One year at Christmas, I got a little game with the 6 cards you'll see below. It was a magic trick that guessed your number. Try it out.
Think of a whole number from 1 to 63.
It's a neat trick. On Christmas, when I got the cards, there was no explanation of how it worked. But I knew it must have something to do with binary, and I was right.
This mystery calculator is apparently pretty old. It's fun to think of the person who first came up with this and how excited they probably were.
Binary is such an interesting system. In some ways it's more intuitive than base 10. I suspect that if we'd come up with a binary counting system before base 10, most of us would have become incapable of thinking in base 10. Base 10 is so inelegant.