Puzzle :-In the middle of a round pool lies a beautiful water lily. The water…

Concept: When a quantity doubles at a constant rate every period (day, hour, etc.), the amount at any point is always exactly twice the amount one period earlier. Equivalently, the amount one period BEFORE a given state is exactly half of that state — this is the defining property of exponential doubling growth, unlike linear growth, where equal time steps add equal amounts.

1. The lily's area doubles every day, and the pool is completely (100%) covered on day 20.

2. Applying the doubling rule backward: the area one day earlier, on day 19, must be exactly half of day 20's area — that is, half of the full pool.

So the water lily covers half of the pool after 19 days.

Cross-check: Going forward from day 19, if half the pool is covered on day 19, doubling that area on day 20 gives the full pool — exactly matching the given information. Checking the other options: if only 10, 15, or 5 days had passed, doubling the area for each remaining day up to day 20 would multiply it by 2 raised to a power much greater than 1 — far more than the single doubling needed to go from half to full — so none of those days can be the halfway point.