MathDB

7

Part of 2006 Stanford Mathematics Tournament

Problems(4)

Engine Failure

Source:

3/15/2010
An aircraft is equipped with three engines that operate independently. The probability of an engine failure is .01. What is the probability of a successful flight if only one engine is needed for the successful operation of the aircraft?
probability
2006 SMT Algebra #7 - $aabb=n^4-6n^3$

Source:

8/24/2011
Find all solutions to aabb=n4−6n3aabb=n^4-6n^3, where aa and bb are non-zero digits, and nn is an integer. (aa and bb are not necessarily distinct.)
2006 SMT Team Round #7 - Greater Than or Equal to 2500?

Source:

8/22/2011
Let SS be the set of all 3-tuples (a,b,c)(a,b,c) that satisfy a+b+c=3000a+b+c=3000 and a,b,c>0a,b,c>0. If one of these 3-tuples is chosen at random, what's the probability that a,ba,b or cc is greater than or equal to 2,500?
probability
Lattice Points for Endpoints and Midpoints

Source: 2006 SMT Advanced Topics Test Problem 7

3/20/2010
A lattice point in the plane is a point whose coordinates are both integers. Given a set of 100 distinct lattice points in the plane, find the smallest number of line segments AB‾ \overline{AB} for which A A and B B are distinct lattice points in this set and the midpoint of AB‾ \overline{AB} is also a lattice point (not necessarily in the set).
analytic geometry