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N horsemen riding along a circle road for N=3 and N=10

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February 8, 2011
algebra unsolvedalgebra

Problem Statement

NN horsemen are riding in the same direction along a circular road. Their speeds are constant and pairwise distinct. There is a single point on the road where the horsemen can surpass one another. Can they ride in this fashion for arbitrarily long time? Consider the cases: (a)N=3;(a) N = 3; (b)N=10.(b) N = 10.
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