Cominatorics
There are 1000 rooms in a row along a long corridor. Initially the first room contains 1000 people and the remaining rooms are empty. Each minute, the following happens: for each room containing more than one person, someone in that room decides it is too crowded and moves to the next room. All these movements are simultaneous (so nobody moves more than once within a minute). After one hour, how many different rooms will have people in them?
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Draw out the pattern and the problem will become obvious. After 6 0 minutes, the first room will have 9 4 0 people and there will be 3 0 other rooms with 2 people in them. Therefore, there will be 3 1 rooms.