (2n+x+u)/2 = n + x/2 + u/2 and (2n-x+u)/2 = n - x/2 + u/2 (assuming the shooter has coordinates (u,v)). So we have two sets of midpoints and these midpoints go on forever with n. When those points are reflected back, as we've seen, they either stay the same mod 1, or become negative mod 1. So we have 4 different results, n+x/2+u/2, n-x/2+u/2, -n-x/2-u/2, and -n+x/2-u/2 (all mod 1). This seems like infinitely many points still because of n, but n can be dropped from all of these because it doesn't change the value mod 1. For example 1+x/2+u/2 = 2+x/2+u/2 mod 1, meaning they are the same point in the original 1x1 room. So we have 4 answers, x/2+u/2, -x/2+u/2, -x/2-u/2, and x/2-u/2 (all mod 1), these are all the x coordinates after the midpoints are reflected back, there can be nothing more. So that's 4 different x coordinates and the same thing can be done for the y coordinates, leaving us with 16 points in total.
Then to finally to answer the other question of how can you be safe with less than 16 blockers, it can happen if the x (or y) coordinates of the shooter and target add to 1. Because then x/2+u/2 and -x/2 - u/2 are now congruent mod 1, and the other two are also congruent. So what was 4 different x coordinates becomes 2.
So, I'm guessing the next video is going to be about modular arithmetic then?
Also, shouldn't it be mod 4, as they repeat after 4 reflections? I'm confused.
@@RussellSubedi he used the continuous version of mod not the normal number theory one. It's like how you can always reduce an angle to it's representation mod 2pi. 3pi = pi (mod 2pi).
@@thedoublehelix5661 I'm not really familiar with it, so got confused. Still looking forward to a video on it though.
I'm gonna pretend I understood it
@@thedoublehelix5661 What's the normal number theory one? I thought mod just gave you the least number greater than 0 left after repeated subtraction. Doesn't that definition rope everything in?
Man i hate when im in a perfectly square room made of mirrors and there is someone trying to shoot me with a laser which will never lose its energy as it reflects, thank you for the video.
Damn, it's so annoying, im so grateful that this video exist.
Also I hate being a point in a 2 dimmensional space
SHOOTER MOVES TO A DIFFERENT LOCATION
Oh shi
@@RoeiCohen go to a corner and make a barrier xddd
Hate it when that happens man
To all people who say math has no applications, what a fool you must feel now! Who can say he has never been in this extremely relatable situation?
You never know man :D
It's not relatable because usually the laser is able to move around where in this the laser can only rotate. Additionally people and blockers are not points.
@Andrew Anderson Since you are much bigger than the laser, you can't just approximate yourself as a point.
No application? The whole our modern world is based on math. The quantitative understanding of every science is based on math, be it "rocket science" or gardening. But this is of course has a great application in video-gaming ;-)
@@iteerrex8166 Okay Sheldon Cooper, understand the context here omg :D
Now we just need someone to individually animate all the laser paths
no
I wanna say challenge accepted so much, but i dont have time/determination to do it lol
Just do a light blub
The rtx 3090 was made for a reason
Red cube
This has happened to me 7 times now and I’ve died every single time. Thanks for the tip for when it happens again!
Yo, has it happened again? You okay?
@@RealBasil143 I’m a survivor.
He´s a cat, last life
just use a totem of undying
Pretty cool how, in a room full of mirrors, this would also completely hide you from a target.
wait what thats actually true lmao
wouldnt just shooting at one of your reflections result in being hit?
Yes lol
@@hannibal8810 did you watch the video
ohh so this is why evolution gave us two eyes. it's not for seeing distance using parallax, it's so you always see your target in perfectly reflective square room in 2 dimentional world with 16 point blockers in exact blocking positions trying to shoot it with laser gun that doesn't loose it's energy after reflection. obviously!
Damn now I know what would happen if I was stuck in a mirror room with lasers
simple solution: wear armor of polished aluminum
reality is 3d instead of 2d.
@@srijitapaul5080 Oh yeah, that's true, there's no reason it shouldn't work in 3 dimensions as well. Or, for that matter, even higher dimensions (I think).
I thought something felt off about my answer: "
Russell Subedi
39 minutes ago (edited)
For a cube, I think it's simple. Just go up to 4x4x4=64 dots. For a triangle though, I'm guessing 9 dots (as it would repeat after 3 iterations) making 27 for a tetrahedral room.
Edit: I just thought of it as a tiling problem, which might not have worked. If someone sees a problem with this, an explanation would be appreciated."
