Optimizing choclate, Combinatorics
You are a pastry chef that comes upon 99 magical chocolate unit squares. The chocolate abides by the following rule: whenever there is a continuous region of chocolate it will grow into the smallest rectangle that covers the continuous region. So that they can be packaged in a candy wrapper.
The question is, what is the most amount of chocolate you can make if you have to place your initial 99 squares on the xy lattice grid.
clarifications:
The puzzle is orthogonally adjacent, so for two rectangles to be a continuous region they must share an edge or overlap.
To keep the construction well defined the rectangles cannot be rotated: i.e. their dimensions are the min max values of x and y in the continuous region.
Finding the max value is decently easy the challenge is proving your construction is max