Five points are placed inside a square of side . Which argument shows that some two of them are a distance at most apart?
ADivide the square into four squares of side ; two of the points lie in the same one, and its diagonal is .
BThe five points cannot all lie at corners of the square.
CThe average of the ten distances between the points is less than .
DDivide the square into five regions; each point lies in one of them.
ENo argument works: the four corners together with the centre is a counterexample.
FThe square has diagonal , and half of is .
GDivide the square into two rectangles; three of the points lie in the same one.
HAny five points in the plane include two at distance at most .