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Going Up

A problem from the 2003 Moscow Mathematical Olympiad:

A store has three floors, which are connected only by an elevator. At night the store is empty, and during the workday:

(1) Of the customers who enter the elevator on the second floor, half go to the first floor and half to the third floor.

(2) The number of customers who get out the elevator on the third floor is less than 1/3 the total number of customers who get out of the elevator.

Which is greater, the number of customers who go from the first floor to the second on a given workday, or the number who go from the first floor to the third?

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