You play a game against Malory, in which you choose points on the 2D plane and Malory wins if she can cover them by using non-overlapping pennies (disks of radius 1). Show a minimal set of points that guarantees you a win.
Hint
At low numbers of dots, Malory is favoured (if there is 1 dot, just cover it with 1 circle), and at high numbers of dots you are favoured (e.g. by using a grid approach like https://www.desmos.com/calculator/gwwcn40xcp)
Here's something that'll let you test out your theories: https://www.desmos.com/calculator/ifhtfwhnqm