HMMT 2004 C1
- Combinatorics
- Answer
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?
Dataset text NuminaMath olympiads. Quoted with source.
Also HMMT 2004 E1.
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