Imagine a bottle recycling skip, empty other than one lonely bottle.

Every hour, on the hour, people come and put bottles into the skip.

The first hour, at noon, one person came and put a bottle in.

One hour later, two people each placed a bottle into the skip.

An hour later, four people each placed a bottle into the skip.

This doubling of people continued until 11pm, when the skip was finally full.

When was the skip exactly half full?