MathDB

5

Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #5: The Round Table of Positive Integers

Source:

4/29/2013
Ten positive integers are arranged around a circle. Each number is one more than the greatest common divisor of its two neighbors. What is the sum of the ten numbers?
greatest common divisornumber theoryrelatively prime
2005 Calculus #5: Towers of x - limit

Source:

4/29/2013
Calculate lim⁡x→0+(xxx−xx). \lim_{x \to 0^+} \left( x^{x^x} - x^x \right).
calculuslimitlogarithms
2005 Geometry #5: Two Cubes and a Sphere

Source:

5/16/2013
A cube with side length 22 is inscribed in a sphere. A second cube, with faces parallel to the first, is inscribed between the sphere and one face of the first cube. What is the length of a side of the smaller cube?
geometry3D geometrysphereMATHCOUNTSrectanglePythagorean Theorem