@@cordlefhrichter1520 triangles don't tile the same way as squares, in the video the square room is used as a unit in the coordinate plane, but u can't do that with triangles… maybe?
*Me when I saw the title:* oh well you just wait until the light dissipates.
*the video immediately:* It never loses its energy.
No it says curiositystream immediately
You may have outsmarted me, but I have outsmarted your outsmarting
@@DoodleNoodle129 I'm gonna pretend that I understand how that makes sense with the context.
@@dannyboi7286 he thought he outsmarted the problem, but his outsmarting was outsmarted by the lack of energy dissipation
@@DoodleNoodle129 joseph
interesting stuff. i'd love to see some sort of interactive demo where you could drag around the two points and see how all the blockers would have to move to compensate.
same i was hoping for one
it might be easy to program it, it doesn't involve any strange formula
Room of mirrors where a lazer that never runs out of energy trying to kill you sounds like an SCP entry
fellow scp lover
Sound more like a Stand ability
Yeah it does
@@resurrectedcandywastaken no he's correct
Lol
the 20 dislikes are from people who surrounded themselves with 8 points thinking they were circles.
false i didn't dislike
@@davidegaruti2582 nonono, he said that people who disliked thought they were circles, not people who thought they were circles disliked.
100% of the people who disliked thought they were circles
not 100% of the people who thought they were circles disliked
@@davidegaruti2582 no
@@vilmavaitonyte2451 but that's just the same but said differently
@@user-rh8re2jf5f no, they're different. The first says everyone who disliked thought they were circles. So 10/10 people thought they were circles and disliked. But the second says 100% of people who thought they were circles, disliked. Which is different. Because 10 more people could've thought they were circles, but only 8 of those 10 disliked. So 100% of people who disliked thought they were circles, but not 100% of people who thought they were circles, disliked.
Just say no and the light won't touch you because it isn't legally allowed touch you without your consent. No need of those fancy 16 blockers
I wouldn't use the word "legally" here. There's nothing in the laws of physics that prevents the light from touching you, even though there's a moral concern.
@@RussellSubedi Sure there is, why do you think it's called the "Laws of Physics"? Because if the light breaks one of the laws, like the speed limit, then it goes to jail.
@@cordlefhrichter1520 Well, it would go to jail before it breaks the law, if the law in question is the speed limit.
Instructions unclear, I turned invisible
Haha black hole succ light
The amount of peope saying "just put 4/5/6 blockers around you" is genuinely worrying
If DVD screens taught ne something: yes if you stay on corners.
Yes, just put a blocker there to be safe.
@@mouthlesshater that’s a good wisdom
Also all hail Winner
winner how do you feel joining TPOT
Tcher jhigl seghrt fhcwerd ghthicmus!!!!
Mathematicians: Uses this information for intellectual purposes
Me: uses this information to beat my friends in air hockey
Except this time your the blocker and it’s not just a point but a thick thing which I don’t know the name of, but I see your point.
@@tomwanders6022 puck, the word you're looking for is puck
@@deathsheir2035 ty good sir. So its the same name in german.
@@tomwanders6022 in Spanish we call it "That thing used to play Air Hockey"
@@ARandomMinecraftVillager huh I’be usually heard it being called “el disco”
I would see myself probably dunno ngl
wtf did I comment lol
@@PapaFlammy69 🤔🤔🤔🤔🤔
@@PapaFlammy69 papa has short term memory loss 😳
Hmm RUclips says this comment was posted 4 days ago and the replies 5 days ago
He was tripping 🤣🤣
Going from comedy sketches to in-depth presentations on something as interesting as this, is a pretty amazing transition, GG
I thought it was the other way around?
Other way around
@@iamcurious9541 Yes
@@youyou475 yeah yeah, still a pretty respectable transition.
Kid, “math is so stupid why do we have to learn it, I’m never going to use it?”
“Yes you will, because lasers.”
the sun is a deadly laser
Not anymore there's a blanket~
“No”
Not yet
Why didn’t he just put the blockers in a circle around the target? Am I missing something?
“to answer that, we need to talk about parallel universes”
10/10 reference
Or do we? To answer that, we need to define "parallel universes".
Super Mario 64 Star through the Bouncing Laser 1x Blocker
It’s weird that the pattern repeats every 4. If mario is qpu aligned then the direct path blocker will always work
Ur logo small pp but u big pp
The solution was surprising and surprisingly satisfying.
I didn't watch it. It depends on the shape of the room.
Very much so!
