A Python Tutorial Case Study: The “Hundred Chickens with Hundred Coins” Instance

The “Hundred Chickens with Hundred Coins” problem, a classic algorithmic challenge, serves as an excellent teaching tool for introducing programming concepts and problem-solving strategies to students, particularly in the context of Python programming. This tutorial case study aims to present a comprehensive lesson plan centered around this problem, highlighting its educational value, Python implementation, and associated learning objectives.

Introduction

The problem asks for finding all possible combinations of roosters, hens, and chicks that can be purchased with exactly 100 coins, given the following costs:

• Roosters cost 5 coins each.
• Hens cost 3 coins each.
• Chicks cost 1/3 of a coin each (i.e., 3 chicks for 1 coin).
  The total number of chickens must also equal 100.

Educational Objectives

1. Problem Understanding: Develop the ability to comprehend and analyze a problem statement.
2. Algorithm Design: Learn to design algorithms that solve specific problems.
3. Python Fundamentals: Reinforce Python programming skills, including loops, conditional statements, and arithmetic operations.
4. Logical Reasoning: Enhance logical reasoning skills by applying constraints and verifying solutions.
5. Debugging Skills: Practice identifying and fixing errors in code.

Python Implementation

Here’s a Python code snippet that solves the “Hundred Chickens with Hundred Coins” problem:

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

# Iterate through potential numbers of roosters (0 to 20, as 21 roosters exceed 100 coins)
for roosters in range(21):
    # Calculate the remaining coins and chickens
    remaining_coins = 100 - 5 * roosters
    remaining_chickens = 100 - roosters

    # Iterate through potential numbers of hens (ensuring 3*hens does not exceed remaining coins)
    for hens in range(int(remaining_coins / 3) + 1):
        # Calculate the cost of hens
        cost_hens = 3 * hens

        # Calculate the number of chick groups (each group costs 1 coin)
        chick_groups = remaining_coins - cost_hens

        # Check if the number of chicks (chick_groups * 3) fits within the remaining chickens
        if chick_groups * 3 <= remaining_chickens:
            # Calculate the actual number of chicks
            chicks = chick_groups * 3
            # Append the valid solution
            solutions.append((roosters, hens, chicks))

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

Teaching Approach

Problem Presentation: Begin by presenting the problem statement and explaining its real-world or metaphorical significance.
Concept Breakdown: Divide the problem into smaller, manageable tasks, such as understanding costs, calculating remaining resources, and verifying solutions.
Algorithm Design: Guide students through the algorithm design process, emphasizing the importance of setting appropriate boundaries for iteration and applying constraints.
Coding Implementation: Have students follow along or independently code the solution, providing assistance as needed.
Debugging & Verification: Encourage students to debug their code, identify errors, and verify the validity of their solutions.
Discussion & Reflection: Facilitate a discussion around the problem-solving process, emphasizing key concepts and strategies.

Assessment

Evaluate students based on their ability to understand the problem statement, design an algorithm, and implement the solution in Python.
Assess their logical reasoning skills through the verification of solutions and their ability to debug their code.
Encourage peer review and feedback to foster a collaborative learning environment.

Tags

Python programming
Algorithmic thinking
Problem-solving
Logical reasoning
Debugging skills
Educational case study