Forming a Marching Band Formation
Source:
November 10, 2005
geometryrectanglequadraticsspecial factorizationsalgebradifference of squaresquadratic formula
Problem Statement
The director of a marching band wishes to place the members into a formation that includes all of them and has no unfilled positions. If they are arranged in a square formation, there are 5 members left over. The director realizes that if he arranges the group in a formation with 7 more rows than columns, there are no members left over. Find the maximum number of members this band can have.