**π‘ Problem Formulation:** Given a pile of stones, we need to find the rate at which stones are removed over a period of *k* hours. The input is the total number of stones and time in hours, while the desired output is the removal rate per hour. For instance, if there are 100 stones and they need to be removed in 5 hours, the removal rate is 20 stones per hour.

## Method 1: Simple Division

This method entails a straightforward calculation to determine the removal rate. We divide the total number of stones by the number of hours (*k*) to find out how many stones are removed per hour. It is a direct approach and the easiest one to implement.

Here’s an example:

def find_removal_rate(stones, hours): return stones // hours # Example: rate = find_removal_rate(100, 5) print(rate)

The output of this code snippet:

20

This code defines a simple function `find_removal_rate()`

that takes in the total number of stones and the amount of time in hours. It returns the integer division result of stones by hours, which is the stone removal rate.

## Method 2: Handling Decimals

When the total number of stones can’t be evenly divided by the number of hours, we need to account for decimal places to precisely determine the removal rate. Python’s floating point division operator (`/`

) is well-suited for this scenario.

Here’s an example:

def find_removal_rate(stones, hours): return stones / hours # Example: rate = find_removal_rate(101, 5) print(rate)

The output of this code snippet:

20.2

The `find_removal_rate()`

function now performs a floating-point division to calculate the removal rate per hour. This is more accurate when dealing with numbers that are not perfectly divisible.

## Method 3: Utilizing Remainders

In certain scenarios, we might be interested in both the removal rate and any leftover stones. This method extends upon the basic division concept by also returning the remainder.

Here’s an example:

def find_removal_rate_with_remainder(stones, hours): rate = stones // hours remainder = stones % hours return rate, remainder # Example: rate, remainder = find_removal_rate_with_remainder(103, 5) print(f"Rate: {rate}, Remainder: {remainder}")

The output of this code snippet:

Rate: 20, Remainder: 3

This code example performs an integer division to find the removal rate and uses the modulus operator (`%`

) to calculate the remainder. This is especially useful for precise tracking of the removal process.

## Method 4: Adapting to Dynamic Inputs

When dealing with varying input values that change at runtime, we can wrap our logic in a function that can be easily called multiple times. This allows the program to adapt to different scenarios effortlessly.

Here’s an example:

def find_removal_rate(stones, hours): if hours == 0: raise ValueError("Hours cannot be zero.") return stones / hours # Example: try: rate = find_removal_rate(150, 0) print(rate) except ValueError as e: print(e)

The output of this code snippet:

Hours cannot be zero.

This function demonstrates error handling by adding a check to prevent division by zero. It raises a ValueError if the input for hours is zero, thus ensuring the program’s robustness against invalid inputs.

## Bonus One-Liner Method 5: Lambda Function

For a concise one-liner solution, a lambda function can be employed to directly calculate the removal rate. Though less readable, it is a compact representation of the logic required.

Here’s an example:

find_removal_rate = lambda stones, hours: stones / hours # Example: rate = find_removal_rate(100, 5) print(rate)

The output of this code snippet:

20.0

The lambda function in this example is an anonymous function that performs the division between the number of stones and hours. It’s a quick and straightforward way to calculate the removal rate on the fly.

## Summary/Discussion

**Method 1: Simple Division.**Straightforward and easy to implement. Best suited for integers and when dealing with numbers divisible by*k*. Not suitable for precise decimal calculations.**Method 2: Handling Decimals.**Ideal for cases where a non-integer removal rate is expected. Guarantees precision but may be slightly more computationally expensive than integer division.**Method 3: Utilizing Remainders.**Useful for accurately tracking the removal process including any leftover stones. Adds additional complexity to the output which may not always be necessary.**Method 4: Adapting to Dynamic Inputs.**Allows flexibility and adaptability to varying inputs with added error-checking. Enhances the program’s capability to handle real-world scenarios.**Method 5: Lambda Function.**Offers a succinct way to calculate removal rates. Enhances code compactness but reduces readability and can be challenging for beginners to understand.