I feel that this problem is too obvious, this makes me really confused. If someone could just confirm whether I am right or wrong would be awesome.
We consider paths from $(1, 1)$ to $(4, 4)$ in the Cartesian plane. Now check each point having integer coordinates, such as $(2, 3)$ or $(0, 4)$, and color it blue if it lies within $0.95$ units of some point on the path. What is the smallest possible number of blue points one could obtain?
I simply think that you can go from $(1, 1)$ to $(4, 1)$ then up to $(4, 4)$ leaving a total of $7$ blue dots.
Thanks in advance!