Mind-boggling Card Trick: REVEALED
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- เผยแพร่เมื่อ 10 ก.พ. 2016
- Here it is, all the maths and logic behind the Mind-Boggling Card Trick.
Watch the original card trick here:
• Mind-boggling Card Tri...
The earliest record I can find of the same dealing mechanic being used is by magician Karl Fulves. The swapping cards bit was added by magician (and computer science professor!) Peter McOwan.
I actually wrote a maths magic book with Peter, you can download it for free.
mathematicalmagic.com/
Here is the Vsauce Math Magic video I mentioned and was mentioned in:
• Math Magic
Saturday Morning Breakfast Cereal comic about a science magician for which Zach used me to generate a pseudo-random name:
smbc-comics.com/index.php?id=4002
Everyone should go to a BAHfest:
www.bahfest.com/
Response videos by PappaMoe and Juan Meleiro:
• Mind-boggling Card Tri...
• Video Response to Matt...
The 27-card and 49-card tricks:
• Beautiful Card Trick -...
• The 27 Card Trick
Prepare your mind to be boggled. This is an incredible card trick which is completely self-working.
This trick relies only on the mathematical properties of a deck of cards. I will put up a complete solution video explaining the mechanics behind the trick soon!
Want your own distorted skew dice like I used in the video? They're here:
mathsgear.co.uk/collections/di...
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Music by Howard Carter
Design by Simon Wright - บันเทิง
R2B2, not the pile you're looking for.
This is not the pile I'm looking for.
+standupmaths Move along.
+Philip Johansson R2B2 is on the black side!?
I love how Matt entices the viewers to do the right thing.
It's his teacher side speaking haha, like when he had his mobile phone stolen that story so hilarious
If people are still confused about the milk thing:
(spt means third of a spoonful, both start out with 2 spoonfuls)
milk glass: 6 spt milk
water glass: 6 spt water
take 3 spt milk from milk glass and add to water glass
milk glass: 3 spt milk
water glass: 6 spt water, 3 spt milk
take 2 spt water, 1 spt milk from water glass (3 spt total but preserving 2:1 ratio) and add to milk glass
milk glass: 4 spt milk, 2 spt water
water glass: 4 spt water, 2 spt milk
Nah, that won't clear up anything.
That cleared it up for me. Thanks!
it's weird, but still not.
You move one spoon that's 100% milk from one glass to the other. Then you move one spoon that's something like 95% water and 5% water back to the first glass.
The first glass regains that 5% of a spoon of milk , so it only lost 95% of a spoon of milk.
The second glass only lost 95% of a spoon in the first place.
Might be easier if scaled up.
We have one container with 1 liter of white wine and one with one liter of orange juice.
Pour half the wine into the other container and we get one with 0.5l of wine and one with 1l of orange juice + 0.5l of wine.
Now pour 0.5l of the mixture back. That mixture contains 1/6l wine and 2/6l (1/3l) of orange juice.
The first now contain 1/2l wine + 1/6l wine + 1/3l of orange juice = 2/3l wine + 1/3l orange juice
The second contain 1l orange juice + 1/2l wine - 1/3l of orange juice - 1/6l wine. = 2/3l orange juice + 1/3l wine.
If the wine was sparkling you now got 1l of Buck's Fizz and 1l of weak Mimosa.
+m8e
This trick doesn't work with alcoholic drinks because alcohol is water-soluble. The volume of water with alcohol dissolved in it is less than the total of the water and alcohol individually. I think it was Richard Feynman who pointed this out.
+IamGrimalkin The "milk" in the video is water soluble, too, due to an emulsifier. What you're trying to point out is that some homogeneous mixtures pack differently than others. The ethanol-water mixture being an interesting mixture where adding 75L of ethanol and 25 L of water results in less than 100 L of total volume.
Eric Zuckerman Emulsifiers don't make lipids water-soluble, they just make them disperse around the water in small micelles.
