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How many basketballs would fit in this room?

Answer:

One. You did not ask what is the maximum number of basketballs you can fit in the room.

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If you have seven white socks and nine black socks in a drawer, how many socks do you have to pull out blindly in order to ensure that you have a matching pair?

Suppose there are three light switches outside a room. Inside is a single light bulb, controlled by one of the three switches. You need to determine which switch operates the bulb. You can turn the switches on and off as many times as you wish (they are all off to begin with), but may only enter the room once. There is no one there to help you. The door to the room is closed, and there are no windows, so you cannot see inside. How can you discover which switch operates the bulb?