Jigsaw Puzzle,10 Distinct Pieces, Shapes and Patterns

thingiverse

In this project, we're going deeper into the mathematics of a special case of the jigsaw puzzle with specific conditions: 1. Each piece is a square. 2. Only two types of connectors are used (e.g., a square and a circle). Mathematically, there are 16 possible shapes (see figures). Twelve (12) of them are mirror images of corresponding pieces, leaving 10 unique pieces. Each row can be assembled into a 2 x 2 square as shown in the figure. So are the center 4 pieces, the 4 corner pieces, and those along diagonals. All 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 four random pieces are picked from the 16 pieces (not necessarily unique), can they always be put together for a square? Seemingly not. 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 16 pieces be put together to make a 4 x 4 square? Have fun!