2 Eggs and 100 floor Puzzle

By | December 2, 2017

 

This is an interesting puzzle. Certainly the kind of puzzle which tickles your mind and get your maths come out of you. 😉

So, Suppose there is a multistory building. Which has 100 floors.

-If an egg drops from the Nth floor or above it will break.
-If it’s dropped from any floor below, it will not break.

And, You’re given 2 eggs. You need to find out the minimum number of trails you need to perform in order to find out the ‘Nth’ floor.

2 Eggs and 100 floor

 

 

How many drops you need to make?

What strategy should you adopt to minimize the number egg drops it takes to find the solution?

 

Try to solve it before reading the solution, which is of course given below. 🙂

 

The puzzle follows the below logic.

Say, the egg breaks at floor n we try to find out by going (N-1) till the first floor by doing linear search.
For example, I throw the egg from 10th floor, and it breaks, I will go to floor 1 to 9 to find out the floor..
Then I would try the same logic for every 10 floors thereby setting a worst case scenario of 19 chances.. i.e. 10,20,30,40,50,60,70,80,90,100,91,92,93,94,95,96,97,98,99

 

To find optimum solution, let’s try this:
If for every n, egg doesn’t break, instead of going to next n, go to N-1, this would save us one drop as we are doing a linear search with second egg when egg 1 breaks…
So the series would look something like this..
N + (N-1) + (N-2) + (N-3) +…+ 1

Now this is a series which is equal to N(N+1)/2

Now since it is given that the egg may or may not break from 100th floor..

We can write it as..

N(N+1)/2>=100
And n=14(approx)

 

So we should start from 14 then move up N-1 to 13 floor I.e. 27,39…

So the floors from where the drop needs to be done are: 14,27,39,50,60,69,77,84,90,95,99,100

So the answer is 14