A single lily pad doubles the area it covers every day. Left alone, the patch covers an entire pond in 48 days. On which day is the pond exactly half covered?

The Pond That Fills Overnight

Issue 13 Warm-up Published 9 Sep 2026 By The Chalkboard Desk

The problem

A single lily pad doubles the area it covers every day. Left alone, the patch covers an entire pond in days. On which day is the pond exactly half covered?

The doubled area happens once per day, not continuously.
The pond is fully covered at the end of day .

Take a minute

Reveal hint 1

You do not need to know the size of the pond or of one pad.

Reveal hint 2

Work backwards: what fraction was covered one day before the pond was full?

Solution

AnswerDay — the pond is half covered with only one doubling left to go.

Derivation

Write the growth law.
Use the known endpoint.
Read off the answer.
See why this surprises people.
Express it as a formula.