MATC Mathematics Club
Mathematically Correct Page
The Puzzle Corner of the MATC Mathematics Club
Madison Area Technical College
The MATC Mathematics Club posts recreational mathematics problems for your enjoyment and possible extra credit, if you have the right instructor... The current problem set is listed below, as well as links to past problem sets .
Email Kevin Mirus with your solutions (both the answers and their justification)
Spring 2005 Problem Sets
#1, Volume #8
Click here for the solutions.
|1. Find all possible sets
of four consecutive integers having the property that the sum of the cubes of
the smallest three is equal to the cube of the largest.
|2. Find the value of k
for which the two equations
(x - 2)4 - (x - 2) = 0 and x2 - kx + k = 0
have two roots in common.
|3. Find all ordered pairs
of integers (x, y) which satisfy x2 + 4x + y2 = 9.
|4. The sum of the ages of
the members of a family is currently 75 years, where the family consists of a
mother, father, son, and daughter. Six years ago, the sum of the ages of
the family members was 53 years. If the father is four years older than
the mother, and the daughter is three years older that the son, find the current
age of the father.
|5. Express in simplest
|Volume 7, Fall 2004 Problem Sets||Volume 8, Fall 2004 Problem Sets|
|Volume 5, Fall 2003 Problem Sets||Volume 6, Spring 2004 Problem Set|
|Volume 3, Fall 2002 Problem Sets||Volume 4, Spring 2003 Problem Sets|
|Volume 1, Fall 2001 Problem Sets||Volume 2, Spring 2002 Problem Sets|
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