Drop the egg without breaking
You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum number of tries needed to find out the solution?
The easiest way to do this would be to start from the first floor and drop the egg. If it doesn’t break, move on to the next floor. If it does break, then we know the maximum floor the egg will survive is 0. If we continue this process, we will easily find out the maximum floors the egg will survive with just one egg. So the maximum number of tries is 100 that is when the egg survives even at the 100th floor.
Can we do better? Of course we can. Let’s start at the second floor. If the egg breaks, then we can use the second egg to go back to the first floor and try again. If it does not break, then we can go ahead and try on the 4th floor (in multiples of 2). If it ever breaks, say at floor x, then we know it survived floor x-2. That leaves us with just floor x-1 to try with the second egg. So what is the maximum number of tries possible? It occurs when the egg survives 98 or 99 floors. It will take 50 tries to reach floor 100 and one more egg to try on the 99th floor so the total is 51 tries. Wow, that is almost half of what we had last time.
Can we do even better? Yes we can (Bob, the builder). What if we try at intervals of 3? Applying the same logic as the previous case, we need a max of 35 tries to find out the information (33 tries to reach 99th floor and 2 more on 97th and 98th floor).
Interval – Maximum tries
1 – 100
2 – 51
3 – 35
4 – 29
5 – 25
6 – 21
7 – 20
8 – 19
9 – 19
10 – 19
11 – 19
12 – 19
13 – 19
14 – 20
15 – 20
16 – 21
So picking any one of the intervals with 19 maximum tries would be fine.
Instead of taking equal intervals, we can increase the number of floors by one less than the previous increment. For example, let’s first try at floor 14. If it breaks, then we need 13 more tries to find the solution. If it doesn’t break, then we should try floor 27 (14 + 13). If it breaks, we need 12 more tries to find the solution. So the initial 2 tries plus the additional 12 tries would still be 14 tries in total. If it doesn’t break, we can try 39 (27 + 12) and so on. Using 14 as the initial floor, we can reach up to floor 105 (14 + 13 + 12 + … + 1) before we need more than 14 tries. Since we only need to cover 100 floors, 14 tries is sufficient to find the solution.
Therefore, 14 is the least number of tries to find out the solution.
Your Answer
More puzzles to try-
What is the answer to the question mark?
Row 1: 13 12 5 Row 2: 17 ...Read More »2 in 54
It is 2 in 54, five letter word, it is known as wild and some say unpredictable. It can raise ...Read More »In spite of what your eyes are telling you?
In spite of what your eyes are telling you, the smaller off-center circle is actually perfectly round.Read More »Single Eye Riddle
What has a single eye but cannot see?Read More »How Many Balls?
Count the number of balls in picture below:Read More »2 Eggs and 100 floor Google Classic question
There is a building of 100 floors -If an egg drops from the Nth floor or above it will break. ...Read More »Make the Line Sorter
Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar. The villagers loved to talk of Birbal’s wisdom ...Read More »Crack the Cipher
The following “Brain Bat” means Slow Down. S L O W Using the same logic, can you tell us what ...Read More »Large and Small
Large as a mountain, small as a pea, Endlessly swimming in a water less sea. What is it?Read More »1 Ball is defected of of 8 can you find in 2 weighs?
There are 8 balls. 7 of them weigh the same. 1 of them has a different weight, (you don’t know ...Read More »Finding name of the ancient king puzzle
500 at the beginning, 500 at the end, 5 in the middle is seen, The first of all letters, the ...Read More »train and Bridge riddle
John walks over a railway-bridge. At the moment that he is just ten meters away from the middle of the ...Read More »Fly travel riddle
Two cyclists began a run, one starting from Delhi and the other starting from Agra. When the riders were 180 ...Read More »Path between natural masses
It is a path situated between high natural masses. Remove it’s first letter & you have a path situated between ...Read More »25 horses 5 tracks Puzzle
Mr John have 25 horses, and he want to pick the fastest 3 horses out of those 25. He has only ...Read More »A non stop marathon Riddle
A non stop marathon is the shared favorite sport of three brothers. The oldest one is fat and short and ...Read More »Judge and thief puzzle
A thief is convicted in Mexico. He gets the death penalty. The judge allows him to say a last sentence ...Read More »Rain Drop Measuring
A rain drop fell from one leaf to another leaf and lost 1/4th of its volume. It then fell to ...Read More »Man life in fraction puzzle
Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. ...Read More »Horses age difference brain teaser
Two horses were born on the same date and at the same time, traveled the world, and then died on ...Read More »