Satisfyingly surprising and surprisingly satisfying.
It's actually surprisingly simple.
@@manuell3505 well, if you’d watch in then you’d know he was using a square.
Just guessing without thinking too hard about it, but I'm going to guess it's 16 because of this: You have 4 sides, so you have 2^4 ways of using those sides - you're using each side either an odd or even number of times. A higher number of odd/even times just ends up cancelling them down to simplify into one of the basic 16 situations.
To simplify, let's just look at the left and right walls. Either you're hitting both an even number of times, the left odd and right even, the left even and right odd, or both an odd number of times. Whether the combination is left 2 and right 1 or left 10 and right 9, the same point ends up being it's center point. That's the 4 dots you put at first.
Anyone who has seen the DVD logo bounce on a screen knows the safest spot is the corner
Tbh the logo should just travel in a shape of a parallelogram
Cuz screens are rectangular and the logo bounces in the same angle as when it’s incoming so it just repeat the same angle when bouncing every two times and that’s parallelogram
Yeah!
Anyone who has watched the office knows that’s not true
This was my exact line of thought
Math puzzles:
"We'll start small and work up to infinity"
4 years later.. Lol
consider: put a point directly on the shooter so no lasers can be shot, they would be absorbed immediately for infinitely many paths
consider: GET NORD VPN NOW! KEEPS ALL YOUR PASSWORDS SAFE FROM HACKERS! USE LINK BELOW FOR 2 MONTH FREE TRIAL!
He can turn around and bounce off the back wall
@@DaBestNub again, it would be stopped at its origin, so no lasers can leave
@@beanslinger2 do you mean right on top or directly in front?
@@DaBestNub right on top, like in the same position
This use of reflections is also one method for calculating bank and kick shots in pool off of one or multiple rails (just factor in a little bit of physics about speed and friction).
This is definitely relatable. The other day I was stuck inside a rectangular room with the four walls made of mirrors. And there was someone trying to shoot me with a laser gun! What a horrifying experience! Fortunately I was able to locate the 16 blockers on the correct coordinates. So I survived
im sure you were glad you were not in a cube or you would have been SOL
@@Quantainiumify
Does the same logic not work adding 1 more dimension? It would just be 4^3 blockers, or 64.
If you were in this totally retatable problem, and someone actually was trying to shoot you with a lazer gun, and it wasnt an immovable robot or something, they could simply move past the blockers.
But i guess not since youre alive still
@@freezo7299 they don't dare lmao, if that's reality I rather not shoot, I don't wanna die since I can't really calculate the lazor path precisely
Getting this comment a lot so just want to emphasize that these blockers are NOT pixels, they are infinitely small (zero dimensional) points. So no you cannot surround the shooter or target with 8 of these blockers (or any finite number), to actually surround one of them you'd need an uncountably infinite number of blockers.
I guess one could ask how can a zero dimensional point block a three dimensional photon that occupies nonzero volume but suffice to say that this thought experiment assumes the reflecting light to also be point-like and zero dimensional.
@@MarkPariente no
I'd just break the mirrors lol
Just place a blocker on the shooters exact x y position. A light cant be spawmed then and yuo win
That doesn't make things better. That means that the situation is even harder to deal with...
I feel like this could work well as a puzzle video game. You have 16 blockers at the beginning, and a very unskilled opponent, who fires directly at you with one laser, but as you get further into the puzzles, the opponent uses more lasers, takes unusual paths, and you get less blockers over time.
The meta would be making a circle around you with the blockers or trapping the shooter
ender's game type beat
@@vindastew frr lol
@@vindastew that movie sucks fr
@@SpeedKing.. ok
If American students paid attention in math class they'd know how to avoid shooters.
"Can't we just do this?"
"No we can't."
"Ok, but we could if we turned this problem into an entirely different one."
nice 69 likes
Yeah for an example you could just suround yourself with the circles
@@jonathanholtlajer2949 or surround the Lazer
@your mother it would?
@your mother then they wouldnt block anything?
so then if set up properly, the target and the shooter wouldn’t be able to see each other in the mirrors
You blew my mind!
Why
if you cant see me, you cant attack me
@@moo8866 if there is no possible path for a beam of light to take from one point to another, you can not see that point as you have no light reaching your eyes from that point
@@moo8866 the only way for a laser to bounce off a mirror and hit a target is if you aim it at one of the reflections.
In this video, all the paths the laser can take to the target have been covered. So from the point of origin of the laser you can't see the target
This was a really cool puzzle. I didn’t entirely understand it but it was cool.
