3blue1brownMathematical Magic: The Great Fettucine's 5 Card Trick
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Tags: information-theorymaths
The Great Fettuccine is a world-renowned mathemagician with an apparently impossible ability. Her assistant selects five cards from a standard 52-card deck, removes one, and rearranges the remaining four. From those four cards alone, Fettuccine can identify the missing card.
The trick raises a fundamental mathematical question: how can we communicate information.
There are 24 possible ways to arrange four distinct cards, which initially seems far too few to identify one card out of 52… However, the assistant is not simply rearranging four fixed cards; he has the freedom to choose which of the five cards to remove. This allows him to choose what information to communicate.
Behind the magic trick is a beautiful idea from combinatorics and information theory. By carefully exploiting the four suits and the 13 possible values, the assistant can encode information into both the choice of the missing card and the order of the remaining cards.
This is an elegant example of a broader mathematical theme: how can we represent and communicate information using limited resources? Problems like this appear throughout mathematics, computer science, coding theory, and information theory, where finding the right way to encode information can turn an apparently impossible task into a surprisingly simple one.
In this video, we uncover the mathematical structure hidden beneath the magic, and see how a little combinatorial ingenuity can make four cards say far more than you might expect.
It’s not magic. It’s maths.
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Comments
Great explanation on how to encode a fifth card using four, great video!
That was fun! Would have loved to see a bit more of a discussion of math in (card) magic.
Motivation: 5 / 9 – it’s always great to see a new card trick explained. I think you could sell it a bit more, that it contains pigeonhole principle in it, or position counting. Tell a bit more about the mathematics behind the trick (clickbait even) within the introduction
Clarity: 4 / 9 – the explanation itself was fine, but it lacked some examples and clarity in it. Also, you could highlight what was going on a bit more, like with text or examples. It was a bit sloppy in my opinion
Novelty: 6 / 9 – cute little card trick I haven’t heard of before, but there are lots of card tricks explained out there. There should be more mathematics involved to make it truly interesting and novel (example – one can explore the idea of this card trick, but generalized – what 6 cards could tell us? What are the limitations of such tricks? etc.)
Memorability: 6 / 9 – visually it was pleasent and the topic itself was very memorable. Maybe a bit more visuals could be helpful!
Overall – 5.25 / 9 – I found this video quite enjoyable, it simply could be a bit deeper and longer.
2:20 you should use the same suit (♦️ rather than ♥️)
And the end of the video you didn’t explain it clear, I can only infer that by using the card’s number, it can reduce the possible number be presentable by 3!
But everything before that is great and clear.
Short and simple but interesting. You could do a better job explaining it and also taking pictures, that could easily bring up the score
This is a really cool magic trick that I’ve heard of before, but never knew how it worked. This video works as a great introduction to it, but the explanation seems to cut off at the end. How exactly does the ordering of the remaining three cards tell you the distance? Why does arranging the cards in this way indicate +4? A slightly longer explanation, with maybe another example, could aid in understanding and be a better teaching tool. In all, this was a well put-together video, but further explanation would have improved it a lot.
Fun. Also, notably, a trick like this goes from “wow how did he do it?” to “oh it’s just maths” to “oh it’s really cool maths” as you get to know it better. Like, suppose you said right at the start “the assistant encodes the chosen card using the other four cards”, there’s still a lot of coolness to unpack in HOW you encode it.
Great video! I would welcome a clearer explanation of how to communicate a number from 1 to 6 using 3 cards. (One way is to order the cards, label them 1, 2, and 3, and use their permutations—ordered lexicographically—to represent numbers from 1 to 6).
I feel like the explanation was really good. It was very clear and motivated.