Can you solve the vampire hunter riddle? - Dan Finkel 

this is basically the DVD screensaver as a riddle

Mufasa: “Any point the light touches will be even or odd” Simba: “what”

"There is no time to draw the line" "Let's draw a grid" Wait a damn minute...

"you only have minutes before the sun is in position" "alright. let me pull out a ruler and make a grid"

Vampires: *Hate sunlight* Also vampires: *Build lair with perfectly smooth, metallic walls that infinitely reflect light*

People: " why do we have to learn angles?" Ted ed: "for vampire hunting silly!"

I honestly don't know why I keep watching these riddles. Every single one of these riddles I thought I could solve but then switched off my phone and felt dumber than ever.

*Puts diffuser in the right spot* *Clouds block the sun* FML..

Walls: are crowded with coffins Also walls: perfectly reflective at every point

Finally, i can use math to count in what point does the dvd hit the corner

'You don't have lot of time...'' *Proceeds to drawing a coordinate graph*

“The walls are covered in coffins” 10 seconds later “The light will bounce off the room’s perfectly smooth metallic walls” Hold up...

if the beam of light bounces around the room at so many different angles is there even a point to that diffuser? looks like the beam filled the whole room as it is lol

Don’t worry, I got this. I’ve watched the DVD screensaver for hours on end.

“Strike your diffuser” Bruh that’s a disco ball

there are 2 cool things about these clips: 1. the riddle itself 2. the comment section

"the light reflects off the smooth metallic walls" WTF! I don't even need this diffuser!

Now I have the ultimate power to predict which corner the DvD screensaver will hit.

If the entire room is metallic what is the purpose of the light diffuser? Shouldn't the the room glow with mirrors on all sides.

Step 1: confirm that the vampires have green eyes Step 2: let them live in peace

Wait I go into the vampire lair and set everything up in the middle of the night for the next morning. Wouldn’t they be awake at night.

*_Dracula has left the chat_*

The room is covered with coffins The light perfectly bounces off the walls Where the muffin does the light bounce off of and why can’t I put the ball there?!

Is it a reference to DVD screensaver meme?

I’ve literally been binge watching these.

How can the light entering from the SW corner bounce off the "perfectly smooth, metallic walls" if the walls are covered with coffins?

Finally, all those years watching the DVD logo boucing on the TV.

1. What Vampire would build their walls with reflective surface. 2. By the time sunlight reaches the point, it would be severely weakened anyway.

Why not just flood the room with garlic?

imaginative and complex riddles like always,keep on going forever ted-ed

You can imagine this as, instead of light bouncing off the walls, repeating the room infinitely many times horizontally and vertically. To hit a corner, you must therefore make a square by repeating the room on each axis. Notice that 49 (= 7 * 7) and 78 (= 2 * 3 * 13) don't share any prime factors, so their least common multiple is their product. The light must therefore cross the room 49 times horizontally, and 78 times vertically to reach a corner. Since an odd number of crossings gets you to the other side, but an even number stays on the same side, the corner it hits will be on the same side vertically (78 is even) and on the opposite side horizontally (49 is odd), making it the south east corner.

No time at all draw a complex drawing Me:what the

Create a grid of mirrored rooms and draw the 45 degree line through those rooms until it hits a corner. This will happen when a corner has coordinates (x,x). Since all room corners are at coordinates (78n,49m), we just have to solve 78n = 49m. We know that 78 = 2 x 3 x 13 and 49 = 7 x 7, so the first corner that gets hit by the line is at coordinates (2 x 3 x 13 x 7 x 7, 2 x 3 x 13 x 7 x 7), which means n = 49 and m = 78. So after 49 horizontal mirrors and 78 vertical mirrors we hit a corner. If both were 1, then we'd hit the NE corner, if n = 2, then we'd hit NW, for n = 3 NE again, so if n is odd and m = 1, then we hit the NE corner. If m = 2 and n is odd, then we'd hit the SE corner, and if m became odd again, we'd hit NE again. So for even m and odd n the light will hit the SE corner. Answer: SE corner.

Nobody: Lisa Lisa: lol imagine needing mirrors.

