I found the Binary Notation connection to this card trick very interesting.  I was struck by the educational possibilities for people who have had an introduction to Number Theory, but needing a practical application to make sense of it.  Young people of the age of ‘formal thought’ are attracted to magic and the challenge of ‘how it is done’ understanding. I put together this brief explanation of the math involved in creating this card trick.  When finished viewing you must click on the back button “<” to return to this page …

To see the trick and my explanation click here:

I wanted to use my new laser cutter, so I made boxes to serve the same function as the cards above:

Each box contains the appropriate number of beads (0,1,2,4,8,16, or 32). The subject chooses a secret number, then empties the box(s) containing that number on its face, counts the beads, and amazingly they add to the secret number!

Here is a video of a analog computer doing arithmetic in Binary …