For those doubting his milk/water contamination example, it's correct! Here's my explanation:
Cup volume = C
Spoon volume = S
Take a spoonful S of milk out of the milk cup.
This lowers the milk cup volume which is now C - S.
Add the spoonful S of milk to the water cup.
This raises the volume of the water cup to C + S.
After mixing, the fraction of milk in the water cup by volume is S/(C+S).
This liquid is thoroughly mixed, so removing any portion of the volume will retain the ratio of S/(C+S) of milk/volume.
Remove a spoonful S of the new mixture from the water cup.
The milk/volume ratio of S/(C+S) is preserved in both the cup and the spoon.
The water (non-milk) to volume ratio in the spoon is found by subtracting the milk/volume ratio from 100% to get the "everything else" ratio:
1-(S/(C+S)) = (C+S)/(C+S) - S/(C+S) = (C+S-S)/(C+S) = C/(C+S) water/volume in the spoon.
Add this mixed spoonful back to the milk cup.
This action combines the milk cup's volume of (C-S) of 100% milk (0% water) with the spoon's volume of S of C/(C+S) water/volume.
The amount of water now in the milk cup is S*(C/(C+S)) = CS/(C+S).
The total volume of liquid in the milk cup has increased back to C.
After mixing, the fraction of water in the milk cup by volume is therefore (CS/(C+S))/C = S/(C+S).
This is exactly the same as the fraction of milk in the water cup above!
So the two cups are equally contaminated, despite one transfer being a "pure" contamination and the next being a "contaminated" contamination.
The key trick that confounds your intuition is that the milk cup has a smaller volume when it gets contaminated and thus is more strongly affected by the contaminant.
If the formulas are too vague for your taste, plug in C=3 and S=1 to get an intuition of what's going on.
i would like to add to this really quickly:
If one were to say: there is more milk in the water cup than water in the milk cup you would say that milk was created in the process. What the milk cup is missing in milk is in the water cup, this taken volume is also the volume of the water that is not in the watercup, therefore it is in the milk cup.
More of a theoretical approach :)
I agree that this is also an excellent way to reason about the problem, but there's something reassuring about seeing the math and verifying that it checks out. Some people might believe some sort of weirdness happens when the liquids mix together that throw off the balances.
For someone who's a more visual learner (like me) this helped me get my head around it... let's say two amounts of equal material,
X & Y. I use 12, so it's easier to see...
XXX | YYY Now, if you take 4
XXX | YYY from X & put it
XXX | YYY in Y, it does get
XXX | YYY more volume, so you
would end up with an uneven amount that looks like this...
XX | XYYY for the milk, the two
XX | XYYY mix evenly, and if you
XX | XYYY see here, each line of
XX | XYYY 4 has the same ratio of 1:3 in it, so if we take just one of those XYYY lines, (which remember, is the same amount that we took in the first place, i.e. 4) and move it back, it will look like this:
XXX | XYYY and see 9x3y, on the
XXY | XYYY left, and 9y3x on the
XXY | XYYY right. What seems
XXY | unintuitive at first glance actually makes sense...
See! It was obvious! :P
+SpySappingMyKeyboard Way too obvious to be called "Mind-boggling"
_knocks on door_ Excuse me, is this the funny guys club or the true geniuses club? It doesn't say on the door.
+Penny Lane it's a law of the universe that true geniuses are, in fact, always also really funny
+SpySappingMyKeyboard Obviously it was obvious. I thought it was obvious that it would be obvious after he obviously uploaded the solution video.
That moment when you turned around the cards and they actually WERE all black in the red pile and red in the black pile! Hahahaha!!
You have an astonishing ability to be hilarious to no end while conveying serious mathematical concepts. Keep up the great work!
Are you thinking what I'm thinking R1B1? I think I am R2B2. It's card trick time!
There's a whole load of flashbacks I wasn't expecting.
At 07:00; I see what you did there.