I thought about this one in an entirely different way: basically, since the light travels at 45 degrees, the total distance it moves north-south has to be the same as the total traveled east-west. In order for it to hit a corner, this distance has to be a multiple of both dimensions of the room. Since 49’s only factor is 7, and 78 is obviously 1 off from a multiple of that, the lowest common multiple of them has to be their product. Therefore, as the light bounces around until it hits the corner, it must travel 49*78 meters in both the up-down dimension and the left-right one, so it travels the north-south range of the room (49 meters) 78 times, which is even, so it ends at the same side it started (south), and the east-west range (78 meters) 49 times, which is odd, making it end on the opposite side from where it started (east). Therefore, the diffuser must be mounted on the southeast corner. Also, once again, who comes up with these titles? Why not call this the Reflecting Light riddle?

3:12 is the most satisfying thing ever

The "pause the video" section didn't include the dimensions of the room.

Oh my god....It’s the bouncing DVD riddle.

I'm a little late to the party, but I think I found another solution to this: Starting from any corner, the next time any corner will be hit is after the amount of squares traveled equals the smallest shared multiple (no idea if that is the correct English term) of the two lengths. Since the leghts do not share a divisor, it happens after 49x78 squares have been traveled, or after the entire longer side has been traveled 49 times and the shorter side 78 times. The short side is traveled an even number of times, so the beam will end up on the bottom where it started. But the longer side is traveled an odd number of times, which means the beam will switch sides from left to right. Result: it ends up in the bottom right. Can anyone confirm or was I just lucky?

I had a simpler solution (sorry for my english): The light travels at a 45° angle, so both X and Y coordinates add equaly. This means that if the first wall is, for example, 43m long and the other one 22m, in a given time the light will travel 22 times the first wall and 43 times the smaller one, at this point, it finds a corner. This will also happen with any other common multiplier (idk if it's called that) of the two numbers. Anyway, if the light travels a wall an even number of times it means it will finish on the same point for that wall, if it's an uneven nuber of times, it will finish on the opposite end. Now take this example and solve the video's riddle with it :).

*Or* you could just put the diffuser at the door, where the light comes in.

"you got no time to spare" "Watch me, ZA WAZUDO!!" Pauses the video*

“The sun will be in position soon” “Let’s draw a graph”

"But there's one insight that can unravel the riddle in almost no tume at all" *whips out coordinate graph and it took 2 minutes*

I think that its harder to come up with these riddles than to solve them..😂😂Kudos to the content creators of Ted-Ed

Just hire a werewolf

When he said it was simple and elegant I just thought he was going to say put it in the same corner where the light was coming through and you don't have to worry about angles

3:12 why do you wanna put that globy thing if there's already so much light reflected by the walls?

I know nobody will see this comment at this point but I want to present another solution that I think is better because it can be used for any angle or room size. Basically you can visualize how light bounces in a room by flipping the room along the side the light bounces off and having the light travel in a straight line. Now let’s flip the room each time light bounces off the wall but also lets leave a copy of the room where it was before the light bounced off the wall until the light hits a corner (we don’t actually need to know which one yet). Now that we have a straight line of light going from one corner to another we can imagine the light like the diagonal of a rectangle created by extending the sides from each corner the line touches until they meet. More specifically it is a square since the diagonals of squares create 45 degree angles. Now thinking back to how we made our square, we know each side is equal to the length of the original rectangle’s side multiplied by how many times we flipped along that side minus 1 (the minus one is because of the original room), but since it’s a square we must have the length of the sides created by flipping up and sideways be equal. In other words we need the least common multiple of 49 and 78 which just so happens to be them multiplied together. Therefore, to get the light to hit a corner we must flip the room 77 times vertically and 48 times horizontally. Now let’s bring it all together. Think about what happens when you flip the room along a side, if you flip vertically bottom becomes top and if it’s horizontal the left becomes right, but if you flip it again it goes back to normal. If we flip the room a odd number of times the orientation of the room flips along whichever axis we flipped along but if we flip an even number it remains the same. Now the light must hit the top right corner of our rectangle so we can use the parity of how many times we flipped the room to find the orientation of that final room in which the light hits the top right corner. So we flipped up an odd number of times so south is on top and we flipped an even number horizontally meaning east is still on the right, so the top right corner in which the light hits is the south-east corner. This may not be as easy to understand or explain as the solution presented in the video but what I love this solutions versatility. You can use the same principle to find the solution for any problem like this and isn’t dependent on the light coming in at a 5 degree angles dice you can adjust the ratio of the big rectangle’s sides according to the angle. Plus it uses a little bit of real optics which is something we don’t think about very much and I think that this way of thinking about light is really cool. The video’s answer isn’t wrong, I just feel it could just be a little better.

