Summary

For this project the story is a little bit longer. I decided that a teacher’s day project could be something that helps me when I am teaching. 
When I teach binary numbers I usually use a legerdemain that help to visualize the way binary numbers work. You have a set of cards with multiple numbers on each card and ask someone to choose a number and pick all the cards that contain this number. Then – magically – you can tell the number within a second.
How it works? Let’s talk about binary numbers first. Binary numbers are a place value system. Binary numbers work similar to the decimal system. In the decimal system the digits represent powers of ten. For example 107 means 7*1+0*10+1*100. The binary system works analogue, the only difference is that the digits represent powers of 2. So 1011 means 1*1+1*2+0*4+1*8. Each number has a unique representation. If you just sum the values of the 1-digits, you get the number. In the example 1011 this would be 1+2+8=11. 
Now this trick is rather simple. We have cards for each digit and write all number on the card where the digit is 1. All the commercially available cards keep the numbers in an order from the smallest to the biggest so you just have to sum the top left numbers which are 1, 2, 4, 8, 16, 32, … and you know which number is the chosen one.
Unfortunately there is a visible structure in the numbers especially on card one (that contains all odd numbers) and the card for the highest digit (that contains the top half of all numbers). This makes things a little suspicious, especially if you show the trick to older pupils or students. Therefore I always wanted a version with mixed numbers. But on the other hand the one with the numbers in an order is easier to explain.
So this is the solution: We design the cards with numbers in order on the one side and shuffled number on the other side.