November 25–December 1, 2008

Problem

The vertices of a triangle T have coordinates (x1, y1), (x2, y2), and (x3, y3). Suppose that for any integers h and k, not both zero, the shifted triangle with vertices (x1 + h, y1 + k), (x2 + h, y2 + k), and (x3 + h, y3 + k) has no common interior points with the original triangle. (That is, if you tiled the plane with shifted copies of triangle T, none of the interiors of the triangles would overlap.)

  1. Is it possible for the area of triangle T to be greater than 1/2?
  2. What is the maximum possible area of triangle T?

Solution

here

List of solvers

Dustin Moody (graduate); Gary Raymond, Lloyd Sakazaki, Dean Anderson (outside).

Dustin Moody wins the prize!