But when you generalized it to be, instead of colors of cards, MOLECULES OF LIQUIDS, my mind was completely blown and put back together better than it was before.
"Awesome" does not adequately describe you, Matt Parker
I'm stuck trying to work out how you managed to set up the equal red/black distribution shuffle.
+Peter “Wizarth” Newman That boggled my mind as well but I figured it out. Start by setting up the deck with strictly alternating red/black cards, then one single shuffle seems to produce the desired effect of guaranteeing a red+black couple for every 2 adjacent cards as counted from one end. I have no idea why this works, I just tested it on my own deck of cards. That would be another fun thing, trying to figure out the logic of why this works! But a nice little sneaky trick he threw in there, I'm glad I'm not the only one who noticed this and was thrown off track by his subtle magic.
+Peter “Wizarth” Newman me too.......& what are the chances of that occurring ?.......pretty sure it was setup just to illustrate the point that even if.....bla bla.....he should have said it though.......nevermind he shuffled 1st ! wtf
+Thor Is Here Games If you look at the cards laid out (all you can see, anyway, which is most of them), there is never a case of three of the same color in a row. I think that the whole point of laying them out was so Dr. Parker could check to see whether the first two cards were the same or different colors. If they were the same, then the red/black would not have been crossed like they were; they would have been all the same color on one side. I think. Can't test it, since my dogs ate my cards. But kudos for figuring out the setup!
Aha! Thanks for the observations Power and jag, you guys have pushed me into thinking about it a little more deeply. Power, you're exactly right that a perfect shuffle with equal decks would produce matching couples, not opposite paired couples. It turns out that for the trick to work, you must cut the deck in such a way that the bottom card is red in one hand and black in the other. You can clearly see that Matt happens to pull this off in the video. It's 50/50 whether he'd cut correctly, but he would probably just re-shoot the video if he cut incorrectly. This is all you need for the trick to work, you don't need to lay them out to verify anything, it's just so us, the viewers, think the cards look "random" because the exact ordering of each individual pairing, whether red followed by black or a black followed by red, is indeed random. Jag, you are right in your observation that there are never 3 cards of the same color in a row (as this would force a matching couple), but Matt did not need to verify this. Here is how the mechanism works logically: Imagine that you have two piles of cards to shuffle, each with alternating colors. In one hand, the bottom card is black, and in the other card, it's red. The first card to fall will be random, either black or red. Imagine the black card falls. This reveals a red card behind the black one that fell. Now BOTH piles have a red card at the bottom, and the next card is GUARANTEED to be red. Now regardless of WHICH red card falls, the next state will be one red and one black card on the bottom of the decks, and we are back to where we started. This process continues until both decks are exhausted and the deck comes out with perfect, but random-looking, pairings. Very clever! Kind of a bummer he didn't mention this himself for everybody to enjoy, but instead left it for us to discover!
The discussion here has pretty much worked it out. I can confirm that I do an imperfect riffle shuffle (I am not good enough to do a perfect one) but the cards were initially in perfect RBRBRB… order. Maybe I'll do a follow-up video. Get some cards and try!
I wish you were my math teacher!
Thanks! I was once a normal high-school math teacher. Now I am everyone's.
And you do a great job!
+standupmaths How did your students like you?
+Some Guy I got on well with them. Teaching is very different to TH-cam videos or stand-up though.
+Ryan Jones nice
Hi, Great videos. I want to be sure if the milk and water example is accurate. Because I see you take 1 full spoon of, pure,100% milk and pour it into water. Than take a blend of (water and some milk, not 100% water) into the same spoon and pour it back in the first glass. For the 2 to be spoiled the exact same amount. Wouldn't you have rather use 2 spoons the same size and pour 100% spoon of pure water in milk and vice versa?
you are right. his water-milk example are not accurate.
+TiriPon That's my line of thinking too - the exchange would have to occur simultaneously for it to be equivalent to the card example. Otherwise it would be like taking 5 cards from one pile, shuffling them into the other pile, THEN taking 5 cards from the shuffled in pile.
