Consider joining Wrath of Math to get early and exclusive videos and music, and to help support what I do: ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin This presentation is based on these MIT lecture notes; I was perusing them and thought this card trick was really fun: ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2005/0d1038c54d262f3cbab53c13d9935f8e_ln10.pdf More math chats: ua-cam.com/play/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO.html
a less mathematically interesting solution: you can get an extra bit of information by the order in which the 4 known cards are revealed. so you have 24 permutations that can correspond to cards 1-24 in a normal 52-card deck ordering (minus the 4 known cards). then, the magician walks in, and if the assistant lays the cards out left-to-right (from the magicians perspective), the 5th card is the corresponding card from 1-24. if the assistant reveals them from right-to-left, just add 24 so the card is somewhere from 25-48. problems: i cant remember if the trick requires that the 4 known cards are already laid out before the magician walks in, and im already done with the comment. the keen observer would also be able to notice that the order in which they're laid out changes, upon viewing the trick several times. i also don't have any mathemagically-inclined friends to do this trick anyway
Excellent explanation. Way more in depth than most mathematical explanations for this trick. The only thing I would add is the name, Fitch Cheney's 5 card trick.
Funnily enough, the (very clever) way you encode the 5th card also totally works as a constructive proof that the trick is possible, and one that is very accessible for people that you would otherwise lose once terms like factorials and n choose k are involved. Not that there is anything wrong with the matching approach.
Nope, it's the order the cards are shown that tells the magician the exact card value and suit. And the magician's assistant isn't necessarily doing this silently. I was taught in CHaSeD order.
A thought I have not even halfway through the video: It's probably relevant that, in the sets of 5 cards, the order of the cards doesn't matter, but the 4 revealed cards can be revealed in a specific sequence.
@@WrathofMath Is there a legit reason to call something TONCAS? I feel like when you say something is TONCAS, you already knew it was at that moment and there is nothing to learn from this. Is it only used to name the concept or no? 🤔
Certainly possible. I did a quick search for card trick videos just to see what the titles and thumbnails looked like, and I didn't see any covering this trick - at least not at a glance.
Consider joining Wrath of Math to get early and exclusive videos and music, and to help support what I do: ua-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
This presentation is based on these MIT lecture notes; I was perusing them and thought this card trick was really fun: ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2005/0d1038c54d262f3cbab53c13d9935f8e_ln10.pdf
More math chats: ua-cam.com/play/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO.html
0:46 That’s not called shuffling. That’s rotating the deck.
13:01 Babe, new cards dropped for standard playing card decks
a less mathematically interesting solution: you can get an extra bit of information by the order in which the 4 known cards are revealed. so you have 24 permutations that can correspond to cards 1-24 in a normal 52-card deck ordering (minus the 4 known cards). then, the magician walks in, and if the assistant lays the cards out left-to-right (from the magicians perspective), the 5th card is the corresponding card from 1-24. if the assistant reveals them from right-to-left, just add 24 so the card is somewhere from 25-48.
problems: i cant remember if the trick requires that the 4 known cards are already laid out before the magician walks in, and im already done with the comment. the keen observer would also be able to notice that the order in which they're laid out changes, upon viewing the trick several times. i also don't have any mathemagically-inclined friends to do this trick anyway
Ah yes, the 1 of Diamonds
Did I say that? What do you expect from a guy who doesn't have a single non-prop deck of cards 😂
Favourite card, whenever someone asks me to think of a card I always pick that and so far nobody has managed to guess it
@@WrathofMath it's even better that you used it as an example of a card other than the Ace of Diamonds
Excellent explanation. Way more in depth than most mathematical explanations for this trick. The only thing I would add is the name, Fitch Cheney's 5 card trick.
Funnily enough, the (very clever) way you encode the 5th card also totally works as a constructive proof that the trick is possible, and one that is very accessible for people that you would otherwise lose once terms like factorials and n choose k are involved. Not that there is anything wrong with the matching approach.
Nope, it's the order the cards are shown that tells the magician the exact card value and suit. And the magician's assistant isn't necessarily doing this silently. I was taught in CHaSeD order.
13:29 what an unfortunate notation
i think it's great notation, but i see what you mean 😂
This would have been easier to follow if you did e.g. 4♦️ instead of 4D. That being said, this is a great trick, at least from a math perspective!
As if hes going to draw a whole club or spade everytime a club or spade needs to be represented
Yeah if I was a decent doodler I would have done that, but using the letters seemed safest for consistent readability.
Coincidentally, I predicted the 4 of♦from the thumbnail before I watched the video based on the card that is most unlike the previous four cards.
@@WrathofMath You could buy yourself a set of four stamps and just stamp the symbols
Hall’s Condition seems like a classic TONCAS.
Definitely!
This is genius, thanks!!
Gonna use it at tomorrows party, wish me luck!
That party has no idea what force of nature is coming!
A thought I have not even halfway through the video: It's probably relevant that, in the sets of 5 cards, the order of the cards doesn't matter, but the 4 revealed cards can be revealed in a specific sequence.
Whether or not you made a mistake at 22:00 depends on which subkey is first. You are correct if the number is the major key. You must have forgotten.
AC, 2C, AD, 2D, 3D
I thought this would be a trick thats actually usable irl.
5 and Q are both 6 spots away from each other
10:22 wow TONCAS strikes again
True!
@@WrathofMath Is there a legit reason to call something TONCAS? I feel like when you say something is TONCAS, you already knew it was at that moment and there is nothing to learn from this. Is it only used to name the concept or no? 🤔
What if we encode using order and also whether it is flipped horizontally or vertically? that's exactly 48 encodings.
Ooh, I think I've seen this from Vsauce
Certainly possible. I did a quick search for card trick videos just to see what the titles and thumbnails looked like, and I didn't see any covering this trick - at least not at a glance.
@WrathofMath I actually can't find the video I'm thinking of, maybe I imagined the whole thing