What didn't you understand?
How the grid and its xy values can correspond to inside the room
@@adm4939 why 4 reflections in x axis? Why not 5 or 3 or even 2? What's so special about number 4 here? He simply told us they will repeat, yet he didn't proved it mathematically.
4: the # of sides of the room?
@@lighthunter8917 he said he would explain elsewhere, and he did. It’s in the pinned comment
In a room with mirrors on walls, for each pair (light source, observer) there is a set of 16 columns that will obstruct not only the light from the source, but also the light from all reflections. Now I want to see how the position of those 16 points changes as the positions of the light source and observer change.
Waiting for the day some bored person that’s good with Python puts this together and links it here, haha
"Switching to your pistol is faster than Reloading."
True but carrying ammo uses less space
@@largeavocado never enter combat without a sidearm
Am I the only confused one?
@@dannyboi7286 No
@@dannyboi7286 profile picture fits.
I’ve played enough laser tag with mirrors to know that as long as you can see them in the mirror you can shoot them. So you would just need enough blocks to block off line of sight. Simplified.
That’s a cool analogy actually.
Ever bounced a laser off three mirrors and hit someone?
I thought about the same thing lol
Yes but if you're in a room where all the walls are mirrors, there's an infinite number of reflections. So there's no way to know how to place a finite number of blockers to break line of sight with every reflection.
@@ZachAttack6089 just do a 360 and so long as you can’t see them in the reflection at all no matter where you turn then you aight.
Before I start watching:
Judging by the experience of looking at DVD logos, stay in the corners.
After I watched the video:
Ah, you mean setting up the blockers, not positioning yourself.
Well, now you know not to put a blocker in the corner
Sit in the corner with 3 blockers and you win
@@maxx8069 no, these are infinitely small dots not circles. It would take infinity of them to surround either you or the shooter, sorry.
@@dan-us6nk Sitting in a corner still reduces the number of sides you can get hit from, so it might be a special case where you need less blockers, same with any case where the shooter and target are rotationally symmetric to the center of the room or the target is sitting on an edge or a line of symmetry of the room, I'd imagine.
@frost bite No, but there is no infinite number of blockers, as the video established, only 16 will block any direction for a general case in a square room, special cases require even less.
I am just realizing that this is the same guy who makes all the comedy sketches that I watch. I had no clue about this, and am doubting life as I know it. I never thought of him as a mathematician.
Ah, yes, now I just need to prepare 16 blockers to be carried with me everywhere I go in case I land in this super relatable situation again.
wait........ again?!
*prepares 1 blocker*
I’m prepared.
*hides on corner*
Yeet the block at the shooter when he's distracted.
lmao
You fuck up and yeet it at his reflection. GG
@@tubax926 you just took down many possible paths. Gg
Yea tell him theres a mirror behind him
You just need to start dancing the distraction dance
Me, a geniuos: Simply place the blocker on the shooter
lol
Same here
That's precisely what my girlfriend said the exact second I finished reading the title of what I was watching to her lol
Mathematics is still fun, but sometimes reality gives you better solutions that a calculation.
Specifically inside the gun
Or on yourself since u r literally a single point
If where u r absorb every laser u cant get killed :)
Late to the party, but does this apply to rooms with differing number of sides?
Would an octoganal room require 64 blockers? Triangular 9?
I just realized that the shooter also wouldn’t be able to see you
Very true
No. The room is filled with mirrors. Oh shit!
one question
if the whole room is made out of mirrors, then how did we got in
@@PotatooCake you obviously walked in when there were only 5 sides and the sixth one was built around you
@@PotatooCake
Because the door is a push door (no handles) that his made out of a mirror on the side of the room (so good luck finding it after your done
Can’t I just stand in a corner and put like 3 blockers together to completely block the laser
Assuming you are an infinitely small point, you would only need one, since the laser can never naturally reflect into the corner, only get infinitely closer to it.
Or just surround yourself with 8 without even moving
@@randomperson1844 you mean surround yourself with infinite points?
@@Pihsrosnec imagine you are a square
You surround yourself in 8 squares
You are protected from all sides
The blocker, you are infinetly small. And the laser is super precise
Having played a lot of Portal 2 community maps, I really can relate to this problem.
my brain just went before any explaination "just use 6 blocker around you (make sure they touch each other) and you'd be good to go" and then you used almost 3 times as many
Stand at any point in the square room, and look around yourself. Anywhere where you can see the shooter, either directly, through a mirror, or through multiple mirrors, put a blocker in between. Once you cannot see the shooter anymore (all places where you previously could see the shooter are now blocked), you are safe.