+TiriPon Oh! I get it now!
Any milk returned in the second teaspoon REMOVED contamination from the water. Therefore, the actual amount of contamination in the glass of water is 1 spoon of milk minus the amount of milk taken back. Which is equal to the amount of water left in the glass of milk.
This can be shown with the cards, because as he showed, any exchange of two cards (regardless of their color) has no effect on the total distribution of cards. Either the amount stays the same, or both sides change amount equally. This doesn't change if the cards are shuffled in, as long as the same number of cards are removed from both sides.
+Peter “Wizarth” Newman Yes! Of course this works perfectly :) Thanks. I get it too now.
It would be nice,if he not choosed liquid/blending example
In college, I learned that when the textbook used the terms “obvious” or “clearly”, there would be about six full pages of proof required to show it.
Just want to say, great job editing this video. Lots of tasteful tricks and details (like the outtro for example). Looking good!
Thanks! I always have more fun editing than I probably should.
If anyone still doesn't get it (I did this to understand it better myself anyway so yeah XD)
Starting with 100ml pure milk and 100ml pure water:
Say we put 5ml milk into water first, we'd get 95ml pure milk remaining in the milk glass.
In the water glass we would have placed 5ml of pure milk in 100ml pure water to get 105ml total vol, so milk = 5/105 = 1/21 and water = 100/105 = 20/21.
Diffusion of the milk was evident from the video footage, so let's assume it all diffuses roughly evenly prior to the second transfer.
Second transfer then contains 20/21 water and 1/21 milk, so a transfer of 5ml would give 5*20/21 = 4.7619...ml water and 5*1/21 = 0.238095...ml milk which would go back into the pure milk. In the water glass, 105-5 = 100ml total volume would remain.
So after the second transfer, what we would have in the milk glass is 100ml - 5ml + (5*1/21) = 95.238095...ml milk, with the remaining (5*20/21 = 4.761904ml) as water, which adds up to 100 (100-5+5)ml total volume.
The second transfer removed 4.761904ml of water from the water glass, so we are left with 95.238095...ml water as well. This means 4.761904ml of milk is in the water glass, which also adds up to 100 (100+5-5)ml total volume.
...I hope this is right because in my mind it sounds a bit weird LOL
Excellent job with the editing at the end Matt, when you erased the links. I love seeing the various videos on all the different channels. Numberphile, Standupmaths & such. I enjoy learning new things every day. 😊🖒
Really good job with the videos! Im always looking forward to new ones (especially the complicated challenges haha!).
Thanks for the awesome work standupmaths!!
Thanks! I'll try to keep the complicated challenges coming.
Hi!
I wanted to let you know that these kinds of videos are great.
I had proven the trick, exactly like you for the first part, but then I had also proven the second section algebraically, showing that the number of red and black cards stays the same for any number n of cars exchanged between the two piles.
I'd love it if you'd make other videos like that, leaving us the time to do our own research. I have discovered your channel not very long ago, and I want to say that it is amazing for someone who loves mathematics as much as I do! All the best!
"If you're watching at tis point, you're not going to stop right now are you?"
I stopped watching at that exact point.
savage. I responed with a 'yes, sir!' and realised how stupid that was at 3:40 AM, so kept watching in silence
+Bob McBob Heh sucks to be you for missing the trick.
The nicest mini rant I've heard in a while. And I was worried you weren't going to get to the Vsauce video. I'm glad you did.
I can't believe you did a whole video explaining this simple/easy card trick!
The algebraic solution is quite elegant. My process was a bit more intuitive, realizing that if you take a sequence of red and black cards (R,B,B,R,R,B,R,B,...) where the number of red cards is equal to the number of black cards, if you pair them up you must have an equal number of (R,R) pairs as (B,B) pairs.
That smug grin when uncovering the sorted piles. Well played.
