MathDB

Consider all trapezoids in a coordinate plane with interior angles of

90^o, 90^o, 45^o

and

135^o

whose bases are parallel to a coordinate axis and whose vertices have integer coordinates. Define the size of such a trapezoid as the total number of points with integer coordinates inside and on the boundary of the trapezoid. (a) How many pairwise non-congruent such trapezoids of size

2001

are there? (b) Find all positive integers not greater than

50

that do not appear as sizes of any such trapezoid.

Problem Statement