Wouldn’t work on a bl2 fibber user lol
I love this solution as well. The first one is the mathematical solution and this is the engineer's solution.
You would need more than 16 blockers after you inevitably place many of them in unoptimal spots
@@kylebroflovski6382 He is referring to standing in that room. Now go stand in that room and try what was done in the video. That's impossible
also...line of sight is the key. The blockers don't need a certain distance. Exact playcement isn't necessary
@Swingtity I can't stand in the room because it's a 2D plane and I'm a 3 dimensional person. What's your point?
Also if you were in a 2D mirrored room with mirrors that absorb 0% of the reflected light, it would form a black hole, but if it didn't, the amount of reflections of you would be virtually infinite.
This feels like the kind of thing that would show up in an anime or sci-fi movie or something. "Why can't my lasers hit you!?" "Well you see..."
They either explain something so simple anyone could have already guessed it or they make some bullshit up on the spot.
My favourite was in Naruot when you saw it happening, one Guy explained it and the other Guy had a flashback of doing it.
"ONE POINT BLOCKERS, SON!"
Jojo)
@@neoxus30 white album: gently weeps
E
Me, an intellectual: *just stand in the corner and cover yourself with 3 blockers lmao*
you are the most intelligent being in this comment section
Or if not just surround ur self
0:24 OOF I guess you could just surround yourself with like 12 blockers
Also I swear to God if someone whooshes me I might be a bit upset
I hadn't read before my coment
Yes
I’m late to the show, and there’s a lot of cheeky comments so far. I just want to say that I was really surprised, and really happy with the result! Thank you for this.
That is an incredible puzzle. At first I was convinced the answer would have to be uncountably infinite, then after seeing the first step of the proof I thought it would be countably infinite, as we can represent each possibility on a NxN grid. And then the pattern starts repeating, very cool stuff!
Me: Eight to surround the target
I had exactly the same line of thought! this problem is fascinating
@@savant_fou9483 You actually only need 6 if you position them right. You arrange the circles in a hexagon instead of a square.
@@megaparsec4 Those aren't circles, but points with zero width. He could just shoot the laser between any two of the six.
@@proot. Thanks for pointing that out. I was going off of the idea that they were like how they were represented in the video graphics, but after watching the video again I realize that he mentions that a couple of times.
Me: just surrounds myself with blockers that slightly overlap
Blocker is a point
so you need infinite blockers
@@koshakvesely8186 but there isnt anything said about a point having a specific size
@@RiskierGoose340 A point is an idealized, primitive notion. It does not have any physical size
@@koshakvesely8186 ok then, u win this time
That card that said “the globe you are staring at” actually caught me off guard
Before watching, I have 3 ideas for an amount to protect myself.
1: if blockers can be any shape of any size: 1. Just a wall through the whole room.
2: if blockers can be rectangles of limited size, 3. Triangular around me, trapping me.
2: if they have to be circles of equal size to my footprint circle, 6. Hexagonally around me. Touching me as well as themselves, leaving no gap.
I know nothing about math so all of this sounded like magic but I felt like I learnt something so I have that going for me. Cool video 😎
Math sounds like magic untill you need to slove it yourself
You are everywhere
That feeling is “almost understanding the solution to the problem you can’t solve it yourself”
Just don't smoke
I just tapped the blocker over the laser.
You're probably not reading this, but could you also do it for 3 dimentional space ?
pretty sure its just 64 points consturcted in the same way then bc the maths dont change significantly by adding more dimensions to reflect in. same with 256 points in 4 dim and so on
@@PHILTente So if I'm understanding correctly, in N-dimensional space you need exactly 4^N blockers to block all sightlines if N > 1?
@@Tuzszo on a 1-dimensional space you just need 1 blocker
edit: wtf, i'm dumb, yes, if N > 1.
@@PHILTente the finiteness of the answer is clear, but it's not clear how the number of available paths grows as the number of dimensions grows. In 1d it's 1 point, in 2d it's 16 points. So the pattern is not really clear.
Be a gigachad and do it for 26 dimensions
It'd be interesting to do this in real life. Have a room with mirror walls, floors, and ceiling.
Add a small light source, and 16 pillars a bit thicker than the light source covered in vantablack, black 3.0, or another really dark substance.
Mark a very specific place where someone can stand (in dark clothing), close one eye, and see no light.
It would be so cool opening the other eye (or just moving a bit) and seeing the light.
