Puzzle: Brazil Vestibular Question #20

The puzzle is thus:  You place a 2×2.  Each time you move the 2×2 square you change the colors in the following:

• The whole 3×3 starts off grey.
• Within the 2×2 grey goes to blue, blue goes to yellow, yellow goes to grey

A sequence of moves were made that resulted in the 3×3 with the question marks in it. Which of the multiple choices below it is a viable possibility to fill in the squares with question marks?

• Original Vestibular Exam here
• My Markup of the Exam here
• My Brute Force Solution
• Olimpiada Brasileira de Matematica Escola Publica – from various years.

Solution of the puzzle by a much more direct route from the OBMEP