And to think I was toning down the smug by about 60%.
I am pleased that he showed the visual demonstration of the extreme case as a proof, as this was how I solved the problem initially.
At 3:06 there was a slight logical error. He said that the respective piles are equal, which now means we now know they bottom piles sum to 26. We already knew they summed to 26 because there are 52 cards in a deck and 26 had already been taken up. We didn’t need to know the piles were equal
Anyone else thinking about Star Wars during this video? R2B2 sounds an awful lot like a famous droid. :D
I knew I couldn't be the only one!
Is the Droid c3po?
I don't believe anyone didn't understand this trick before the explanation.
I love your card videos!
Great trick and video Matt!
Cool end screen! I hope it makes a reappearance in some form or another.
So to generalize for any number of cards:
T = total number of cards in deck
R0 + B0 = T/2
R = total number of red cards in Deck
B = total number of black cards in Deck
R + B = T
For R = B and only then:
2B = T or 2R = T
So B(or R) = T/2
So: B = B0 + B1 + B2 = T/2 (Same for R)
B0 + B1 + B2 = T/2
and R0+R1+R2 = T/2
Now replace R0 with the R1 + B1. And replace T/2 with B0+B1+B2
R1+B1+R1+R2 = R1+B1+R2+B2
R1 = B2
Like he mentioned in the first video. R must = B for this to work or you can't do the B0 + B1 + B2 = T/2 or R0+R1+R2 = T/2
great video. also enjoyed your work on red dwarf.
9:38
You said different 'to', not different 'from'. I cried
I think a good proof is also:We pair up all Cards. After that we have 3 differant types of pairs. Red-Red, Red-Black, Black-Black. The number of R-R and B-B is the same. Now we choose from each pair an Indikator. For each R-R we get a Red Card on the Red Pile and for each B-B we get a Black Card on the Black Pile. For the R-B there are two possebileties. Ether you put a B on the R pile or you put a R on the B pile
that editing at the end was really simple but really cool! :D
These are some great quality videos! Definitely this channel deserves more subscribers!
Thanks! The subscriber level has been growing pretty strongly. I really appreciate everyone sharing the videos with other people.
+standupmaths if and when you get to 100,000 subs, will you do something special and extra mathsy about the number, or something like that? Great vids and editing btw
R2B2: the Great Value version of the beloved R2D2
I was waiting so long for this! Thank you so much! Great proof!
This channel deserves more subs.
Nice deck cut and riffle shuffle, Matt 😉
IT killed my mind when he split the Reds and black evenly
I agree, although in the liquid case you mix first then pick water, instead of "picking water first and then mixing both glass with the other's spoon simultaneously", which is more akin to what you did to the cards.
I like the thinking behind this. Very academic. Good teaching on how math works and stimulates the mind.
It will also work if you take the 2 unturned stacks, shuffle them together, and then make 2 stacks, of m and n cards (obviously m+n=26).
So glad I subbed to this channel :p. Great stuff.
I'm so glad you're here.
Matt, so you basically made a low fat milk... My reaction is the same, when I buy the wrong milk. 0.1% milk should not be even called milk!
In my opinion, anything with more milkfat than 0% is too rich. However, I've always grown up drinking skim, so I am biased by habit.
"Milk flavored water beverage" That makes me a little queasy just thinking about it...
+origami katakana I've been grown up with natural homemade sheep, goat & cow milk and let me tell you... the less processing a milk has the better it tastes.
Divine Evil
I guess we're both biased by habit, then. I'd like to see how someone who hasn't drunk milk would compare the two.
For your final swap you don't need to keep the swap piles separate. You could take n cards from the black pile, mix them into the red pile, then take n cards at random back and it still works.
I did this with one of my classes today (and work colleagues) and blew their minds.
thanks for making math a joy with your videos 😊
Nice perfect riffle, Matt! I'd have had to have made do with a Faro!
