美国数学竞赛题（都英语进）

美国数学竞赛题（都英语进）1.Make two random marks on a long stick.(a) If you then break the stick into k pieces of equal length,what's the chance the two marks are on the same piece?(b) If you then break the stick into k pieces of random lengths,what's the chance the two marks are on the same piece?2.Leonhard has ten rods having lengths 1,2,...,10 respectively.How many different ways are there to make a triangle by choosing three appropriate rods?3.A point is chosen randomly inside a square of side length 5,and a unit circle is drawn with that point as its center.Calculate the probability that the circle does not intersect either of the square's diagonals or any of its sides.4.Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.5.In the complex plane,let u and v be two distinct solution of .Find the probability that .