MathDB

9

Part of 2009 Math Prize For Girls Problems

Problems(1)

counting circles in a grid

Source:

11/15/2009
The figure below is a 4×4 4 \times 4 grid of points. [asy]unitsize(15); for ( int x = 1; x <= 4; ++x ) for ( int y = 1; y <= 4; ++y ) dot((x, y));[/asy]Each pair of horizontally adjacent or vertically adjacent points are distance 1 apart. In the plane of this grid, how many circles of radius 1 pass through exactly two of these grid points?