Instructables
Picture of 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:

 
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Step 1: What you Need

Picture of 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

Picture of 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.

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Eat ice cream. Typically induces brain freeze. That should fix a melted brain. Tastes good, too!
Hahaha...I'm sure there's an instructable on here to fix that problem.
corey113 years ago
This is so cool! Very well executed instructable! I'm goin to make one, and show a couple of my friends! How did you come up with this?
It's a well-known geometric puzzle, with numerous variations. Think about (or use a ruler to see) what's happening with the sides of the two square configurations. You could also look at the two extreme limits of the problem (cut the big square into four smaller equal squares, or cut the big square into four triangles along the diagonals), and think about the intermediate cases. After a little while, perhaps the author will post the link to the Wikipedia article.
jeff-o kelseymh3 years ago
Thanks for the link... so the two squares actually differ in size by about 0.8%. Not enough to tell the difference just by looking at it, but enough to form that little square in the middle.
greeenpro (author)  kelseymh3 years ago
I'm not aware of a Wikipedia article on puzzles like this. I had only seen one version of this from a friend. Actually I'm pressed for time at the moment. If you have the link...by all means..please feel free to post it.
Will do! I didn't want to give away the "secret" unnecessarily.
greeenpro (author)  corey113 years ago
Thanks! A good friend of mine showed me a similar version of this and I HAD to make an instructable to share with the world. Period :) I was blown away too. Thanks again.
Dude! Great illusion. Also thanks for the props :) Very much appreciated!!
greeenpro (author)  3BricksHigher3 years ago
Thanks for the idea!
Kaiven3 years ago
At first I was thinking "Sooo...? You just rotated the pieces..." The second time I looked at it, I thought "WHOA WHAT THE HECK?" Yeh, I still don't know how it can fit in the same surface area xD
Arano Kaiven3 years ago
they don't ;)
Kaiven Arano3 years ago
Ah yeah, after a while of staring at a triangle example, I finally got it. Haha.
wibrle3 years ago
Wow! Thats a cool trick. :)
greeenpro (author)  wibrle3 years ago
Thanks!
luvit3 years ago
i'm so epic... i simply enlarged this on my printer & cut it out.
greeenpro (author)  luvit3 years ago
That sure is mighty epic of you... :)
Tomboys3 years ago
It works.
kelseymh3 years ago

After checking with the author (see below), here is a link to the Wikipedia article which explains this and related geometric puzzles.

This visual illusion is one form of the so-called "dissection puzzles", such as Tangrams.

Amazing!
kelseymh3 years ago
Very nice! The Sharpie (or even better, a chisel point Marks-A-Lot) is critical to make the boundary. People seem to commonly (and subconsciously) assume that framing lines have no thickness.
greeenpro (author)  kelseymh3 years ago
Good point (pun intended) :)
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