Half-full bank account
You put money in your new bank account every day. You deposit money in your bank account in such a way that the money doubles with each passing day. If you put in 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your bank gets full on the 9th day. On which day will your bank account be half-full?
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Since the money in the bank account doubles with each passing day, the bank account will be half-full the day previous to the one on which it gets full. Therefore, the bank account will be half-full on the 8th day.
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