CombinatoricsDifficulty 2.6JuniorFind the answerCanada
Four of the five puzzle pieces shown can fit together without overlap to form a square.
Hide/Reveal Description of Diagram for Question 17
The puzzle pieces are made from identical square shapes. Each top side has a shape that sticks out (a tab) and each right side has a shape that is cut out (a hole). Each tab and each hole has one of the following shapes: trapezoid, semicircle, or triangle. Each tab of a particular shape is designed to fit into the hole of the same shape. The tabs and holes on the pieces are as follows:
If the pieces can be rotated but not flipped, which piece does not get used?
Pick one
Solution
In this solution, we call the part of the puzzle piece that sticks out, the tab. We call the recessed space, the hole. A tab in one piece is designed to fit into a corresponding hole in another piece.
Piece 1 has a tab in the shape of a trapezoid. This is the only piece with a tab in this shape. Piece 4 and Piece 5 both have a hole in the shape of a trapezoid. Since there is only one trapezoid tab, either Piece 4 or Piece 5 will be the piece that does not get used to form a square.
Piece 4 has a tab in the shape of a triangle. Piece 1 is the only piece with a hole in the shape of a triangle. However, it is not possible to insert the Piece 4 tab into the Piece 1 hole while also inserting the Piece 1 tab into the Piece 4 hole. Thus, it is Piece 4 that does not get used to form the square. The completed puzzle is shown.
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