Egg Dropping: Going beyond just solving the classic puzzle

Each floor of a 100-story building has a balcony over which you can drop an egg and watch it hit the ground. The egg either breaks or survives the fall (and if it survives, it can be used again for another drop). You want to classify each floor as either an egg-breaking floor or a non-egg-breaking floor, and you have just two eggs for this job! What is the least number of egg-drops you should plan for in order to classify each and every floor? (Is it even, for sure, possible to do so?)
I offer my emotional reactions and personal process for thinking about this puzzle.

[@HarshitRajIITB]

Amazing solution to this problem. I searched a long time for a mathematical generalised proof but found none other than just blind algorithms. This video ends my search! Great job!

[@architatrey5018]

The best tutorial available on egg dropping problem

[@saumyaiisc]

The best video on egg dropping puzzle. .. you made my day

[@thevijayraj34]

Subscribed.. You just taught me the efficient way to tackle this world famous Egg Drop problem.

[@foreverursabhi]

If we are on floor x + 1, and the egg doesn't break, all we know is that we can get to the y floor, not y floors above x + 1. I don't understand why y is added to x + 1.

[@emenikeanigbogu9368]

i didn't get that to

[@ashwinnema06]

I also did not get that

[@vigneshganesan7390]

How the hell are you writing that way🤯

[@AradhyaMudgal]

I came across this video after solving the puzzle, even then, loved it!
Great video.
+1 subscriber

[@monikayaduvanshi6428]

i was listening to him with the same energy level, but I lost it after like 15 min, because i was so into the enthusiasm the guy had about the problem, that's how it goes with every mathematician,
p.s this guy did great great job

[@rahulgarai4822]

This is really awesome...🤗

[@jerryhehe217]

mind blown away!

[@pcpardon]

Thank you James you really saved my day.

[@sudhanshupandey6096]

Amazing , Great ;

[@glennbutera9197]

Question for James: If you have 1 egg and 1 experiment and you want to maximize the number of floors you can classify, wouldn't you always want to drop it from the middle floor of the building? This is mathematically the n/2 floor where n is the number of floors in the building. That way if it breaks you know that the floor you dropped at is a "breaking" floor and all floors above it are "breaking". This at least classifies half the floors in either outcome (breaking or non-breaking).

[@JamesTantonMath]

And that is a good variation of the classic puzzle to consider. The classic version definitely wants floor 1 classified .. along with as many floors above it (consecutive numbered floors) classified too. So .. you question: Given a building with finite number F floors, and k eggs, and N runs of the experiment, what is the highest percentage of floors you can be sure to classify? That's worth thinking about!

[@shang_chi4651]

Here we need to classify the floors from.bottom to top, starting from a floor.midway and classifying all the floors above it is not.what we want because we want to find how high a building can be classified with those N experiments and height is counted from the bottom floor not from a floor mid way.
This was confusing to me as well but i think now i have figured it out

[@athenalin6360]

I still got confused about why the O is (x+y+1), and what if it is pair of ( eggs left, floor left), how can we draw a table for this pair?

[@harshit.jindal]

This is brilliant!

[@Daeckarkatten]

Excellent video but jeez so many ads. 15 minutes in and Ive had 4 ad breaks with 2 in each so far?

[@ashwinnema06]

James can you please explain why y is added to x+1 I mean it can also be any other number for example 1,2. I mean how can we exactly say that we have found answer of y floors above

[@sideways9264]

Really good video

[@vincentcozzo3207]

This is very interesting. I recall having a similar emotional response to this same problem when I first heard it, but I love your approach to it. As a matter of fact, it reminds me of dynamic programming in computer science. Also, the solution you got (14) is actually better than the number I used to think was correct (2sqrt(100) = 20). I'll have to study this some more, to find the algorithm actually used that only uses 14 experiments in the worst case.

[@martinharris4416]

Holy shit this is awesome

[@alwysrite]

nice Easter problem !

[@robertcraig2662]

Am you are so hyped up abouth thsis puzzle

[@amanbhadauria2881]

are u writing from backside ?? that means u are writing mirror alphabets , man thats amazing

[@jayeshswami5207]

He mirrored the video