Kinesys skims the surface of a lake on Veritas and stops a few yards from shore, bobbing there with a guilty air. A gigantic water lily is growing on the water. The sign beside it reads: “This water lily doubles in size every day. Soon it will cover the whole lake. The sign has nothing further to add.”
A Veritasian fisherman sitting on the bank confirms it without enthusiasm: he has counted every single day since the first sprout. Dord is scandalized by a plant with so little self-restraint. Liz, waiting for the engine to dry out, improvises a little dance on the ship’s float.
M00N, bursting with curiosity, wants to know when the lily was exactly half that size.
The Riddle
A water lily falls into a lake. Every day it doubles its area, and in 100 days it covers the entire surface of the lake. How many days did it take to cover half the lake?
Hint
The lily doesn’t grow by the same amount every day: it doubles. Don’t trust your first instinct—ask yourself how much of the lake was covered just before the end.
Solution
The correct answer is 99 days.
If the lily covered the whole lake on day 100, and its area doubles every day, then on the day before it must have covered exactly half. Instinct often says 50 days, but growth by doubling isn’t proportional to time.