Writing a Python Program to Solve the “Hundred Chickens for a Hundred Coins” Problem

The “Hundred Chickens for a Hundred Coins” problem is a classic algorithmic challenge that involves finding all possible combinations of three types of chickens (roosters, hens, and chicks) that can be purchased with exactly a hundred coins, given their respective costs. In this blog post, we’ll delve into the specifics of writing a Python program to solve this problem, breaking down the steps and explaining the logic behind each part of the code.

Step 1: Understanding the Problem Constraints

The first step in solving this problem is to understand the constraints:

• Roosters cost 5 coins each.
• Hens cost 3 coins each.
• Chicks cost 1/3 of a coin each (or, equivalently, 3 chicks cost 1 coin).
• We need to buy exactly 100 chickens with 100 coins.

Step 2: Setting Up the Problem

In Python, we’ll need to iterate through possible combinations of roosters, hens, and chicks, checking if they satisfy the constraints. However, to simplify calculations, we can express the number of chicks in terms of groups of 3 (since 3 chicks cost 1 coin).

Step 3: Implementing the Solution

Here’s how the Python program might look:

python# Initialize an empty list to store valid solutions
solutions = []

# Iterate through possible numbers of roosters (up to 20 since 5*21 > 100)
for roosters in range(21):
    # Iterate through possible numbers of hens (up to 33 since 3*34 + 5*20 > 100)
    for hens in range(34):
        # Calculate the number of groups of 3 chicks that can be bought with the remaining coins
        # Note: We subtract the cost of roosters and hens from 100 to get the remaining coins
        # Then, we divide by 1 (since each group of 3 chicks costs 1 coin) to get the number of groups
        chicks_groups = (100 - (5 * roosters + 3 * hens))
        
        # Check if the number of chicks groups is an integer (since we can't buy partial groups)
        if chicks_groups % 1 == 0:
            # Convert the number of groups into the total number of chicks
            chicks = chicks_groups * 3
            
            # Check if the total number of chickens equals 100
            if roosters + hens + chicks == 100:
                # If all conditions are met, add the solution to the list
                solutions.append((roosters, hens, chicks))

# Print the solutions
for solution in solutions:
    print(f"Roosters: {solution[0]}, Hens: {solution[1]}, Chicks: {solution[2]}")


Step 4: Reviewing the Code

The program uses two nested loops to iterate through possible numbers of roosters and hens.
For each combination of roosters and hens, it calculates the number of groups of 3 chicks that can be bought with the remaining coins.
It checks if the number of chicks groups is an integer (to ensure we can buy whole groups) and if the total number of chickens equals 100.
If both conditions are met, the solution is added to the solutions list.

Step 5: Running and Testing the Program
Running the program will output all valid combinations of roosters, hens, and chicks that satisfy the constraints of the problem.
Conclusion
Writing a Python program to solve the “Hundred Chickens for a Hundred Coins” problem is a great exercise in problem-solving and algorithmic thinking. By breaking down the problem into manageable steps and carefully implementing the solution, we can develop a clear and concise program that accurately finds all valid combinations.