Being totally honest, it was late when I saw the first video and I'd been at the pub so I chose not to drink and derive, but after watching you set up notation [simply the R,B 0,1,2] I had a quick (~2line) algebraic doodle and had the answer. Isn't algebra great! :)
When you go to the pub you should have a designated deriver. But good job on working it out later. And that riffle shuffle was not a perfect one.
Sorry about my clear as mud explanation. I'll go into more detail next time.
Awesome presentation and content! Thank you.
been subbed to this since it was a smalllllllllllllllllllll channel. proud to see it grow!
Thanks for being an early adopter! Hopefully we're still in the early days of growth.
You *can* start the analysis assuming that all piles have 13 cards, so long as you *also* consider what happens if you swap an indicator card for a bottom card. But that's the harder way (as I well know) …
There was more milk in the glass of water because when you put water into the milk, the spoon contained milk, meaning that milk was put back into the milk.
I am a real fan of maths, and also support practical explanation of problems. Really a mind boggling card experiment.Also shows power of human intelligence
Does this work if you do it with the 4 suits in 4 piles instead of the 2 colours in 2 piles?
You got it wrong with the milk and the water, once you put the spoon of milk in the water, you got some percentage of milk in the water. which you bring back to the milk glass. so it's not a full spoon of water. so the water is more contaminated by that same percentage.
Now with that logic.. try this trick with a deck of a 1000 cards!
Haim Bilia I saw another thread that explains why you (and I) were wrong. Yes you are adding milk back to the milk, but you removed that same amount of milk from the water.
I'm sure someone has pointed this out already, but anyway: When you took the spoon full of water/milk and put it into the Milk; that means it wasn't a fair exchange. Unless you had taken a spoon full of just water out before and poured it into the milk. Then the differences would be equal like using cards. :) Edit: yep i see comments talking about this exact thing lol.
Dear Matt,
My I give a little suggestion on your production?
Please add a rim light because the top of your head is sinking into the black back drop. Just put a light behind you (even a small one) if you are afraid of leaking light onto the back drop and you have no more space to move you and the light far enough forward, you can use a gobo to block it.
Your production value will go up and it's artsy too ;)
BTW LOVE THE CHANNEL MATE!
Great suggestion. My set-up at the moment is whatever spare kit I had lying around the house. I'm making these videos on a zero budget for now. But I'll add that to my list of things to do the moment I up my production game.
standupmaths
Thanks for the reply and plz keep the videos coming. I used to suck and math in school and never had a liking for it. The teachers were puzzled how I could ace physics and engineering and not comprehend maths. Now somehow I start to see it and enjoy it. And your videos the last 2 weeks really taught me a lot! Thanks!
All of the fiddly algebra in the first part seems over the top. If you think of the initial pack as coming in 26 pairs (of an indicator card followed by a distributed card), then because there is the same number of reds and blacks in the whole pack, the number of red-red pairs has to equal the number of black-black pairs. Otherwise there would be more reds than blacks or vice versa (the red-black and black-red pairs might as well not be there for this accounting procedure).
It's completely equivalent to the algebraic method, but it's more transparent, and no pen and paper required!
They swapped the same amount of fluid, milk and water, however, the one that is more contaminated is the water. The milk is still usable however the water is less usable.
your videos are awesome
I solved it differently, without algebra. The second part of the trick led me to the solution of the first part. The indicater card is dealt, if followed by a card of a different colour, then no change the deck remaining has the same number of red and black cards.If red is followed by red, add 1 to the red count, but also the remaining deck now contains 2 extra black cards. The only way the extra black cards can leave the the deck is black following black, 1 indicater and 1 adding to the black count.Same for black follows blackHope that made sense.
When you mention the R2B2 pile, I was thinking of a certain robot for some weird reason.
The 'switch' explanation is what I remember writing a comment about in your last video-- but I think left it unposted. What a shame!
The important thing is that you thought about it.
standupmaths :) I was pleased to see that your explanation was almost a mirror of my thoughts: starting off will full black in one deck opposed to full red in another.
what if theoretically you had the random draw where every indicator card was red r0 would be 26 and b2 ould be 26, r1 would be 0? just trying to figure this out :)
7:10
How did he manage to equally seperate the colors even though he riffle-shuffled the cards?! It's magic!
He sortes the cards in a way that when he did a perfect shuffle, the cards were BRRBBRRB all the way through the deck.
I have to admit I was one of the commenters saying it was easy and made the mistake of assuming that all 4 piles would be equal. I've played with so many of these kind of tricks in my life that I understood that the total number of blacks and reds in the face-down piles together had to be equal. From there I sort of followed the logic as shown here in the 'practical' explanation (either all reds are in one and all blacks in the other pile or any variation is just a exchange of x red from pile one for x black from pile two). Maybe next time I should actually DO the trick instead of reacting after just watching the video in the train. That way I would have clearly seen that the piles weren't equal.
How did you split the piles into pure colours like you did in this video?
You should take D for Dark, not B for Black, so you'd get R2D2 :)
Wait. His milk and water explanation is wrong. If you take one spoon of milk and put it in the water the glass will be the initial volume of water plus 1 spoon of milk. If you then take a spoonful of that you're picking up part milk and part water, not an entire spoonful of water. The milk will have less water in it than the water has milk.
During the swap, the friend I was showing the trick to swapped the cards from one pile, then shill fed them in and swapped cards back. Could that have messed it up or is it like the milk?
If only instead of black for the second color of cards we had... i dunno... dark blue, then one of the piles would be named R2D2
Its obvious. That I am sincerly impressed.
ahh that sound when you started drawing made me shudder and made me anxious waiting for it to happen again. did your fingernails touch the board?
for some reason I love how the pattern on your shirt matches the colors of chalk on the board behind you (4:52). I wonder if this was intentional... :)
There's a typo in the description, Matt! "The swapping cards bit was added MY magician"
Well spotted! Well, I like to think of Peter as my magician, but I've changed it to "by".
I do not agree with the milk example. Because the amount of milk added to the water was more compared to the amount of water added to the milk, as that amount of water contains some part of milk.
Matt, about the Milk and Water demonstration, I (Admittedly not the most skilled with maths puzzles) am confused as to how your demonstration equalizes contamination, and will attempt to explain my thought process below.
I assume that each glass is measured in a unit which totals one hundred, thus, M(ilk)+W(ater)=200L(iquid)
G(lass)1 contains 100M, and G(lass)2 contains 100W (G1=100M, G2=100W)
Removing 15M from G1 and placing it into G2 leaves: G1=85M, G2=100W+15M (To equal Solution at Ratio of 0.89).
Removing 15S from G2 and placing it into G1 would move 13W and 2M (rounded), which leaves G1=98M+2W and G2=87W+13M.
For equal contamination, G1W=G2M, which isn't true in this case because, unlike with cards, which are clearly separated in a solid (and binary) form, liquids mix seamlessly into gradients, thus, when you remove 15S from G2, just like you did with the 15M from G1, only 89% of S is W, and the remainder is M.
I think.
+XaleManix This is less an attempt to disprove your demonstration or call you out on a mistake as it is myself being very confused shortly before midnight local time and attempting to show my work so someone can point out where I goofed.
+XaleManix you added incorrectly. G1 had 85M and you added 13W + 2M, so you should have (85+2)M + 13W, which is what you had left on the G2 side also.
+jagmarz Thank you.
i think i'll stop watching maths videos at night ^^ it took me at least 10 minutes to figure out the milk and water thing .... and now my head hurts
When you are used to whiteboards blackboards are a pain in the ear
Hi Matt, sorry a lil bit off topic. Have you heard of Tsujikubo Rine ? what do you think of her skill ?
