12 Coins Puzzle - Manim Animation Project

An educational animation series explaining the classic 12 coins puzzle using Manim (Mathematical Animation Engine). This project demonstrates algorithmic thinking, problem-solving strategies, and the power of systematic approaches.

🎯 Project Overview

The 12 coins puzzle is a classic problem where you have 12 identical-looking coins, but one is different (either heavier or lighter). Using only a balance scale and 3 weighings, you must identify the odd coin and determine if it's heavier or lighter than the others.

This project creates 12 animated scenes that walk through:

• Problem definition and constraints
• Why naive approaches fail
• The optimal solution strategy
• Real-world applications of the thinking process

🚀 Setup Instructions

Prerequisites

• Python 3.7 or higher
• Git (for cloning the repository)

Mac Setup

1. Clone the repository

   git clone https://github.com/ronalking182/csc309.git
   cd csc309/coins_puzzle_manim

2. Create and activate virtual environment

   python3 -m venv venv
   source venv/bin/activate

3. Install dependencies

   pip install -r requirements.txt

4. Install system dependencies for Manim

   brew install ffmpeg
   brew install cairo
   brew install pkg-config
   brew install pango

Windows Setup

1. Clone the repository

   git clone https://github.com/ronalking182/csc309.git
   cd csc309\coins_puzzle_manim

2. Create and activate virtual environment

   python -m venv venv
   venv\Scripts\activate

3. Install dependencies

   pip install -r requirements.txt

4. Install system dependencies for Manim

   • Download and install ffmpeg
   • Add ffmpeg to your system PATH
   • Install MiKTeX for LaTeX support (optional but recommended)

🎬 Running the Animations

Option 1: Render All Scenes at Once

python render_all.py

This will render all 12 scenes and save them to the media/videos/ directory.

Option 2: Render Individual Scenes

# Basic quality (faster rendering)
manim -pql scenes/scene1_definition.py Scene1Definition

# High quality (slower rendering)
manim -pqh scenes/scene1_definition.py Scene1Definition

# 4K quality (very slow)
manim -pqk scenes/scene1_definition.py Scene1Definition

Option 3: Using the Main Script

python main.py

This provides a menu of available scenes and rendering options.

📽️ Scene Overview

Scene 1: Definition (scene1_definition.py)

• Title: "The 12 Coins Puzzle"
• Content: Introduces the problem with 12 coins, explains that one is different (heavier or lighter)
• Key Message: Sets up the challenge and basic constraints

Scene 2: Why It Matters (scene2_why_it_matters.py)

• Title: "Why This Puzzle Matters"
• Content: Explains the importance of systematic thinking and algorithmic approaches
• Key Message: Connects to broader problem-solving skills

Scene 3: Key Insight (scene3_key_insight.py)

• Title: "The Key Insight"
• Content: Reveals the crucial realization about information theory and binary encoding
• Key Message: Each weighing provides maximum information when designed properly

Scene 4: Math Behind (scene4_math_behind.py)

• Title: "The Math Behind"
• Content: Explains the mathematical foundation using information theory
• Key Message: 3 weighings can distinguish between 24 possibilities (12 coins × 2 states)

Scene 5: Strategy (scene5_strategy.py)

• Title: "The Winning Strategy"
• Content: Outlines the systematic approach to solve the puzzle
• Key Message: Divide and conquer with information-maximizing weighings

Scene 6: First Weighing (scene6_first_weighing.py)

• Title: "The First Weighing"
• Content: Demonstrates the optimal first weighing (4 vs 4 coins)
• Key Message: How to interpret the three possible outcomes

Scene 7: Interpretation (scene7_interpretation.py)

• Title: "Interpreting Results"
• Content: Shows how to analyze weighing results and narrow down possibilities
• Key Message: Each result provides specific information about coin groups

Scene 8: Logic Tree (scene8_logic_tree.py)

• Title: "Why Random Guessing Fails"
• Content: Demonstrates the inefficiency of random approaches
• Key Message: Systematic thinking beats random guessing

Scene 9: Why Random Fails (scene9_why_random_fails.py)

• Title: "Think Like a Detective"
• Content: Uses detective analogy to explain systematic investigation
• Key Message: Methodical approach leads to guaranteed success

Scene 10: Real Life (scene10_real_life.py)

• Title: "The Big Lesson"
• Content: Summarizes the key learning points from the puzzle
• Key Message: Algorithmic thinking is powerful and transferable

Scene 11: Big Lesson (scene11_big_lesson.py)

• Title: "This Thinking Appears In"
• Content: Lists real-world applications of the puzzle's thinking process
• Key Message: Binary search, debugging, medical diagnosis, and more

Scene 12: Ending (scene12_ending.py)

• Title: "Final Thought"
• Content: Concludes with the power of algorithmic thinking and Computer Science
• Key Message: CS thinking transforms how we approach problems

🎨 Customization Options

Rendering Quality

• -pql: Low quality (fastest, good for testing)
• -pqm: Medium quality
• -pqh: High quality (recommended for final output)
• -pqk: 4K quality (slowest, best quality)

Output Formats

• Default: MP4 video files
• Add --format gif for GIF output
• Add --format png for image sequence

📁 Project Structure

coins_puzzle_manim/
├── scenes/                 # All animation scene files
│   ├── scene1_definition.py
│   ├── scene2_why_it_matters.py
│   └── ... (scenes 3-12)
├── media/                  # Generated output files
│   ├── videos/            # Rendered videos
│   ├── images/            # Generated images
│   └── texts/             # Generated text assets
├── main.py                # Entry point with scene menu
├── render_all.py          # Batch rendering script
├── test_scenes.py         # Test all scene imports
├── requirements.txt       # Python dependencies
└── README.md             # This file

🛠️ Troubleshooting

Common Issues

1. ffmpeg not found

   • Mac: brew install ffmpeg
   • Windows: Download from ffmpeg.org and add to PATH

2. Cairo/Pango errors

   • Mac: brew install cairo pango pkg-config
   • Windows: Install through package managers or precompiled binaries

3. LaTeX errors

   • Install MiKTeX (Windows) or MacTeX (Mac)
   • Ensure LaTeX is in your system PATH

4. Memory issues during rendering

   • Use lower quality settings (-pql instead of -pqh)
   • Close other applications
   • Render scenes individually instead of all at once

🎓 Educational Value

This project demonstrates:

• Algorithmic Thinking: Systematic problem-solving approaches
• Information Theory: How to maximize information gain
• Binary Encoding: Representing states with binary decisions
• Divide and Conquer: Breaking complex problems into manageable parts
• Real-world Applications: Connecting abstract concepts to practical scenarios

🤝 Contributing

Feel free to:

• Add new scenes or improve existing ones
• Translate scenes to other languages
• Create alternative solution approaches
• Add interactive elements or quizzes

📄 License

This project is open source and available under the MIT License.

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Happy animating! 🎬✨