The only flaw I see is how flat we can make mirrors, but it seems doable.
Also the fact that light becomes fainter
Cool idea. I could totally see something like this being done at a science/ discovery museum. A cool practical demonstration of math.
you know, one day you might appear in the room with 3 pathways. and you'll be standing in the exact right spot. trying to get some wifi. and you'll be wondernig "why can't i catch a wifi in that damn place?"
the first thing i thought was hiding in the corner and adding 2 blockers to block the 2 sides
"We'll work up to infinity" I don't know man, I haven't got all day, or the lifetime of the universe for that matter
The death of the universe will happen in a finite, countable number of years, so since they're going over an infinite, uncountable amount of possible mirror-room scenarios, this video should still be playing quintillions of years after all life forms are long gone
kinda suspicious that it's only 11 minutes then /j
@@zypper7213 whooosh
@un ko double whooosh
bruh the universe will like die in 2021 (btw after 2020 dec 31 59:59 it will be 2020 dec 31 60:00).
1:32 I was just thinking "woah what's that cool spinning thing in the background" and then the i-card appeared
Same here
Lmao
Yeah I wasn't even listening and then I saw that I card and I was like wtf how does he know
same
I was confused when that popped up since the lecture immediately covered the orb so I didn't know what it was referring to
Me: puts a blocker directly at the shooter *"Sometimes my genius is almost frightening"*
Just surround yourself with blockers if you wanna go reversal
@@cyan_tree4907 But then you are trapped. Better to block in the shooter instead. Also, that wouldn't actually work, because although he scaled up the points size so you could see it, all the points are still infinitely small. So you would need infinitely many of them to fully block him in.
Exactly
@@aguyontheinternet8436 the points would the to be scaled relative you the target (you). So all youd need is a few you sized blockers.
@@aguyontheinternet8436 you can obviously move the blockers if you were able to put them anywhere in the room
Thanks! Now, I know what to do if I'm stuck in a room of mirrors and someone's trying to shoot me with a laser!
This is actually very similar to a coding interview I got from Google! The difference was that the laser did lose energy and you had to count all of the ways the laser hit the target, and the shooter was a target. I still landed on the reflection strategy, tho.
First instinct: countably infinite, were gonna talk about Ulam's spiral and counting rational fractions
Did they expect you to solve that one on the spot?
@@fakharyarkhan5848 No, it was an online coding challenge thing; I think I had a day to solve it?
@@AMTunLimited oh ok that's more fair. That sounds like a pretty cool variation of the problem then.
@@fakharyarkhan5848 Yeah, for those worried at home Google interview questions are nowhere NEAR this wild, and they make it a point to try and not rely on "aha" moments
Is there any way for you to link the problem? I'm curious to see what the correct answers are because I'm sure I must be missing something, but it seems to me that if it loses, say, 10% of its outset energy that means 10 reflections which I'm fairly sure means 4^10 possibilities.
Starting from today I'm gonna always take 16 bricks with me! You never know...
"Why do you have 16 bricks with you?"
"Well let's say I'm a single point..."
Can we extend this solution for 3D? I mean, I am ready to be still considered a single point, but in a room with mirror walls and ceilings
@@rampukaradhikari4716 It's easily extended to n-dimensional by the same argument, and it's 4^n (except for n = 1 🙂)
@@rampukaradhikari4716 That would mean we'd have 64 points?
@@rampukaradhikari4716 4for the x coor x 4 for the y coor x 4 for the z coor
Crazy how 16 one CM blockers block ALL paths
Me, an intellectual: puts the blocker infront of the shooter
Shooter: turns around.
@@AllExistence puts blocker around shooter
@@chriskoutroubanos7497 thats an easy way to do it
and you have a lot of space to run around, no laser bothering
I would stand on the blocker
This is so interesting. Math used like this expands the mind I believe.
Cringe
What's a mind ?
We re junkies....
@@520_metal image saying cringe to someone that probably actually watched the whole video.
@@520_metal how is this cringe?
What would happen in different shaped rooms? (Triangle, hexagon...)
Perhaps even 3 dimensional rooms, like say a cube, I wonder what you would get as an answer then!
Also want to know
For a cube, I think it's simple. Just go up to 4x4x4=64 dots. For a triangle though, I'm guessing 9 dots (as it would repeat after 3 iterations) making 27 for a tetrahedral room.
Edit: I just thought of it as a tiling problem, which might not have worked. If someone sees a problem with this, an explanation would be appreciated.
