James ❤️ A Card Trick - Numberphile 

I'm going to have nightmares of cartoon James pulling an infinite number of rabbits from a hat.

Matt Parker came with a very similar trick few years ago. The only difference was that his version sometimes works and sometimes doesn't.

Cartoon James looks like he just rearranged something in my house in ascending order and is waiting for me to notice what it was

2:59 Did James do something to upset the animator?

James: *Goes on Penn and Teller "Fool Us." does trick fools Penn and Teller but immediately explains the math behind it.*

okay cool, but why did you make animated james nightmare fuel?

Why was 6 afraid to go camping with 7? Because 7 1ted 2 bring 3 knives 4 sur5al, but 6 knew that 7 secretly h8ted him and did not have be9 in10tions

2:58 Here’s your free Cartoon-James-pulling-bunnies-out-of-a-hat button

James grime still looks better in real life

Whoever drew the cartoons did my boy James dirty, they did him dirty they did

I love the framed section of brown paper from the Graham's Number episode!

James and Magic? I think we all know who to call Brian Brushwood

This was a question in Indian RMO(Regional math Olympiad)

I think that the beginning and the middle are great, but you could improve the "prediction". For example, you could put the James of hearts in the 25th position in the deck and you leave all red aces until nines beneath it. So when you are subtracting the values of the 5 pairs, you just take cards that are below the James of hearts. He will then be in the 25th position after taking the red cards out and you can say that James of hearts knew it and chose that place. If you really want to improve it you could also learn some false shuffles, so you leave James of hearts in the 25th position from the top and do some false shuffles, so that the spectator thinks its totally random where James is. Don't forget that before showing the 25th card, you should remember the spectator that the deck and the spades were shuffled and that he chose which cards would be his and which cards would be yours. You could also let the spectator choose what suit you will use for the trick, so they believe even more that they chose everything. The only tricky thing would be to arrange the deck not knowing what suit they were going to choose, so you would have to arrange it after they said it. Hope you could understand everything and if you have any questions,feel free to ask

2:30 Is that Graham's Number on the wall?

I propose we make 'A James Heart' the opposite statement to 'the Parker Square'

So the video goes into this at length, but letting the the participant choose 10 cards, show you and then letting them divide into piles of 5 each. You write down your prediction then, turn them over and order them, find and sum the differences. Letting them have complete control over the cards is usually really impressive for a 1 on 1 trick.

am i the only one bothered by the fact he wrote on the back of the card!?

James is a decent-looking guy but cartoon James is an ogre

At this very instant, Penn and Teller are shivering in their boots!

Grimy is the best Numberphile by far.

Reminds me of the story that Gauß as a child was ordered by the teacher to summarize all numbers from 1 to 100 to keep him busy. After a minute little Gauß came back with 5050. He arranged the numbers from 1 to 100 like 1+100+2+99+3+98+...49+52+50+51 = 101*50 = 5050.

You are friends with Brian Brushwood, make it happen😁😁😁😁

Great! Used this on my friends, they were mind-blown when they saw my prediction card in his backpack (I put it in there beforehand)!! I put the wrong answer under the "J" card and told him to actually check his bag for my REAL prediction :D sneaky sneaky....

I love you James! You’re the best

Wait, so this just boils down to the associative and communicative properties? If the smalls are always negative (subtracted) and the bigs are always positive, then it doesn't matter what order they're arranged in, of course they'd come out to the same value. The way they're dealt only affects one meaningful thing in the whole problem, and it's the sign applied to each number, but because the way they're dealt and then ordered, you're guaranteeing the big-small pairing and therefore guaranteeing the signs of the numbers. Crazy how simple the math is once you strip it down to the basics. Great presentation here.

It works the same with any even number of card. Difference between them. 2 = 1 4 = 4 6 = 9 8 = 16 10 = 25 12 (J = 11, Q = 12) = 36 14 (K = 13, Joker = 14) = 49

Found a different, more graphical, but more complex way to prove it: Imagine the cards laying on the table in order. Then you mark half of them blue and the other half red(for the two sides). You know that the cards will each find a partner of the other colour and you know that they are going to start matching from the longest distance to the shortest(if you do the counting in the same order as they did in the video). We will count the connections between the cards for the result. So lets start with an example: no matter what colour the Ace has, it´s connection will always go over the middle, because the other 4 spots between the ace and the middle are not enough for the 5 cards of the opposite colour to fill and the ace will connect to the highest of them. So at least one connection going between 5-6 from the ace. The same will happen with the 2: 3 spots left and 4 cards of the opposite colours to fill. So another guaranteed crossing over the middle(between 5 and 6) this works until we reach 5. So we know that 5 connection go over the middle point, resulting in a value of 5. The same game will work for the connection between 4 and 5, except for the last connection(with the 5 involved) resulting in 4 connections between 4 and 5. this goes down until we reach 1 - 2 so it´s 5 + 4 + 3 + 2 + 1 for one half. because the situation is symmetrical the total has the be 1+2+3+4+5+4+3+2+1 = 25 If we spin this further with other numbers than 5, we can explain why raising x in x^2 will raise the result of mentioned formula by 2x + 1

“Mom can we have a Numberphile mathematician?” “We already have James Grime at home” James Grime at home: 2:59

At 1:58 that 4 of diamonds has a mistake on it.

I think the trick will be more amazing if a spectator could pick up random, let's say, 10 cards and after some mental calculation you can make a prediction based on those cards; and then you perform the trick.

You know how you can do completing the square for quadratics...can you find a way to complete the cube for a cubic?

The main thing you could do to dress it is not TELL them that you're using only the spades, infact I would use as many suits and colour as possible but do a false shuffle, stack the deck so that you get Ace through ten.

☼ Get 25 scantily clad models, and a saw that is intent on cutting them in half, if the audience member chooses wrong. That's as far as I have got, what do you think so far?

I really enjoyed this video and nice explanation. thank you so much.

Mathematicians frame the proofs to famous mathematical concepts and use them for decoration. 0:37

3:38 why is it 126 ways or arranging the cards? shouldn't it 10C5 = 252 ways? Edit: I think I get it. Is it cos when u choose 1 combination, ur actually choosing 2 combinations and aligning these. So the cards in a sense have rotational symmetry

Cool trick! Numberphile always has new things to learn

You could give them the impression that they have more free will by letting them place their cards in any order they like, and then putting your cards down, so that the smallest card is next to the biggest card etc. Then you could let them move any pair around as they like (this will not affect the pairs themselves).

Love me some Penrose card backs

I was watching a Numberphile card trick video from 2012 while this was uploaded/publicized. Eerie

Interesting, but my intuition (uninformed guess) told me the number would be the same regardless of which player got which cards before the trick was over. So a magician would need to dress this up a bit (make it less straightforward).

I'm not a magician but I think you should let people choose all the cards they want and not tell them it doesn't matter.

Ah, cartoon James is even holding his Little Professor.

Amazing! I've seen a very similar concept as a proof for some exponential equations using groups as multiplication

Since the value is always fixed no matter the cards, how about a variation where you calculate the value as you and the volunteer pick cards at random?

for this to be used in a magic trick i feel that there are too many fixed things to have to work through, but with at least a force it can be made work a bit better

I appreciate the penrose tiled card backing.

Great video as always. The idea that a lot of magic tricks are dressed up mathematical effects is really intriguing, it would be interesting to see more videos exploring this idea.

This is really incredible. How did James find that out?

Well, I solved this problem quite some days before. It is published in crux mathematicorum from which I think the inspiration is taken from

Is it just me or does this guy look like the squirrel from over the hedge?

You could map the restult to a letter of the alphabet ('y') and do something with that. 🤔

mathematician showing trick

... Did he actually get a fully custom deck printed?

I knew I had seen that singing banana before

Gm sir... Even know the answer... Always eager that what and how will you explain... You always explain v very nicely... Thank you..

I recognized this right away since I do loads of kakuru. 30 in 4 places is always 6,7,8,9.15 in 5 places is always 1,2,3,4,5. The only factor you added was a 10. So 40-15=25.

I didn't catch something from this video, James said there are 126 ways of arranging the cards but 5!=120. How?

I love how they've got the peper from graham's number episode signed and framed on wall

Very nice video κανω εκπαιδευτικα βιντεο μπορει να σε ενδιαφερει

Related to Magic Squares.

The very first time I tried this, my pairs were...10-1=9; 8-2=6; 6-5=A; 7-4=3; 9-3=6: I only have one 6 card. Do I use the 4 &2??? (They still add up to 25.)

This is in the same family of tricks as one based on the following : Think of any 2 digit number. Sum the digits and subtract from the original number. The result is always the first digit times 9. Eg, 64, sum of the digits is 10, subtract from 64 gives 54 equals 6 x 9. There was a magician's web page which did a mind reading trick on the viewer, based on this fact.

Does it matter that they be ordered? Apparently, but I wonder. The Russians died from ergot poisoning from the rye bread.

