Cover the board with the right shapes using Pyomo.

Consider the following 10*10 board. There are 6 distinct shapes that you need to use to cover the board (as far as possible). The following rules should be respected:

• There is enough number of each shape available
• Every two shapes should not overlap (the most difficult one)
• If shape i is used n_i times then shape j less that | n_i-d | times.
• All the placed shapes should remain within the board's boundries

The idea is simple ! Each cell should not be covered more than once . But how to write it mathematically?

if we put a shape s on cell i (there are N^2 cells) it will cover some specific cells j

We can store these cells for each individual (i,s) and call it cover (it is a dictionary in python)

Here is the problem formulation: (it is mixed integer linear )

Here is the Pyomo code: (solved with CBC solver and visualised in Matplotlib)

for a 20*20 board:

The applications:

• Covering an area with assets of different shapes
• Covering the project skills with team members with different skillsets
• Effective radiology
• Solving your weekend puzzles quickly
• Distracting you from other things

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