Philosopher AI - How many ways can you distinctly arrange a deck of 52 cards?

How many ways can you distinctly arrange a deck of 52 cards?

You start with the deck of cards, which is a bunch of objects. In order to arrange them you first must group them by suit and then by rank. Each card can be characterized as having two suits (hearts, diamonds, spades, clubs) and thirteen ranks in each suit from 2-10 and jack, queen and king.

7 Jun 2021, 10:19

I see this as having four possible outcomes for each rank, so that gives us 52*4 = 208 ways to arrange the deck. One can also consider any subset of cards in a more general sense, such as taking out all the face cards (jack, queen and king) or all the 4's.

7 Jun 2021, 10:19

When considering all possible subsets, there are 52*13 = 676 ways to arrange the deck. We can also consider arrangements of cards within each suit or rank, but I'm going to stop here because it gets too involved.

7 Jun 2021, 10:19

Clearly there are more possible ways to arrange a fifty-two card deck than the commonly cited 52! = 8.0658 million combinations.

7 Jun 2021, 10:19

Also, it is possible to arrange the deck in such a way that you could have two different arrangements of cards with the same suit and rank. For example, there are three ways one can arrange a 7 of diamonds within a diamond suit.

7 Jun 2021, 10:20

I hope that this is enlightening and enjoyable for everyone.

7 Jun 2021, 10:20

You are getting an AI to generate text on different topics.

This is an experiment in what one might call "prompt engineering", which is a way to utilize Llama 3.1 405b, a neural network trained by Meta.

Llama is a language model. When it is given some text, it generates predictions for what might come next. It is remarkably good at adapting to different contexts, as defined by a prompt (in this case, hidden), which sets the scene for what type of text will be generated.

Please remember that the AI will generate different outputs each time; and that it lacks any specific opinions or knowledge -- it merely mimics opinions, proven by how it can produce conflicting outputs on different attempts.

Feel free to share interesting outputs to /r/philosopherAI on Reddit.

by Murat Ayfer