# Drop the egg without breaking

1,267.1K Views

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?

JamesBond Pundit Asked on 23rd July 2015 in

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.

John123 Expert Answered on 23rd July 2015.

• ## More puzzles to try-

• ### What color was the bear?

I left my campsite and hiked south for 3 miles. Turned east and hiked for 3 miles. Then turned north ...Read More »
• ### Combination of bags

A man went into a bank with a thousand dollars, all in dollar bills, and ten bags. He said, “Place ...Read More »
• ### Guess the Father’s name

Monday Tuesday and Wednesday are three sisters. What’s their father’s name?Read More »
• ### Weight of cement block

A cement block balances evenly in the scales with three quarters of a pound and three quarters of a block. ...Read More »
• ### What did the person say to you that proved his statement ?

You are hanging around in NYC when a person approaches you. “Leaving the bald people aside, I can bet a ...Read More »
• ### Two triangles with identical part shows difference, how is it possible?

Both triangles are made of identical parts. In the bottom one is one empty square though. How is it possible?Read More »

• ### Baby falls out

How could a baby fall out of a twenty-story building onto the ground and live?Read More »
• ### Measure the weights

You can place weights on both side of weighing balance and you need to measure all weights between 1 and ...Read More »
• ### Magic Letter

It is a letter; It is made of four V’s. One on the left, One on the right, one on ...Read More »
• ### What is my aunt’s share?

When my uncle in Madura died recently, he left i will, instructing his executors to divide his estate oi Rs.1,920,000 ...Read More »
• ### Unlock the Vault

One day a robber got into a bank to rob its vault. However, he noticed that the vault had an ...Read More »
• ### Chocolates Bricks Riddle

How many steps are required to break an m × n sized bar of chocolate into 1 × 1 pieces? ...Read More »
• ### When did the girls went for picnic puzzle

Sofia, Angelina & Emma went for a picnic. After a few days they forgot the date, day and month on ...Read More »
• ### What to open puzzle

It\’s 5:00 AM in the morning. You are sleeping. The doorbell rings. It\’s your family, they want to have breakfast. ...Read More »
• ### Unlist phone number

In a certain city, 5% of all the persons in town have unlisted phone numbers. If you select 100 names ...Read More »
• ### What happens in a month?

What happens only in the middle of each month, in all of the seasons, except summer and happens only in ...Read More »
• ### Choose Men

A man is on a game show. He is presented with two doors, one on the left, and one on ...Read More »
• ### Unbroken Eggs

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three ...Read More »
• ### Eight married couples Challenging Puzzle

Eight married couples meet to lend one another some books. Couples have the same surname, employment and car. Each couple ...Read More »