I just realized at the end it was basically the legend of the dvd screensaver

Even better solution 1.Invite all vampires to a party at night 2.Wait till everyone's there 3.Activate a disco ball

the first i have ever gotten right!! (first i have ever guessed right)

"yeah i think i could use this method . . . . . . . *died 1 minute later*

The vampires in the thumbnail: Is asleep That one vampire on the far left: *i don’t need sleep, I need answers!*

Honestly, If the light bounces off the walls _that_ many times, you don't even need a diffuser.

I think it makes more sense to stand in each corner of the room looking outward at 45 degrees. When you can see the reflection of the entrance tunnel dead-on, you're in the corner where you should mount your diffuser.

The perfectly smooth metallic walls, against which are stacked all the coffins? so how exactly does the light bounce?

I used my smarts to pass the test because I knew that the diffuser was big enough that the light would hit it long before it ever hit directly on a corner, so any corner will work, but also it's okay to just stay in the room and hold the diffuser. Be your own wall.

The solution in the video is poor as it allows for the SW corner to be a valid solution; it isn't, only because it was not an option in the riddle. To prove that it will hit the SE and not the SW corner, you can just imagine the rooms mirroring themselves upwards and rightwards infinitely, forming a rectangular grid. Because the beam moves at a 45 degree angle, we know that the light beam will only touch the opposite corner of a square block. To solve this, we can exploit the fact that the length and width are integers, and find the lowest common multiple (LCM) of 78 and 49. The reason is because the first corner that the beam will hit after leaving (0, 0) is (LCM, LCM). The easiest way to find the LCM is to multiply them and to divide the result by the greatest common factor (GCF), which can be quickly calculated using Euclid's algorithm. Since 78 and 49 have no common factors, the LCM is 78 × 49 = 3822. The first corner the beam will hit is at (3822, 3822). At this point, the beam would have reflected horizontally (3822÷78)-1=48 times (even number), and vertically (3822÷49)-1=77 times (odd number). This means that its horizontal direction will not be flipped, but its vertical direction will be flipped. It will be moving rightwards and downwards, and will hit the SE corner first.

Who else is not even trying to answer the riddle?

Why bother if the light bounces of everything anyways. Or it will hit a coffin and that’s that.

Now that I’ve finally taken a good look at this puzzle and it’s elegant solution, I thought to myself, “but what if the room had different dimensions?” As it turns out, anytime that the room has an even and an odd dimension, the trick works out nicely, but what about when the room has two even or two odd dimensions? After having looked at the problem through an odd representation which I can explain later, the solution becomes simple. Find the greatest common factor of the two dimensions and divide both dimensions by this greatest common factor. Switch the values of the dimensions. Subtracting one from each dimension gets you the number of bounces the light makes off of the horizontal walls (for the modified horizontal coordinate) and then off of the vertical walls (for the modified vertical coordinate) excluding the last “bounce” that the light makes with the corner, hence the subtraction of one bounce each. This then can be used to tell you the direction of the light beam relative to the original direction when it’s about to make contact with the corner. Even numbers tell you that the light must be traveling the same direction relative to the original direction in that component, and odd numbers tell you that the light must be traveling in the opposite direction relative to the original direction in that component. This then tells you which corner it must strike first simply from the direction of the light beam.

Yes because drawing a perfect grid with all the coordinates lined up with perfect precision takes less time then drawing a few lines

The light bounces so many times in the room that you wouldn’t even need a diffuser anymore...

