Puzzle! 8 pieces, over 2500 ways to solve. How is it possible

There is a puzzle with 8 pieces and one single board to put them.
The board is labeled with months and dates.
Your goal is to place this 8 pieces in a way that leaves only 2 squares open.
That 2 square declare the date you have solved.

You can place them on the board and solve every possible date, meaning 366 solves in total.
Also for one date there are multiple ways to solve it. I have even made 44 solve for 25 Jun!
How is that possible? Would it work with different pieces or a different board? Is there some way to prove that is solvable or that it is not? Is there any topology approach we could use?

I have spend hours in this as you can see and solved the all 366 dates, so I can say for sure that it is working but HOW!? http://prntscr.com/21lumhp

You can currently find the app only on play store, it is called 365 Days Puzzle
https://play.google.com/store/apps/details?id=com.CoffeeStudios.puzzle365