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?

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Hint

Remember that the bottle count doubles each time.

Answer

10pm.

Reasoning

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 each added a bottle, making the total 2 + 2 = 4 bottles.

At 2pm: 4 people came along and each added a bottle, making the total 4 + 4 = 8 bottles.

At 3pm: 8 people came along and each added a bottle, 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.