Teachers Day - Binary Magic Carddeck
Instruction
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.
I have chosen the rectangle with rounded corners. I also decided to have an inner frame – another rectangle with rounded corners – to make the card a little bit more attractive. Then we need a third element, a text, where we write down all the numbers for the card.
I decided to build this for the numbers up to 63, so I needed 6 cards for the digits 1 to 32. So I copied the card five times and just changed the text. You could also decide to use less cards to reduce the amount of numbers here.
Everything but the outer frame needs to be scored (60mm/s at 80%), the outer frame needs to be cut (4mm/s at 95%).
After finishing step 1 mark all the cards (CTRL+A) and copy them to the clipboard (CTRL+C). Now add another worksheet and paste the cards (CTRL+V). Make sure that they are at the exact same position as XCS moves objects when they are pasted.
Now remove all the outer frames (we do not need to cut again for the backsides) and shuffle the numbers in the text. Keep the top left number (1, 2, 4, 8, 16, 32) somewhere where they are easy to find. On my deck I placed them always in the first line.
Place the wood in the machine and fix it (for example with some tape). Ensure that it cannot accidentally move. If you use a M1 without honeycomb: place the triangular prisms in a way that each card will be supported by multiple prisms and will not fall down. Now process worksheet 1 (with the outer frames). After this is finished, stick a small piece of tape on every card to get these out of the wood without moving the material. Remove the tape, turn the cards and place them back in the holes. Now engrave the second worksheet.
This gives you a very simple way to align the texts on both sides of the cards.
Note: If I have more objects than these 6 cards, I would do it the other way around and first engrave the backside, turn the whole material and process the front. But this needs a perfect aligned material. In the M1 this will only be possible by placing the material at the back and side of the machine and therefore will waste some material.
Before performing this trick make sure that you train it several times!