Can you solve the egg drop riddle? – Yossi Elran


The city has just opened its
one-of-a-kind Fabergé Egg Museum with a single egg displayed on each floor
of a 100-story building. And the world’s most notorious jewel thief
already has her eyes on the prize. Because security is tight
and the eggs are so large, she’ll only get the chance to steal one by dropping it out the window
into her waiting truck and repelling down
before the police can arrive. All eggs are identical in weight
and construction, but each floor’s egg is more rare
and valuable than the one below it. While the thief would naturally like
to take the priceless egg at the top, she suspects it won’t survive
a 100-story drop. Being pragmatic, she decides to settle
for the most expensive egg she can get. In the museum’s gift shop,
she finds two souvenir eggs, perfect replicas
that are perfectly worthless. The plan is to test drop them to find the highest floor
at which an egg will survive the fall without breaking. Of course, the experiment
can only be repeated until both replica eggs are smashed. And throwing souvenirs out the window
too many times is probably going to draw
the guards’ attention. What’s the least number of tries
it would take to guarantee that
she find the right floor? Pause here if you want
to figure it out for yourself! Answer in: 3 Answer in: 2 Answer in: 1 If you’re having trouble getting started
on the solution, it might help to start
with a simpler scenario. Imagine our thief only
had one replica egg. She’d have a single option: To start by dropping it
from the first floor and go up one by one until it breaks. Then she’d know that the floor below that is the one she needs
to target for the real heist. But this could require
as many as 100 tries. Having an additional replica egg
gives the thief a better option. She can drop the first egg from different
floors at larger intervals in order to narrow down the range
where the critical floor can be found. And once the first breaks, she can use the second egg to explore
that interval floor by floor. Large floor intervals don’t work great. In the worst case scenario, they require
many tests with the second egg. Smaller intervals work much better. For example, if she starts by dropping
the first egg from every 10th floor, once it breaks, she’ll only have to test
the nine floors below. That means it’ll take at most
19 tries to find the right floor. But can she do even better? After all, there’s no reason
every interval has to be the same size. Let’s say there were only ten floors. The thief could test this whole building
with just four total throws by dropping the first egg
at floors four, seven, and nine. If it broke at floor four, it would take
up to three throws of the second egg to find the exact floor. If it broke at seven, it would take up to two throws
with the second egg. And if it broke at floor nine, it would take just one more
throw of the second egg. Intuitively, what we’re trying to do here
is divide the building into sections where no matter which floor is correct, it takes up to the same number
of throws to find it. We want each interval to be one floor
smaller than the last. This equation can help us solve
for the first floor we need to start with in the 100 floor building. There are several ways
to solve this equation, including trial and error. If we plug in two for n,
that equation would look like this. If we plug in three, we get this. So we can find the first n to pass 100 by adding more terms
until we get to our answer, which is 14. And so our thief starts on the 14th floor, moving up to the 27th, the 39th, and so on, for a maximum of 14 drops. Like the old saying goes, you can’t
pull a heist without breaking a few eggs.

100 thoughts on “Can you solve the egg drop riddle? – Yossi Elran”

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  2. I have another solution.
    What if we start from midway through 50th if 1st egg broke then above all r waste if not below r waste and we can use them for more trail, and we do same thing again and again.
    I think that will take less than 10 trail.
    50th 25th 12th 6th 3rd and finally the ans. 6 trails

  3. She believes the priceless egg won't survive the 100 – story drop
    I don't think any of the eggs will survive the drop. THEY'RE EGGS
    Also why are eggs valuable?

  4. City: let's build a 100 – floor building. And display just ONE EGG on every floor.
    Builder: sounds good to me

  5. What if we throw an egg at f50, then f75 if the egg from the previous attempt didn't break or f25 if it did? If you repeat the process of throwing the egg from the middle height of the remaining floors, we can find the answer with 6 attempts.(I think)

  6. Good you use a girl in this example, to show they exist too.. but do NOT do it very often then they will complain "they portrays theives etc etc as women always why why why" so for now you are good.

  7. Y to yeeet the egg ,when she can just carry it along with her and slide down onto the rope. Now don't say she need both hands to slide down…😂.

