Week 9 - problem-solving episode

This week, I came across a problem from a 2009 International Mathematics Tournament of Towns, held at the University of Toronto. I decided to solve it following Polya's approach. The problem is as follows:

Is it possible to cut a square into nine squares and colour one of them white, three of them grey and five of them black, such that squares of the same colour have the same size and squares of different colours will have different sizes?

(1) Understanding the problem: To prove that it is possible, an example must be provided. Otherwise, it is necessary to prove that there can be no possibilities.
(2) Devising a plan: Try to find an example. If this fails, consider why it is failing in order to prove why it is not possible to find an example.
(3) Carrying out the plan: An example was found, shown below.

(4) Looking back: Check to make sure that all requirements of the question were fulfilled (yes).