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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?

[Ref: ZFKX]

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 skip is doubling every hour, as it was full at 11pm, it must have been half full at 10pm.

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