Problem #5 EASY
The Lily Pad Exponential Pond
Meta Math Pattern Recognition
Problem Statement
In a quiet lake, a single lily pad is growing. Every day, the size of the lily pad doubles in area.
If it takes exactly 48 days for the lily pad to completely cover the entire surface of the lake, how many days does it take for the lily pad to cover exactly half of the lake?
Answer & Quick Explanation
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It takes 47 days because the lily pad doubles in size every day, so it must have covered half the lake on the day before it covered the whole lake.
Detailed Editorial Solution
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This riddle highlights the counter-intuitive nature of exponential growth. People often think the answer is 24 days (half of 48), but that assumes linear growth.
Let's work backward from day 48:
- On Day 48, the lake is 100% covered.
- Since the lily pad doubles in size every day, it must have been half as large on the previous day.
- Therefore, on Day 47, the lake was exactly 50% (half) covered.
Going back one more step, it was 25% covered on Day 46, and so on.