Egg Dropping Puzzle with 2 Eggs and 100 Floors #interview #SimpleLogic #dsa #puzzle #job #career

Egg Dropping Puzzle with 2 Eggs and 100 Floors | Microsoft Interview Puzzles | Google Interview Puzzles #SimpleLogic #dsa #puzzle #job #career

Question :-
A building has 100 floors. One of the floors is the highest floor an egg can be dropped from without breaking.
If an egg is dropped from above that floor, it will break. If it is dropped from that floor or below, it will be completely undamaged and you can drop the egg again.
There are two eggs Given, find the highest floor an egg can be dropped from without breaking, with as few drops as possible

There are certain which you have to follow -
a. All eggs are identical.
b. An egg that survives a fall can be used again.
c. A broken egg can't be used again.
d. If the egg doesn't break at a certain floor, it will not break at any floor below.
e. If the egg breaks at a certain floor, it will break at any floor above.

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Solution :-

If the first egg breaks at first attempt, since we have only one more egg left, we will have to try sequentially from 1 to n.
So the worst case number of attempts will be n

If the first egg doesn't break at nth floor, the question is which floor we try next?
Lets say we step up (n-x) floors and try at n + (n-x)th floor. So the worst case number of attempts will be 1 + (n-x).

Since we are trying to minimize the worst case number of attempts, we should go for a uniform solution that is the number of attempts should be the same with each step up.
n = (n-x) + 1
x =1

This means if first egg doesn't break at nth floor, we need to try at (n + n-1)th floor. Similarly if the first egg doesn't break at (n + n-1), we need to try at (n+ (n-1) + (n-2)) floor and so on till we reach 100 the floor
So we now have this equation

= n + (n-1) + (n-2) + ... 1 greater than or equal to 100
= n(n+1)/2 greater than or equal to 100
= n greater than or equal to 14

So we need to try at floors 14, (14 + 13), (14+13+12),....till we reach 100
If first egg breaks at 14 we try from 1 to 13 sequentially with the second egg - worst case attempts will be 14 if egg breaks at 13th floor.
If first egg doesn't break at 14 , try at 27, if it breaks try sequentially from 15 to 26 with the second egg - worst case number of attempts is again 14 if egg breaks at 26th floor.

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