MathDB

8

Part of 2010 Harvard-MIT Mathematics Tournament

Problems(3)

2010 Algebra #8: Polynomial Permutations

Source:

7/15/2012
How many polynomials of degree exactly 55 with real coefficients send the set {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\} to a permutation of itself?
algebrapolynomial
2010 Calculus #8: Factorial and Power Summation

Source:

7/15/2012
Let f(n)=∑k=2∞1kn⋅k!.f(n)=\displaystyle\sum_{k=2}^\infty \dfrac{1}{k^n\cdot k!}. Calculate ∑n=2∞f(n)\displaystyle\sum_{n=2}^\infty f(n).
calculusfactorialintegration
2010 Geometry #8: Maximum Area of Triangle

Source:

2/14/2015
Let OO be the point (0,0)(0,0). Let AA, BB, CC be three points in the plane such that AO=15AO=15, BO=15BO = 15, and CO=7CO = 7, and such that the area of triangle ABCABC is maximal. What is the length of the shortest side of ABCABC?
geometry