What's going on here?
A few years ago while playing cards, I had an idea. More like a question, really: could you encode a message in a deck of cards? Is that mathematically possible?
A few weeks ago, I realized hey, you can Google that sort of thing. Google lead me to a stack overflow article called Fast permutation -> number -> permutation mapping algorithms. That introduced me to the word I was looking for: Factorial number system, and the related concept of Lehmer codes, so I went straight to Wikipedia and began to figure out what I had gotten myself into. The good news was that mathematicians have studied this thing and come up with some great research.
Once I figured out how it was possible to encode a message in a deck of cards, I made this web app to demonstrate it was possible, and that brings us to what you're looking at now.
How long can the messages be?
That depends on two things: How many cards are in a deck, and how many
letters are in your alphabet. Since there are fifty-two cards in a deck,
there are 52! ≈ 8✖️1057 possible orders for a deck
of cards. If your alphabet has 39 letters (26 proper letters, 10 digits,
space, quote, and period), then you will need to be able to store
39l messages, where l is the maximum length of a
message.
This gives us the following formula to solve for l:
52! ≥ 39l
This equation can be solved for l by asking Siri, "What's the log of 52 factorial divided by the log of 39?" The answer will be about 42.68, which rounds down to a maximum length of 42 characters, since it doesn't make sense to encode part of a character.
Why is it named Codeck?
A codec is a word for something that encodes and decodes messages, and I'm not one to pass up a good pun. Or a bad one, apparently.
How was this built?
The styles and code are my own, but I got a lot of help from a data visualization library called D3.js (not affiliated with this project). All the code I wrote is available on Github at Codeck.