The Confuzzle

Simplicity and confusion don't often go hand in hand.  Here's a confusing puzzle, or "confuzzle", that can be made in minutes.  Although it involves simple geometric principles, it is surprising and even baffling to some people.  In short, it's a quick, easy project that is tons of fun to show others.

Here's a short video showcasing the presentation and effect of the puzzle:

Step 1: What You Need

For this project, only the following household items are necessary:

1) Two different colors of posterboard (each measuring at least 8.5" x 8.5"). 
2) Scissors
3) Pencil
4) Ruler
5) Black magic marker

Step 2: Measuring and Cutting

Start with one piece of posterboard.  Using the ruler and the pencil, measure and draw a 8.25" x 8.25" square on it.  Then, from the bottom right corner of the square, measure in 4.5" towards the middle of the base and mark a dot with the pencil.  From the bottom left corner of the square, measure up 4.5" along the edge and mark a dot with the pencil.  From the top left corner of the square, measure in 4.5" towards the middle of the top and mark another dot with the pencil.  From the top right corner of the square, measure down 4.5" along the edge and mark a final dot with the pencil. 

Connect the dots as shown in one of the photos below.  This will create a slanted cross pattern. 

Use scissors to cut out the square .  Then create four pieces by cutting along the remaining lines.  The pictures below show all of the necessary dimensions.

Step 3: Creating a Background Frame

Framing the confuzzle is essential.  To do this, create a background with a frame by keeping the square "intact" and tracing it on another piece of poster board.  Use a black magic marker to trace it.  White posterboard works very well for this.  Then cut out the square (leaving the black marker lines visible). 

Another option is to trace it before you cut the original square into four pieces.  This is actually easier.

Step 4: Presenting the Confuzzle

Now that a finished puzzle is in hand, it's time to present it to yourself and/or others.  This is the best part!!

With the puzzle assembled as a square, rotate each of the four pieces 180 degrees and line them up together.  They will fit perfectly inside the background frame, but there will be an open spot in the center.  Rotate each piece 180 degrees again and the open spot will not be there.  This is the baffling part to most people. 

How is it possible for the four pieces to fill the background frame completely and then, when rotated, not fill the frame completely?  Shouldn't the physical area be the same no matter how the pieces are arranged?  These are questions that you and others may ask yourself/themselves.  Of course the area is the same.  It's just confuzzling!

Again, here's a short video showcasing the presentation and effect of the puzzle.  Enjoy!: