Consider a rectangle with sides of length m and n, were m, n are integers. We want to place the maximum number of dots inside it however the dots must have a minimum spacing of 1 . Given a minimum spacing d which is a factor of both m and n, and assuming the dots may be placed along the edges of the rectangle, how would one find the maximum number of dots that can be placed inside the rectangle?
I was shown this problem, and tried the naive approach of spacing the dots along both edges by spacing 1 (which I believe would give (n+1) and (m+1) dots along each side) and multiplied them together. However, apparently we can fit more dots that this in using a different packing arrangement however I don't know where to begin with that kind of problem. Would anyone have any advice?
