The Confuzzle

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Introduction: 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!:

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    62 Comments

    Hello,

    Not sure if you received my PM concerning production of your Confuzzle?

    Jerry

    Haha...Thanks!! There are some great instructables to contend with on here.  Note to the world: Vote for this instructable.  There will be no raised taxes,  free quality healthcare for all, actual implementation and usage of alternative energy..ummm....no crime (none) and 27 other globally-enriching policies put into place immediately.  Oh yeah...delicious cookies for everyone too!  :)  

    Seriously...best of luck to all of the other authors. 

    Bacon is the worse nightmare of the free healthcare system.

    Lol read this whole page and then make it ROFL

    My MICRO confuzzle at 1inch squared! (1 1/4 inch with frame)
    Sorry if the photo resolution isn't good. The photo was taken with a phone cam and a magnifying glass.
    Thanks for the GREAT puzzle!

    Photo0336.jpg
    1 reply

    Hey, that's awesome! Thanks for the contribution!!

    Here is another well known illusion, in he same category; triangle with base 13 and height 5; if you rearrange the pieces, a gap appears. how come!

    triangle1.gif
    7 replies

    Great illusion, thanks. The answer, of course, is that these are not really triangles. The apparent hypotenuse is not a straight line. In the top case, the apparent-hypotenuse is slightly concave; in the bottom case, the apparent-hypotenuse is convex. (The smallest angle in the yellow triangle is 20.56 degrees, while the smallest angle in the green triangle is 21.80 degrees. For a true-hypotenuse these would have to be exactly the same.)

    Neither hypotenuse is concave or convex-- The hypotenuse of the main triangle is drawn so that at the intersection of green, blue, orange in the first drawing there is a grid intersection.
    The reality is that on a 13 x 5 triangle the hypotenuse at that intersection falls slightly above the grid intersection. The drawing is drawn wrong to mislead you.
    If you carefully draw a  13 x 5 triangle on a 1/2" grid and then carefully place each figure in their first relative position, you will see the sliver of space above the green and orange triangles, That sliver of space amounts to one grid square. ( 1/2 sqin if measured in inches)

    Rearrange the shapes and that extra 1/2 sqin shows up immediately.

    Proof : (in inches) (area = 1/2 base x height)
    13 x 5 main triangle = 32.5 sqin

                    8 x 3 orange triangle = 12 sqin
                    5 x 2 green triangle = 5 sqin
                    red shape                 = 8 sqin
                    blue shape               = 7 sqin

                    total shapes           = 32 sqin

    Sorry, but DHagen is right. The picture is drawn correctly.The shapes are not triangles. The one is slightly concave and the other slightly convex. Use a cad program and arrange 2 x 5 and 3 x 8 triangles. Below is an image proving the point. Click for the large image, see that if it were a triangle where the hypotenuse would have been (dashed line). Also note that the top and bottom containing rects are the same size, hence no cheating was done on the ilustration above

    Illusion.png

    They're both concave. The hypotenuse is slighlty bent in on both so that makes them both concake.

    The illusion is revealed in an exaggerated example. I hope this settles the argument. The illusion is that these are NOT triangles, but a concave and convex structures that *look* like triangles.

    Exaggerated.png

    well, no, they're triangles, but since the slopes of their hypoteneuses arent equal, the resulting "big triangle" is actualy bent.

    When I am refering to "these" I am of course talking of the combined structure that appears to be a triangle in the resulting illusion. The pieces cut in the original puzzle are defined as triangles per the instructions, so there is no real ambiguity here as you imply.

    The length of the hypotenuse does not directly relate to the problem, but rather it is the difference in angle of the right triangles that creates the illusion. I can easily provide a counter example where the hypotenuses are different and the illusion does not happen.