10

Part of 1997 Moldova Team Selection Test

Problems(1)

Let there be a regular hexagon with sidelength $1$

Source: Moldova TST 1997

Let there be a regular hexagon with sidelength

1

. Find the greatest integer

n\geq2

for which there exist

n{}

points inside or on the sides of the hexagon such that the distance between every two points is no less than

\sqrt{2}