A lake has a small patch of lily pads and every day the patch grows to double its size. It takes 32 days for the patch to cover the lake – how long would it take the patch to cover half the lake?

It took 31 days for the patch to cover half the lake

Step-by-step explanation:

The patch grows to double its size everyday

the patch completely covers the lake in 32 days

Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.

Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake