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River Crossing Problem - You have a fox, a chicken and a sack of grain.

In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily. After how many days will half of the pool be covered by the water-lily?

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?