100 floors with 2 eggs puzzle
There is a building of 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. You’re given 2 eggs. Find N, while minimizing the number of drops for the worst case.
First thought which comes to our mind is to use binary search, we first drop Egg#1 from 50th floor, if it does not break, then try the middle of second half, if breaks then we have to try each floor in first half. But this will give worst case number of drops as 50(if it brakes on 50th floor, then we have to try from 1 to 49 floors sequentially).
Second thought is to try xth floor then 2xth floor till 100th, in this case worst case time will be (100/x)+(x-1). worst case will be when Egg #1 breaks at 100th floor then we have to try Egg #2 from (100-x)th to 99th floors. In (100/x) + (x-1) equation, with increase in x, 100/x decreases while (x-1) increases, thus we can minimize it when 100/x = (x-1), this gives x ~10, which gives worst case number as 19 drops.
But increasing the floor every time by x is not a very nice idea, as with each new increase in Egg #1 drop, we should decrease Egg #2 drops to minimize worst case number. so if we drop Egg #1 from xth floor initially, then in next turn we should try x + (x-1)th floor(to keep the worst case number same).
Thus we can say X + (x-1) + (x-2)…1 = 100
X(X+1)/2 = 100 => X=14.
So we should drop Egg #1 from 14th, then 27th, then 39th and so on.
Your Answer
More puzzles to try-
What is the logic behind these ?
3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »Defective stack of coins puzzle
There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »Which clock works best?
Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »(Advanced) Cheryl’s Birthday Puzzle
Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »Five greedy pirates and gold coin distribution Puzzle
Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »Magical flowers!!
A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »Tuesday, Thursday what are other two days staring with T?
Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »How could only 3 apples left
Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »How Many Eggs ?
A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »HARD MATHS – How much faster is one train from other Puzzle
Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »Most Analytical GOOGLE INTERVIEW Question Revealed
Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »Lateral thinking sequence Puzzle
Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »How did he know?
A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »Pizza Cost Math Brain Teaser
Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »Which letter replaces the question mark
Which letter replaces the question markRead More »Which room is safest puzzle
A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »Richie’s Number System
Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »Srabon wanted to pass
The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »Become Normal!!
Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »Sakib Knows The Number!
Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »