Some of our favourite maths and numbers based QI clips! Follow QI on Twitter ▶ / qikipedia Follow QI on Facebook ▶ / officialqi Follow QI on Instagram ▶ / theqielves Subscribe on RU-vid ▶ / theqielves For more visit ▶ qi.com
Take 3 random digits (the first and third can't be the same) and forma a 3 digit number from them, also form the reverse number then subtract the smaller from the larger. So we get "abc"-"cba", where a>c; let n=a-c -> n is between 1 and 9 (thus a digit) The difference is (100a+10b+c) - (100c+10b+a) = 100(a-c)+10(b-b)+(c-a) = 100n+0+(-1)(a-c) = 100n-n (this is why the first and third digit can't be the same) Now to get the digits of this difference we do the following 100n-n = 100n -100 + 100 - n = 100(n-1) +90 + (10-n) The first digit is (n-1), the second is 9, the last is (10-n) Now we can add that to its reverse number 100(n-1) +90 + (10-n) + 100(10-n) +90 + (n-1) = 100(n-1+10-n) + 10(9+9) + (10-n+n-1) = 900 + 180 + 9 = 1089 Bamm! French.
@@TanjoGalbi Some of the most classic comedies like Mr Bean or films made by Charlie Chaplin are slapstick, and were made by very inteligent people, so I don't think it's fair to consider that solely for "the simple minded".
It's often used as trivia that the Principia Mathematica took hundreds of pages to prove that 1+1=2. This is incorrect; while the proof does appear hundreds of pages into the book, the proof is contained in what you see on the screen, even though it does contain references to previous parts of the book. Such a fake fact would be similar to saying that the dictionary takes hundreds of pages to define what a zebra is.
Indeed. But - as you said - it does require *some* of the earlier material. So while not taking hundreds of pages it is not a one page job either. I have never even tried to check this myself - but many years ago someone that supposedly knew what he was talking about - told me that it would still take some tens of pages (if my memory serves).
Thats not true though. I can write the sentence as A + B = C while A is the sum of 100 pages, and B is another 100 pages. Just because someone can simplify an equation to a single page, doesn't mean that the 200 pages aren't needed. The single page of logic is useless without the 200 pages of axioms needed. Thats like saying E=mc² is the just one simple line to explain mass-energy equivalence without noting its a simplified version of E²=(mc²)²+(pc)² in which that is expanded even more to include M = μ + E0/c2 & a frame relevant M_rel = E/c2 without 10,000 pages of priors, mass-energy equivalance being written as a single line would not be possible. Math is just descriptive. Its not like someone plucked a platonic E=mc² measurement from space. Theres too many armchair commenters thinking they have a grasp on things because they have listened to a science communicator tell them a story. [BRA | KET] and Psi are alien concepts to you and QED. Its easy to describe the path a ball takes rolling downhill. but to understand a geodesic path in curved spacetime that can loop infinitely while never changing it's vector, shows gravitation is a pseudo force, and a force should change a path according to newtonian mechanics, but gravity isnt actually a force, it doesnt change your path, it changes the road youre traveling on (3space). You can travel straight down a straight road, and you can also travel straight down a road that curves. you wouldnt know the difference without relativity, a 2nd observer to show the pathis different for each person and the combination of both perspectives leaving the difference to be the true path. Same thing happens with path integrals and the path of least action to form the arrow of time. Its easy to tell when someone parrots science communicators vs someone who took the courses to actually understand it.
All very well, however I think anyone who needs a book to explain that one plus one equals two is going to struggle with some of the most fundamental problems of the world.
Worth noting that Russell got three books into the Principia before Gödel came along and proved that Russell was tilting at windmills, by showing that it's impossible for any system of axioms to be consistent and complete, rendering the goal of a complete and consistent set of axioms for mathematics a fool's errand.
Not any system of axioms, Gödel just showed those of the complexity of the Principia (aka Peano arithmetic) are incomplete. There are weaker axiomitizations of arithmetic (e.g. Presburger arithmetic, and Skolem arithmetic) that are both complete and consistent. There are also weaker axiomitizations that are incomplete, i.e. Robinson arithmetic, which shows that it is not axiom schema of induction that is the cause of the incompleteness, but the ability to code Gödel numbers that is essential to show incompleteness.