Sorry My brain is too broke to solve riddles

"there's no time to draw, so let's draw on a grid coordinate paper you probably don't have so you'll spend a few minutes making." Ah yes. A riddle that uses what I can't use as a answer. Thank you.

I don't know if it's only me but these scenarios seem a little bit forced

Damn vampire hunters, been dodging them for 500 years

03:27 RAINBOWS

It's essestially "Will the DVD logo hit the corner?": The riddle

Vampires: *dies in sunlight* Also vampires: *survives moonlight which is technically also sunlight*

Props to the animator for animating the light path.

Another interesting way of solving this: Instead of reflecting the beam off a wall, imagine mirroring the room on the wall the beam hit. This way, you can view the beam as still moving in the same direction as before, but in a mirrored room. Because of the 45°, the beam shot from coordinates 0, 0 will always be on coordinates that are equal in x and y and eventually hit the upper right corner of a mirrored room. It will hit the corner of a mirrored room at the smallest multiple of 49m and 78 (which is 49*78), meaning 49 rooms in the horizontal direction and 78 rooms in the other. If you now simply realize the odd number of rooms has the last mirrored room mirrored back to its original direction in that dimension, and an even number does the opposite, it becomes clear the room is not mirrored in the horizontal direction (the corner the beam will hit is on the right side) but mirrored in the vertical direction (the corner the beam will hit is on the bottom) you have solved the puzzle. I know in text this seems like a huge thing but once you follow along and visualize it in your head it should become quite clear 😊

Plot twist: Vampire abandoned the room way before we come

Him: Makes an entire grid and does some math. Me: Just holds the diffuser up until the sun comes...

The only riddle I finally got right, by just guessing of course.

dude just use Hamon duh

The puzzle is quite hard when you don't have the size of the room on the summary screen.

*Bring a goddamn flashlight*

Ted ed: Can you solve- Me: Ok lets go straight to the comments to see how people react

My solution without calculation: just put the diffuser in the corner that you're coming from, as the light is guaranteed to pass by there.

When will the DVD logo hit the wall turned into a riddle

I thought of another solution. It doesn't matter at all where you place the diffusion mirror. If the walls are so reflective that the light will continue to bounce until it reaches a corner, where the mirror would be placed, there's already enough light filling the room to kill the vampires anyway. I thought of that the moment he said that the light would continue to bounce off the walls.

TED: "But there's one insight that can unravel this riddle in almost no time at all." Also TED: "LEt'S dRaW tHe ChAmBeR 0n A cOoRdiNaTe GriD."

You can just use Star Platinum by the way

I moved my finger on screen trying to imitate where the light will pass and the closest was SE and I said close enough and it ended up being the right answer

0:56 that's not how physics work

Me, an intellectual: Meh. The two top points seem too obvious to work. Imma go with the south east one. *gets answer correct* Me: I-

Simple, hold the diffuser and stand in front of the entrance, it may be wall mounted but nothing says it wont work

2:51 Lol , my eyes hurt

Can't we just go to all the three corners, shine a beam of light at 45°, and see from which corner the beam of light goes through the the SW corner?? 🤔🤔

I got the right answer but different solution. I got the LCM of the length of both sides of the room. Since the light has to hit at a corner, so the light has to travel to a number that is divisible by both numbers to hit a corner. Divide the number (LCM) by the length. If its an odd number, its towards the side of were the light started to come, if its even, its opposite of the origin on the light. Now we do the same but by the height. If its even, opposite to origin, otherwise, towards origin

Unless you accidentally leave the trap door shut...

This is a wonderfully elegant mathematical puzzle, not a riddle. Blew my mind when I first saw a variant of this problem

the room is not a rectangle but a rectangular prism in other words your calculation works on 2D shape that is why the graph that you used only hase x and y axes but the room is a 3D shape so your graph need an additional z axes therefore your calculation MIGHT be wrong

I thought I should watch this for fun, I didn’t know I would encounter those graphs 🤦🏻‍♀️

i love how all these "riddles" is just math questions xD

Answer: go to the surface and calculate where the beam is gonna go and come back tomorrow

"You can't make a drawing and figure it out" "SO LET'S MAKE A GRAPH"

How did i predicted it was math, glad i didnt waste enough time to try and figure it out.