# 2 Eggs and 100 Floors Puzzle

## Puzzle - 2 Eggs and 100 Floors

Given below are a puzzle based on 2 eggs and 100 floors building. Let’s see the following:

There is a 100 floors building.

There are two possible scenes we need to analyze:

• If an egg drops from the N’th floor or above it will break.
• If it’s dropped from any floor below ‘N’, it will not break

Note: You’re given only 2 eggs

Questions:

1 – Find the N’th floor.

2 – How many drops do you need to make?

3 – What should be the best strategy to minimize the number of egg drops?

## Solving 2 Eggs and 100 Floors Puzzle

### Method 1: Divide a Little, Conquer a Bit:

Let’s start the method from the 10th floor and go up to 10 floors at a time.

What we have to do:

Step 1: Throw the egg from the 10th floor, and if it breaks, then we can conclude that the ‘N’ floor is between 1-9.

Step 2: Repeat the same process if the egg is unbroken on the 10th, and now throw it from the 20th floor. Repeat the process until the 100th floor.

Step 3: So, even if the first egg is unbroken, we can now try the second egg and throw it from floors 91 – 99.

Let’s count the drops:

• 10 drops on each 10th floor (1 – 100)
• 9 drops in between the floors (91 – 99)

So, the number of drops in the worst-case scenario is 19.

### Method 2: Balancing Linear Drops:

Let’s assume the egg breaks at floor N.

We try to find out by going (N-1) to the first floor by doing the linear search.

To find an optimum solution, let’s try this:

If for every N, the egg doesn’t break, go to (N-1). This would save us one drop as we are doing a linear search with the 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 gives us an equation as ———> $n\frac{\left(n-1\right)}{2}$

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

We can write it as.

$n\frac{\left(n-1\right)}{2}>=100$

= 13.651 or 14 (approx)

### N = 14

#### Implementation:

Step 1: We should start from the 14th floor and then move up (N – 1) 13 floors i.e. 27th floor.

Step 2: If the eggs break on the 14th floor, try from all the floors below it, i.e. (1 – 13)

Step 3: Following the same linear pattern, we can move to (N – 2), (N – 3), and so on.

Step 4: So the floors from where the drop needs to be done are: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 100

Let’s count the number of drops:

• Dropping from 14 and if it breaks then dropping from 1 – 13
• Dropping from 14 and if unbroken, then trying from floor 27. If it breaks then try it from 15 – 26.
• So you have now tried on the 14th and 27th floor along with 15 – 26. So total of 14 floors.
• This continues with every attempt.

So, the number of drops in the worst-case scenario is 14.

### Result:

Answer 1 – N is 14

Answer 2 – The total number of drops we need to make is 14

Answer 3 – The strategy we need to adopt is Balancing Linear Drops,

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