The reason that 142,857 is an anagram of itself when multiplied by 1 through to 6 is because it is simply a higher version of the old "one over seven" idea. One divided by seven equals 0.142 857 142 857 recurring. Two divided by seven has the same numbers, but as 0.285 714 285 714 recurring. Likewise for 3, 4, 5 and 6 over seven. So the 142,857 of that problem is the same set of six numbers, producing the same results.
not always. if the audience chose 3 times the same number, like 222 or 333, etc... it's always 0 equally if it's a number like 242 or 525 etc... it's gonna be 0
2:14 The multiples are not just anagrams. They're "cyclic", as she said a few seconds earlier. Write the original digits in a circle, then the multiples can be read starting at different digits in the circle. This works because 1/7 = .142857142857142857... Maybe Sandy mentioned all of that after this clip.
"This works because..." doesn't actually explain why that makes it work. It's a bit like me asking how a car moves and you saying "Because you put hydrocarbons in to it." I think it's numberphile that have a really good video about it :)
@@JimC Well at the time I was a bit busy and thought anyone who cared would be able to search RU-vid themselves for the two words "numberphile" and "cyclic" and click on the first video. But if that's too tricky, here you go! :) ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WUlaUalgxqI.html
@@andymcl92 Always a mistake to imagine anyone on RU-vid can do anything for themselves. Hence the creation of "let me google that for you" I'm sure you can find the link yourse...oh bugger.
At 5:21 there is a missing set inclusion symbol in the Russell's theorem. It's on p.379 of Volume I of the Principia if anyone is curious. They have: ⊢:. α, β ∊ 1. ⊃: α β = Λ . ≡ . α ∪ β ∊ 2 It should read: ⊢:. α, β ∊ 1. ⊃: α ∩ β = Λ . ≡ . α ∪ β ∊ 2 In modern notation: ⊢ (α, β ∊ 1) ⊃ [ (α ∩ β = ∅ ) ≡ ( α ∪ β ∊ 2 )] Which states that if α and β are discrete unitary sets the intersection (the members of the sets α and β they have in common) of α and β is the empty set if and only if α and β's union is a member of the set of duals (the set of sets that have two discrete items).
It's still amazing to me how some intelligent people (talking here about Susan Calman, who is a lawyer, and very clever) can have such an aversion to maths, that even reciting a math based limerick reduces them to giggling heaps
He shares the same sense of humour as me, angry logic. The difference between him and me is that he has self confidence and can perform his comedy in front of other people and has become a success. I lack any form of self confidence so I am a nobody. Oh well. Good on him :)
@@oscargr_ He uses angry logic for his comedy, that's his style of humour. That is also my style. Though you are right that here I was using self pity humour but you should hear me when I am ranting about random things or things people say wrong ;)
6:34 Oddly enough, Aislynn would go on to portray Rachel Riley on 8 Out Of 10 Cats Does Countdown. EDIT: I meant Aisling! I blame everyone named Aislynn for my blunder!
2:04 She went a little speedy with that one. The number doesn't seem so special, but maybe for a keen mathematician's eye, you can realize this is 1/7. (not exactly, obviously, but rather the repeating part of the decimal) 1/7=0,142857 142857 ... It has some other properties, but I can't recall. I usually remember it because it almost have the table of 7 within itself. Like Start with 14, then (repeating the 4)there is 42, 28, 85 (7 times 15), then almost 56... (yeah, the rules breaks, sorry) When I say that multiplied by 7 gives 999,999 I was sure that that was the number,
I recall that it made more sense in the context of the episode. I think it was to be the treatment for a 19th century alleged ailment suffered by women.
