🍩 k→∞ and Donut Packing 🍩

Welcome to Donut Packing!

Objective: Pack as many delicious donuts as possible into your donut box while maximizing the total area!

How to Play:

  1. You'll receive a quadrilateral donut box and a variety of donuts
  2. Select a donut from your pile by clicking on it
  3. Position it using the arrow keys (↑↓←→)
  4. Rotate it using the < and > keys
  5. Place donuts without overlapping each other or the box edges
  6. Watch out for mice! They'll appear randomly and take bites out of your donuts
  7. You can return donuts to your pile, but mice bites stay!
  8. When done, click "Done Packing" and calculate your total area

Math Challenge:

Each donut shows its dimensions. Calculate the area using these formulas:

  • Circle: A = πr² (where r is radius)
  • Square: A = s² (where s is side length)
  • Triangle: Use Heron's formula: A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
  • Trapezoid: A = ½(b₁ + b₂)h (where b₁, b₂ are bases and h is height)
  • Glazed Donut (ring): A = π(R² - r²) (outer radius R, inner radius r)

Tips: Plan your packing strategy! Rotate and position carefully to fit more donuts.

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🍩 Setup Your Game 🍩

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📦 Packaging Your Donuts... 📦

🎁
k→∞ Donut Packing
Time 0:00
🍩 Pack delicious donuts and maximize your area! 🍩
Select a donut to start packing!

📚 Help & Formulas 📚

Area Formulas:

  • Circle: A = πr² (where r is radius)
  • Square (Beignet): A = s² (where s is side length)
  • Triangle: Use Heron's formula:
    A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
    (a, b, c are the three side lengths)
  • Trapezoid (Long John): A = ½(b₁ + b₂)h
    (b₁, b₂ are the two parallel bases, h is height)
  • Glazed Donut (ring): A = π(R² - r²)
    (R is outer radius, r is inner radius)

Game Tips:

  • Calculate each donut's area using the dimensions shown
  • Pack efficiently to maximize total area
  • Watch out for mice - they reduce your score!
  • Remember to subtract mouse bites (area = 1 each) from your total
  • Use rotation to fit donuts better in corners

Controls:

  • Arrow keys (↑↓←→) to move the selected donut
  • < and > keys to rotate the selected donut
  • Click a donut in your pile to select it
  • Click a donut in the box to select it for moving or returning