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n cars participating in a rally

Source: Turkey NMO 2003 Problem 1

February 24, 2009
inductioncombinatorics unsolvedcombinatorics

Problem Statement

n≥2 n\geq 2 cars are participating in a rally. The cars leave the start line at different times and arrive at the finish line at different times. During the entire rally each car takes over any other car at most once , the number of cars taken over by each car is different and each car is taken over by the same number of cars. Find all possible values of n n
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