Thanks
Thanks for the great explanation! I didn't manage to figure it out by my self entirely, though, and in the end gave up due to lack of time that had to be spent on other things. I guess I started out okay by thinking that both the open and closed piles had to have the same amount of cards, but then went on to try something else that proved less productive :p If you have more mathematical tricks like this, I'd love to try to wrap my brain around it!
The important thing is that you have it a go. I'll definitely have more tricks to follow.
I'm italian and I admit I didn't understand if you are specified that you use the Gilbreath principle in the trick :)
Awesome videos!
Did you manage the almost perfect-shuffle on the first try? That was amazing!
I got as far as knowing I had to do some substitution and cancellation but I couldn't figure out which equality to use :(
Figured out the shuffling at the end didn't matter right away though. Silver linings and everything :)
The indicator cards add up to 26. So do the face down cards. There are also 26 red and 26 black in total. Therefore the number of red indicator cards equals the number of cards in the red pile, and also the total number of face down black cards. So if there are n indicator red cards, there are n cards in the red pile and there are n black face down cards in total. The number of red face down cards in the red pile will be n - the number of black cards because the pile has n cards. The number of black cards in the black face down pile will also be n - the number of black cards in the red pile because the total number of face down black cards is n. Simple.
Fantastic Video :D
Shouldn't it be R2 and D2 for the blackside?
"you people really excelled yourself" Well you did give us a tool to do that on your website.
"Just don't be a jerk" +1
You are my favourite British/Australian person, Matt! :)
7:10 ... my head exploded. What just happend?!
I liked the bit where you drank the really diluted milk. Do more of that :)
I'm a little iffy on the milk and water trick. Let's look at the algebra behind it, shall we? :D
Suppose you have X tsp of milk and X tsp of water. If you remove 1 tsp of milk from the X tsp of milk, You are left with (X-1)tsp of milk. Then if you move that 1 tsp of milk into the Xtsp of water, you have Xtsp water + 1tsp of milk. Now if you take 1 tsp out of the water/milk mixture, your one tsp (assuming the water and milk are completely mixed) would contain X/(X+1) tsp of water and 1/(X+1) of milk. Now added back into the milk glass, there is 1/(X+1)+(X-1)tsp of milk and X/(X+1)tsp of water. In the other glass of "water", there is X-X/(X+1)tsp of water, and 1-1/(X+1)tsp of milk
This got a bit complex, didn't expect that O.o
In the "milk" glass, if we add together both quantities of milk and water, we see 1/(X+1)+X-1+X/(X+1)=X
Good, that's what we should expect!
So now according to Matt, the amount of water in the "milk" glass = the amount of milk in the "water" glass. That would mean X/(X+1) = 1-1/(X+1)
X/(X+1) = (X+1)/(X+1)-1/(X+1)
X/(X+1)=X/(X+1)
And that is...true....
Well then, I was wrong! I don't trust reasoning, but I sure do trust my own math. The glasses are equally contaminated. Although I bet the "water" glass would taste way worse XD
Vsauce is why I'm here. I love the intellectuals of TH-cam.
Hey Mr.Parker, I learned a fascinating mathematical card trick. I have not seen an explanation and it is still hard for me to understand the pattern behind the trick. Is it possible for me to make video showing you how the trick goes and will explain the steps?
Absolutely! Make a video and email me a link.
I think that glasses are not equally contaminated. First you put a spoon (x) of milk into the glass of water but then you put a spoon (which consists of some water and some milk) back into the glass of milk. by doing that you brought some milk back to the glass of milk.
And by doing that, he also took some milk out of the water cup. Then there's a little less than a spoon of milk in the water and a little less than a spoon of water in the milk. It happens to be the exact same amount.
I dont understand, why the faced down cards all red or all black?
Should have labeled the R2D2 - Red 2, Dark 2.
How do you feel about vsauce giving away the explaination (and credit!) before this was posted?
I feel a light-headed dizzy joy over everything Michael does. (And he only half-explained the trick, which was very kind.)