A puzzle is made of pieces with tabs and slots that join tog

A puzzle is made of pieces with tabs and slots that join together to make a whole. Assume each piece is square and any tab can fit into any slot. The figure below illustrates the shapes of the puzzle pieces. The corner pieces arc identical with one tab and one slot; see the left picture. The edge pieces have a slot on the left and a tab on the right. Half of the edge piece have a slot on the bottom and half have a tab; see the two middle pictures. The middle pieces have two slots across from each other and two tabs across from each other; see the right picture. How many ways are there to put together a 2 times 2 square puzzle? How many ways are there to put together a 3 x 3 square puzzle? How many ways are there to put together a 5 times 5 square puzzle?

Solution

a)

There is only one possible way to make a 2x2 square puzzle because the 2x2 puzzle will be made only by corner pieces. Because there will be 4 units and 4 cornors. So, you take 4 pieces of the corner type and arrange them to get a 2x2 puzzle. If you rotate it you would get the same pattern again and again.

Hence, only one way possible.

-----------------------------