Imagine a pond. in it sits one lilypad, which reproduces once a day. each of its offspring also reproduces once a day, doubling the number of lily pads in the pond every day. if the pond is full of lily pads on the 30th day, on what day is it half-full of lily pads

On the 29th day

Step-by-step explanation:

According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.

On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.

The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are lilypads on the 30th, and lilypads on the 29th. This can be deduced multiplying succesively by 2.