Jigsaw Puzzle,10 Distinct Pieces, Shapes and Patterns

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####Jigsaw Puzzle,10 Distinct Pieces, Delving Deeper In this project, we delve deeper into the mathematics of a special case of the jigsaw puzzle, under the following conditions: 1. Each piece is a square. 2. Using **only 2 types of connectors** (e.g., a square and a circle). Mathematically, there are 16 possible shapes (see figures). Twelve (12) of them, however, are each the mirror image of a corresponding piece. Therefore, there are 10 unique pieces. As shown in the figure, each row can be assembled into a 2 x 2 square. So are the center 4 pieces, the 4 pieces at the corners, along the diagonals, etc. Further, all the 16 pieces can be assembled into a 4 x 4 square. #### About the files Pz11 refers to the piece at (Row 1, Column 1); Pz14 refers to the piece at (Row 1, Column 4) and so on. #### Questions 1. If I pick **4 random pieces** from the 16 pieces (not necessarily unique), can I always put them together for a square? **Seemingly NO**. 2. In how many different ways can one pick four pieces and make a 2 x 2 square? 3. In how many different ways can all the 16 pieces be put together to make a 4 x 4 square? Have fun!