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 placed a bottle each into the skip.
An hour later four people placed a bottle each into the skip.
This doubling of people continued until 11pm, when the skip was finally full.
When was the skip exactly half full?
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