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MathNet 2026 — Part 10 Question 181

Math Olympiad Vault · MathNet 2026 — Part 10

Question 181

In the game Pogémon, Pogé Balls contain Pichagus with a $50\%$ chance and otherwise contain nothing. The new Pogémon universe started with one Pichagu and has existed for five hours. Every hour, every Pichagu at the time opened a new Pogé Ball.


a) What is the expected number of Pichagus created in the last hour?


b) Every two currently existing Pichagus will now battle each other. What is the expected number of battles?