# Recycling bin

Question:

There is a bottle recycling bin, with one lonely bottle inside. 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 bin was finally full. When was the bin exactly half full?

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Solution: The bin was half full at 10pm.
The skip started with 1 lonely bottle.
At Noon: 1 person came along and added a bottle, making the total 2 bottles.
At 1pm: 2 people came along and added a bottle each, making the total 2 + 2 = 4 bottles.
At 2pm: 4 people came along and added a bottle each, making the total 4 + 4 = 8 bottles.
At 3pm: 8 people came along and added a bottle each, making the total 8 + 8 = 16 bottles.
Therefore the number of bottles in the bin is doubling every hour, as it was full at 11pm, it must have been half full at 10pm.