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Found problems: 2

2010 Tournament Of Towns, 5
$33$ 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 ?
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2009 AMC 12/AHSME, 24
For how many values of $ x$ in $ [0,\pi]$ is $ \sin^{\minus{}1}(\sin 6x)\equal{}\cos^{\minus{}1}(\cos x)$? Note: The functions $ \sin^{\minus{}1}\equal{}\arcsin$ and $ \cos^{\minus{}1}\equal{}\arccos$ denote inverse trigonometric functions. $ \textbf{(A)}\ 3\qquad \textbf{(B)}\ 4\qquad \textbf{(C)}\ 5\qquad \textbf{(D)}\ 6\qquad \textbf{(E)}\ 7$
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