IBM Ponder This #049 · May 2002

Definitions:
In the plane, call a point a "lattice point" if both its coordinates are integers, so that (2,-3) is a lattice point but (1,3.5) is not. A "circle" is the curve, not the 2-dimensional figure enclosed in that curve; it is described by giving its radius and the coordinates of its center.

Problem:
Part 1:
Describe a circle in the plane which passes through exactly seven lattice points.

Part 2:
Find such a circle with minimum radius.

Part 3:
Find (up to symmetries) all such circles with radius less than 50.

Unfortunately we won't be able to respond to answers to parts 2 and 3 this time.

Solution

Best opened after a real attempt

To be added.