A lily pad grows so that each day it doubles its size. On the twentieth (20th) day of its life, it completely covers the pond. On what day day was the pond half covered ?

19.

To find out on which day the pond was half covered, we need to work backward from the twentieth day when it was completely covered.

Since the lily pad doubles in size every day, on the 19th day, it would only cover half of the pond. This means that on the 19th day, the size of the lily pad was half of what it was on the 20th day.

Now, to find the previous day when the pond was half covered, we repeat the process: on the 18th day, the lily pad would be half the size of what it was on the 19th day.

We can continue this backward progression until we reach the day when the pond was initially empty. Let's see the pattern:

20th day: Completely covered
19th day: Half covered
18th day: One-fourth covered
17th day: One-eighth covered
16th day: One-sixteenth covered
15th day: One-thirty-second covered
...
and so on until the day when the pond was empty.

From this pattern, we can observe that the lily pad covers half of the pond one day before it's fully covered. Therefore, the pond was half covered on the 19th day.