Collect Them All

The coupon collector’s problem

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• With $k$ of $n$ collected, the next new item takes $\frac{n}{n-k}$ tries on average.
• Collecting all $n$ takes $nH_n \approx n(\ln n + 0.577)$ tries on average.
• The final few items take most of the effort.

Steps

1. The sticker album
2. Buying boxes
3. The last toy
4. Adding up the stages
5. Twice the album
6. A hundred stickers