Source: 15 Puzzle
Problem: The 15-puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle that consists of a frame of numbered square tiles in random order with one tile missing. The object of the puzzle is to place the tiles in order (from figure at left to figure at right) by making sliding moves that use the empty space. Prove that the 15 puzzle in the configuration as shown on the left is not solvable.
I made this fb game yesterday night - 9 Puzzle over Movie Posters - Movie Sliding Puzzle
Sam Loyd published some great puzzles in his time. One book that gets recommended a lot is "Sam Loyd's Cyclopedia of 5000 Puzzles tricks and Conundrums" (Amazon , Flipkart)
Solution provided by Raghuram Kowdeed (IIT Kanpur) in comments!
Same solution posted by Sai Teja Pratap (IIT Bombay CSE Final Year Student) and Eeshaan Malhotra (IIT Bombay) on Quora Board.
I have taken the facebook game down.