When It Becomes Ten Times Bigger
by Anonymous · ⭐ 1 · 🍴 0
📈 There’s one question: “Does anyone have the same number?” The answer never changes, but the number of steps can be completely different. 🤝 Compare every pair, and the squares stack into a triangle—that triangle is “people × (people−1) ÷ 2.” When the number of people doubles, the steps grow to nearly four times as many. 🏷️ Make a table once (20 setup steps), then it takes one step per person, so with 8 people the two methods meet exactly at 28 steps. With fewer people, you can even check by hand that the “slow method” is actually faster—slow isn’t always bad. 🔟 Finally, make the number of people ten times larger. The number of comparisons grows by a little more than 100 times, and gets closer to 100 times as the group grows, but it is never exactly 100 times.
About this app
When It Gets Ten Times Bigger is an interactive coding-basics lesson about comparing two ways to detect whether two people share the same number. Explore the quadratic all-pairs method, where the work is people × (people−1) ÷ 2, and compare it with building a lookup table once before checking each person in one step. Three guided activities demonstrate triangular numbers, the crossover at 8 people, and how scaling the group by ten makes the comparison method approach—but never equal—100 times the work.
Use cases
- Students learning algorithm efficiency
- Teachers demonstrating quadratic versus linear-style work
- Beginners exploring duplicate detection
- Anyone practicing step-by-step computational thinking
Features
- Adjust the number of people with plus and minus controls
- Compare every pair one step at a time or to the end
- Build a table with a 20-step setup and scan people individually
- Show step counts, compared pairs, answers, and table progress
- Test tenfold growth with a ×10 control
- Guided challenges about triangular numbers and scaling