In a cube i would assume it would be 64 blockers
Or pentagons, which cannot be proven geometrically by tiling like the square, triangle, and hexagon
@@herobrine1847 ooh, that would be an interesting puzzle. You can tile the plane with pentagonal symmetry but it is aperiodic, so I would guess that for a pentagon, you would need infinite blockers.
Here is a (greatly altered) version of the problem. Let's assume that there are no blockers, but the shooter can place static mirrors before shooting the laser. If the laser's path will not be affected by hitting the target, is it possible that the shooter does not shoot themselves?
Now i finally see the purpose of Raytracing, somebody needs to whip out their RTX and make this into a simulation.
THIS IS SUCH A GOOD COMPUTER SCIENCE PROJECT. It will be hard to do this though, because of rounding errors...
@@WavyCats oh and the fact that rtx is expensive as hell
@@Alan-ek3ko yeah today it is because of upselling but I’m lucky I already have one :)
@@WavyCats oh, nice!
You can see that simulation here: ruclips.net/video/Lnp46-qj5cE/видео.html
Also, I suggest you checkout his channel. It's full of gems like this one. :)
Here’s the solution: Tell the shooter that they might have green eyes.
is this a reference to that one logic problem with all the green-eyed people?
Run.
bahaha ik that riddle
TED ED
Since he does have green eyes, everyone is legally allowed to leave the room.
If there even is a way out.
Oh damn, now I'm totally not scared to go with 16 blocks into the perfect square room, made of perfectly reflecting glass with someone else who has a laser gun.
My thoughts directly told me to just surround the shooter with the blockers and call it a day.
Question! This only applies to a 2-dimensional plane, so I'm genuinely curious how it would apply if you had another axis, making it 3-dimensional; in this example, the ceiling and floor would also be made out of mirrors, and the shooter is able to aim for them to go over or under your blocker points.
I hypothesize because math reasons that, instead of 16, you'd perhaps need 64 points to block it? The number 16 is a little too convenient not to be produced by some kind of exponential formula- that's my guess, at least. Curious if that's right or wrong?
i don’t know the answer but an alternative to 4^dimension or 16=4^2 could be 16=2^2^2 or d^d^d so 3d plane would be 3^27..? just my guess i don’t think it’s right because i don’t understand why it repeats after the 4th (i understand the model i just don’t get why it’s *4* in particular)
@@cnidocyte It repeats after the 4th in all three dimensions giving 64 blockers!
@@cnidocyte its cause when the laser has been reflected 4 times, it will have the same angle as when it started.
and for each angle, there is only one point on each corresponding wall that will lead to the target. so you only have to block each angle once.
I'm not 100% on this one, this is just a guess. But in a one dimensional space, you'd only need one blocker, since there is only one line the laser can follow. So I think the way to define the number of blockers is 16^(n-1) where n is the number of dimensions.
16^(1-1) = 1 blocker
16^(2-1) = 16 blockers
16^(3-1) = 256 blockers, the 16 we had earlier only repeated on the vertical dimension.
The blocker points could just expand to touch both the ceiling and floor, thereby covering those spots
you can solve it by making the blockers pillars that are touching the ceiling and floor. ye?
That was a major call-out to me staring at the globe lol
Thank you for this. I’ll remember it the next time I’m in a two-dimensional room full of mirrors with a man shooting me with non-energy-consuming lasers and I’m free to place single points to stop the laser.
Fun Fact: If you put the mirror walls in front of the shooter all ways and connect them together the laser will be trapped and can’t get out so you only need 4 - 8
infinite*
commenting this before watching: just stay under the laser
*It was completely off topic*
Not allowed!
LOL FR
you are two dimentional
Now I’m curious how many you would need if the space was 3d rather than 2d. I’m gonna guess 64, as the number needed for a single axis is four, and as there would be 3 axis, 4^3=64
Sounds right 😄
Something tells me it would be 6^3, because 6 faces it can reflect off instead of 4 edges
@@cros108 so how it works is the 2 opposing faces will reflect the same image after its 2nd reflection
So the square has 4 sides (2 opposing faces) so that us why the number is 16 (4^2) 😄
A cube has 6 sides (3 opposing faces) hence the 3 in 4^3 😄👍
Hope that clears things up
@@Zoltria Ohhh I'm an idiot. Thanks for that explanation.
No, it would be 4^4, if in 2d you need 16 balls in one line and the third dimension line is the same lenth, you would need sixteen times sixteen, not 4^3, that means four times sixteen. Obviously suposing that this theory is correct
I came back to this after a couple of years. What if I'm in a cube where each of the walls are mirrors, and the shooter and I are at any point in the cube?