  8. I think i've might have a better solution using dichotomic sort but it need much ressources but l'ESS try ( start a 50th floor if it break try 25th floor if not try 75th then you affine the interval until you round the one. Since you divide the interval by two each try , and since 100 IS beteween 2^6(64) and 2^7(128) you only need seven try (but you need seven egg)

  9. Y'all are overthinking it. Just put a purple matress in your truck. Boom. Or just climb down with the egg

  10. Me: tries to buy 14 eggs
    Gift Shop Owner: Soooo… Whatcha doin with 14 eggs. Ya know, just the other day some lunatic threw 19 eggs of the 20th floor

  11. Who else just binge watches these riddle videos and can’t figure out the answers, so they just watch the answers??

  12. Lmao just throw out every egg from the lowest floor to the highest until you ee3 that the eggs can't survive anymore

  13. Did no one else think about starting on floor 50, if it breaks go to floor 25, if that breaks go to floor 12, if that breaks go to floor 6, if that breaks go to floor 3 if that breaks you only have 2 more tries. This works for either side. Only takes about 7 tries I believe.?😕🙃

  14. I'm with everyone here says that this ted-ed's problem could have several solutions that doesn't require dropping eggs after reading comments, so here's my answer: Freaking jump out through the 100th story building window holding the egg, while having the pick up truck really open (and I mean the whole top of the truck open) and have that truck have foams or pillars filling up the whole truck so that way, nothing is harmed.

  15. But the real question is: why are we helping the thief figure out a way to perfect an egg heist?

  16. Is there a proof why the 14th method is the best? I get it intuitively, but a rigorous proof would be nice

  17. Search in her phone : How high can an egg survive before breaking?. Then divide the ans she get by 2.8 (Average height of a floor) then go to that floor. Easy

  18. Couldn’t she get the egg on the 100 floor go down a few floors then drop it? If she’s a thief she could go through vents :/

  19. In conclusions this video was pointless any true thief could take the 100 floor egg even a robber this vid was nice but it was easier to solve with logic

  20. Cant u just drop the egg at 100th and if it breaks, drop at 50th, of it didnt break, drop at 75 and if it breaks, drop at 63 and so on

  21. the first one is easy to do get a soulvenear and then replace the egg that looks the same with the soulvenear and no onw will suspect a thing they will just think its a soulvenear that you bought

  22. You can reduce the number of throws. Once you find the interval, you can throw the egg every other or every third floor, starting from the top of that interval. If the egg breaks, you are too high. If it survives, work your way up one floor at a time, till the most recent break.

  23. I believe that the answer is wrong….i looked at it this way…..
    1) Throw the first egg from 50th floor….we will have 2 outcomes…a)it breaks b) it doesn't break
    if a) it breaks- then we have to move to lower floor(half of it)
    else b) it doesn't break – we have to move to higher floor(half of the number)
    2) So the second egg will be thrown at the 75th floor or 25th floor …..again we will have two outcomes….a)break b) no break
    again if a) breaks- move to a lower floor( but above 50th( in case of 75) )
    else b) no break- move to higher floor( but till 50th ( in case of 25))
    ………in this way select half each time and move up or down accordingly……..
    and we can do this in 6-7 throws

    just an idea…give your views

  24. If you split the available options in half then it will only take 6 eggs to find the highest floor. Start at 50, if it breaks try 25. If it doesn't break go to 75, and so on….

  25. Okay but wouldn’t the egg be weaker after every throw so the experiment would be influenced…
    Also, just stuff the egg in your clothes so that you don’t have to throw it???

  26. "Throwing souvenirs out the window too many times is probably going to draw the guards' (or maybe it's 'guard's' if they just have the one) attention."

    Guard 1: Hears noise What was that?
    Guard 2: Oh, that must be that girl throwing another replica egg from the gift shop out of a window again.
    Guard 1: Isn't that kind of suspicious? I mean, we have all these valuable eggs in here, and somebody could probably steal one by dropping it out of a window into a truck or something.
    Guard 2: Eh, maybe. But I don't read too much into that kind of stuff unless it happens at least 15 times. So far, she's only done it 12 times in the last hour, so I don't see a problem.

  27. If u watch this video u should know that she could have taken the priceless egg

    https://m.youtube.com/watch?v=3oIakJekCZU

  28. There's one problem here: the replica eggs may survive a fall from a certain height, but they are still fragile. Therefore, if it survives a fall, it still loses some of its structural integrity and becomes less likely to survive being dropped again from the same height.

  29. Correct me if im wrong what if she throws the egg at 50% then either she goes up or down 50% again then she lower how many intervals and lessen the drops

  30. Start at 1 and go all the way to 100 whenever the egg breaks use the second egg to throw under that level
    For example you drop at 1 2 3 and it breaks at 4 so then u should throw the egg at 3

  31. If the thief is going to jump the same way the egg will be thrown, than why can't she just put the 100th floor egg in her pocket and jump with it…

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