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# 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?

## Puzzle - 2 Eggs and 100 Floors

## 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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