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When It Becomes Ten Times Bigger

📈 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.