The “Hundred Coins for Hundred Chickens” puzzle, a classic problem in algorithmic problem-solving, challenges us to find all combinations of three types of chickens—roosters, hens, and chicks—that can be purchased with exactly 100 coins, given their specific costs, and that add up to a total of 100 chickens. In this blog post, we’ll dive into the Python code that solves this puzzle, examining its logic, efficiency, and the concepts it illustrates.
Understanding the Puzzle Constraints
- Roosters cost 5 coins each.
- Hens cost 3 coins each.
- Chicks cost 1/3 of a coin each, meaning 3 chicks can be bought for 1 coin.
We need to find the combinations of these chickens that satisfy both the cost and quantity constraints.
Python Code Breakdown
Here’s a Python program that solves the puzzle:
python# Initialize an empty list to store solutions
solutions = []
# Iterate through possible numbers of roosters
for roosters in range(21): # Roosters cost 5 coins, so max 20 (5*21 > 100)
# Iterate through possible numbers of hens
for hens in range(34): # Hens cost 3 coins, so max 33 (3*34 + 5*20 > 100)
# Calculate cost spent on roosters and hens
cost_spent = 5 * roosters + 3 * hens
# Calculate remaining coins for chicks
remaining_coins = 100 - cost_spent
# Calculate the number of chick groups (each group costs 1 coin)
chick_groups = remaining_coins
# Check if we can buy enough chicks to make up the total of 100
if chick_groups >= 0 and roosters + hens + chick_groups * 3 == 100:
# Convert chick groups to total number of chicks
chicks = chick_groups * 3
# Append 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]}")
Logic and Efficiency
The program employs a nested loop to iterate through all possible combinations of roosters and hens. For each combination, it calculates the cost spent and the remaining coins. It then checks if the remaining coins can buy enough chick groups (each costing 1 coin) to satisfy the total number of chickens being 100. If both conditions are met, the solution is added to the list of valid combinations.
This approach is efficient for the given constraints, as the search space is relatively small. However, for more complex problems with larger search spaces, optimizations or more sophisticated algorithms might be necessary.
Educational Value
This puzzle and its Python solution offer several educational benefits:
- Problem-solving skills: It encourages critical thinking and algorithmic problem-solving.
- Understanding constraints: It illustrates the importance of understanding and applying constraints in problem-solving.
- Coding practice: It provides an opportunity to practice coding skills, especially loops and conditional statements.
- Mathematical concepts: It reinforces concepts such as iteration, arithmetic operations, and variable manipulation.
Conclusion
The “Hundred Coins for Hundred Chickens” puzzle is a fun and educational challenge that showcases the power of algorithmic thinking and problem-solving. By writing a Python program to solve it, we’ve not only found the solutions but also honed our coding skills and deepened our understanding of algorithmic concepts.