Hmm, will this be an actual card trick or a mathematical game with oddly specific rules Edit: yup, not a card trick

Hey guys 👋 today I recognized that 1.8×1.8 (can't do the 2 up there) multiplied with 2.4×2.4 is 9.....just like 3×3! Is there any law and are there other cases, where you can do sth like that?

Should be easy to calculate the number for N cards. Since we know the end total is the same for all different ways the cards come out we can solve for the easiest set. Assuming one person gets all the small numbers and the other person gets all the big cards then the smallest small card will be matched with the smallest big card. The difference between them is N/2 (i.e. the smallest small card will be 1 and the smallest big card will be (N/2)+1). The next pair will be the same since on both sides the values increase by 1. So the end result will be N^2/4 (N/2 multiplied by the number of pairs which is also N/2, so N^2/4).

Perhaps the amazing Steven Bridges could give James a hand in improving this trick.

I see James I click :)

Feel like there needed to be just a little more emphasis on the "I don't know what the value will be" - important distinction from the consecutive set, the answer is not simply N^2 at that point, and you'll have to do the maths properly to determine your value.

Jaaaaaaaames?

(6+7+8+9+10)-(1+2+3+4+5)=25. I need the hint. 5:24

Dress it up as a magic trick? You're over a pit of spikes or some other danger while someone else manipulates everything to get your weight which is placed on a counterbalance for you so when the pulley is released, you don't die. :D

The "average difference" is 5. What I mean by that is with 5 cards you always get 5*5 with 5 cards because when your difference is 7 for example there has to be a difference that is 3 so you get two pairs of 5 and so on until you are left with one difference that is 5.

I liked this a lot not because of its magic trick feature but because it had an interesting fact about sets of numbers. As James mentioned the effect works no matter what the colection of 2n numbers is - and you can have repeats and non-integers as well. The answer is always the sum of the n big numbers minus the sum of the n small numbers. If there are repeats these two subcollections may overlap but it doesn't matter.

The effect can be increased using two volunteers I think. Either they choose alternating a card or bring more fake randomness by letting them play rock paper scissors each time.

This is the one of the best mathematical card trick I've ever seen.

If you take all the large numbers in one set and all the small one in another the differences becomes the consecutive odd integers and you get as a corollary the well-known fact that the sum of the first N odd integers is N^2.

The crazy part of a small RU-vid can feel is daily you wake up in the morning and sleep dreaming about getting more subs and nothing has changed on your channel😂 lool

so really wierd thing happened to me, i have a set of cards so i decided to start using it a long the video ehen i got the ide i shuffled my cards did the 2 groups and got the exact same set up as th one in 3:50, i even had them match top and bottom... that was probably my winning the lottery chance

So the value for 1 to 2n is n^2. That immediately makes me think of integrals. Does it have to do with integrating?

6+7+8+9+10-1-2-3-4-5=25. Yeah great magic trick, for 3 year olds. Wtf is this?

that's some nice math, and it satisfies Poincaré's saying : "A true mathematics concept must be elegant"

That drawing does not look like James Grime.

Where can I get the deck of cards with Grime on it?

I really like this but my eight year old is less impressed. 😁

He mentioned any set of integers, does this hold for decimal numbers aswell?

Anyone watching in 2016?

"And I'll show footage of me engaging with the product while petting a dog wagging its tail."

There's over 3 million combinations possible.” Or Really 126. (?)

I wanna see the queen and king cards! Queen is Hannah Fry maybe?

Three minutes in, I'm not working out the details in my head, but it is clear that it does not matter how the cards are shuffled or how they are distributed on the table, because the differences of the cards individually are unaffected by their position on the table, and presumably all of the differences that result (the middle cards) will result in 25. since there are 5 cards from 1 to 10. But instead of adding pairs of numbers in that way that yields the n(n+1)/2 formula, we have the difference of pairs. Clearly, that must always be 25 (using 10 cards).

Someone show this to Michael from Vsauce!

Do you ever just... 4 of diamond-hearts? 2:00

Magic tricks are mathematics or physics or chemistry. That's a generalization.

last time I was this early my gf left me

James showed how you can't have two small/large numbers paired up so you're always left with groups of (large)-(small). Using the associative property of addition you can rearrange the numbers to have all the addition of large numbers on one side and all the subtracted small numbers on the other side (treat subtraction as addition of negative numbers so the property holds). You'll end up with 10+9+8+7+6-5-4-3-2-1 =(10+9+8+7+6)-(5+4+3+2+1) =40-15 =25

Who wants James Grime back on Numberphile? I do.

I came after 3 years to watch this . Thanks to Eddie Woo . This Channel is great ✨