It's a simple generalization, 4^3 = 64 blockers will be enough.
But what if I am the cube and I don't want to get shot by any of that lazer!
@@kujojotarostandoceanman2641 at that point you will need uncountably infinite blockers to make a full wall.
E
@adayah2933 What if I'm in a tetrahedron?
Gotta say, knowing Zach only from his skits and not checking the channel name when clicking the video, seeing him pop up was an absolute shock lmao
I’m wondering how this theory can be applied when setting up sound studios or listening rooms, where it’s important to treat reflections off the walls/ceiling/floor to ensure good/controlled room acoustics.
Fortunately for you, your blockers aren't 1 dimensional points, you can just set up those things on the walls and not have to arrange 16*16 points of perfect matter
this is why acoustic engineering exists
How to avoid the laser:
Step 1. Turn off the Laser.
Step 2. avoid
Step 3. evade
Wait, but you can't move.
@@Penguinza oh ok
alternately: enclose yourself in mirrors facing outside
EH, Martin Gardner doesn't "make" books now, he died in 2010 at the age of 95. But I do have several of his books, highly recommended.
rest in peace
@@thedoublehelix5661 what a bummer
this dude straight making books from hell, what a crazy madlad
So my theory is that if the floor and ceiling were also mirrors you would need 36 blocker points if you were the laser victim and a ton of windex if you were the laser-assassin
I love how “off the wall” these videos are
This is extremely relatable but I didnt pull out my book to calculate all the possibilities, like the boss I am, I placed four blocks around the shooter.
I put them round the shooter instead in my head
Same
the blockers dont have an area though... you cant surround the shooter with the blockers unless you have an infinite number of them.
or am I about to get wooshed
@@diht blockers are an entire block of wall so then surround the shooter and then he is trapped there, cant escape
@@NeedyGreedy blockers are a single point with no area tho
The problem was incredibly cool and the solution was even cooler. You should continue on with such problems.
This is cool stuff.
If you had controlled force field.
You could save a bunch of energy with only 16 points instead of a sphere.
“The globe you’re staring at”
HE KNOWS!
timestamp please?
1:35
the main theme i see with every video he makes is to look at things in a different way. very good lesson to learn, helps you solve seemingly impossible questions
Instructions unclear, I am now going into my first professional laser tag tournament for 50,000 dollars as winnings.
What I would do is just go into the corner and set up like 4 blockers really close to me until enough is needed to block the whole way
that is infinite blockers
As a kid I often wondered what would happen in a mirror ball with a laser beam. As a teen I still wonder what would happen
Laser would run out of energy
@@vyor8837 but what if it didn’t un out of energy?
@@sco0t26Newton would come back to life
@@Meso.Botamia cool let’s ask him
@@sco0t26 the ball would get steadily hotter until melting occurred.
0:06 ah yes, very relatable
If you just put 6 blockers around you or the shooter, no matter the size of objects you will always be safe
He said the blockers are single points, he only used circles because you cant see single points
he asked for the minimum amount needed
@@Dinoboy676 yes, but it just becomes 8 +++
+x+
+++
@@jimmypatton4982 they are points with no size, it requires an infinite amount of blockers to form an enclosure like you describe
Counter solutions: put the blocker on top of the attackers head so that their dead and can’t shoot you anymore
“How many blockers do u need”
Me: 8
Person: how?
Me: shield
The blockers are points
@@Owen_loves_Butters wat is that supposed to mean
@@randomperson1844 It means they have no width, a shield would take an uncountably infinite amount of blockers.
@@Owen_loves_Butters so how will something that small block a laser?
@@randomperson1844 The laser is the same width
Zach: you can put single blockers to block the lazer-
Me: *surrounds agressively*
The problem with this is you don't know how large the blockers are so surrounding you could take a 100
@@stevenwier1783 in the diagram they are the same size as the shooter and target
@@Greenlog12 this is because it is surprisingly hard to picture an infinitely tine dot. It would be a little hard to see. Also the question is the leading source, not a youtubers diagram
@@stevenwier1783 than explain to me how you are supoosd to place them so perfectly since they could not be visible
@@laddershuffle9998 because its a math problem not you in the school playground.
This same technique of representing reflections off of walls with an uneven grid of points can be used to determine how long different paths from a sound source take to reach a listener, which you can then use to simulate reverb.
Ugh, I hate it when this happens, thanks for this, it will really help me now