How The Heck Does This Magical Tile Board Work?

How The Heck Does This Magical Tile Board Work?
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This board of tiles, or Azulejos, which is a form of Portugese artwork that involves tilework, is making my brain lose its grey matter. The tile board somehow maintains the same number of tiles even when some individual tiles are removed.

How did all the tiles fit in the first place? How does it still fit after getting rid of three tiles? Where is the missing square? What sorcery is this?

Maths, as logical and deductive as it may be, is all sorcery. I’m sure of it. It’s better to not even try to figure out these illusions, if you ask me. [Norberto Jansenson via The Awesomer]