1. Pick an integer between 1 and 1000 2. Multiply your number by 3 3. Add up the digits of the product (e.g. 69420 -> 6+9+4+2+0 = 21) 4. Multiply the sum by 6 5. Add up the digits of this product 6. Subtract 5 from the sum 7. Get the letter of the alphabet for the number (1 = A, 2 = B, 3 = C, etc) 8. Think of a country that begins with that letter 9. Think of an animal that begins with the last letter of the country 10. Think of a color that begins with the last letter of the animal There are no orange kangaroos in Denmark.
every possible three digit number will give a multiple of 99 in the first step (unless its something like 101, 252, 686 etc.) the reverse of a multiple of 99 is going to be a multiple of 99 mirrored from the tenth number (99990, 198891, 297792, which is 99x199x10, 99x299x9, 99x399x8) so the addition of these two numbers will always be 99xn+99x(11-n) = 99x11 = 1089.
To get my physics degree, one of the things I had to do was teach a topic and do a 20 minute presentation where I derived how to do something. They do it for that very reason, because math gets harder the closer you get to the board in front of an audience LOL!
"Pause"? It's simple mental arithmetic ... I did it in my head while watching. The top line adds up to 182 .. which was instantly recognisable as a multiple of 7 - I saw it as 140 + 42 ... (20*7)+(6*7) - others might see 91*2 or 210-28 ... then 26+55 ... it's always going to be 81=9² ... or -9² :P The only issue with it is that there are two possible solutions for √4, but I guessed that QI (or the creator of the limerick) wasn't geeky enough to consider that.
Basically it is the periodic result you'll get if you divide 1/7. That will be 0.142847142857... (repeat 142857 ad infinitum). Which will result in 7/7=0.999999 (repeat 999999 ad infinitum). 0.9999999999... equals 1. So basically the "1" you're losing at the end by shortening the periodic number will be added to the part beofre the decimal point.
@@n200518 Thanks for the correction, I got sloppy when copy-pasting from the 14x line. btw, the pattern holds for negative numbers too, just hold the minus in front and do the positive thing inside the parenthesis: -26 x 142857 = -(3714282); -(3 + 714282) = -714285
The McNugget number (43) can actually be met since it is also possible to order 4 McNuggets on their own (Usually sold in happy meals), when using the 4 piece nuggets the highest number of McNuggets that it's impossible to order is now 11.
The Mcnugget link always reminds me back in the day I ordered 18? Girl serving said we do 6, 9 or 20 you can't order 18! Cant I have two portions of 9 then?? 😆
What Russell did wasn't proving that 1+1=2. What he and Whitehead were trying to do, was define a set of axioms (things that are taken to be true without proof) and inference rules from which all mathematical truths could be deduced. This proof that 1+1=2 was merely showing that this is something that could be proven with their choice of axioms and inference rules. Gödel later showed that no set of axioms and inference rules can be sufficient to deduce all mathematical truths.
Aye... there comes a point where you have to define your terms... like proving what your own name is, it's a faulty concept, because you don't discover your own name, you decide it (or your parents do, but the point being, the meaning of the word is given, not found). So "two" is defined as being "one plus one" by the equals sign, so "1+1=2" is a statement that defines what the terms mean in relation to each other, there's no question mark, it's just like what I'm doing here... saying the exact same thing in multiple ways *lol*
Thanks for giving Whitehead part credit. Re "wasn't proving 1 plus 1 equals two": correctimundo. And the incompleteness theorem is a beautiful thing :-)
If you acutally know some mahs, that mind reading trick (1089) is pretty obvious. The numbers you use are: 100a+10b+c and 100c+10b+a respectively. It is pretty obvious from the start that the initial subtraction removes the b from the equation. You next number is 99 (a-c) if we makes sure that a>c which we do by requesting the smaller number is subtracted from the larger number. If a=c the whole trick falls flat because the first sum is 0. :-) So I would _always_ repeat a digit if possible, just to see how the magician solves the issue. If b is equal to a or c it does not matter of course so one save is to sort the digits before the first subtraction. The number we get: xyz has some interesting properties: x = a-c-1 y = 9 (always) z= 10+a-c The last addition is xyz + zyx: 100x+10y+z + 100z + 10y + x = 100 (x+z) + 20 y + (x+z) But x+z is a-c-1 + c-a+10 so x+z is always 9, and we remove the last two variables from the expression. Ending up with 9* 121 = 1089.
I just realized I haven't manually subtracted anything in ages. I was a bit shocked to find out I couldn't remember what I'd learned in primary school.
"Altissimum planetam tergeminum observavi" refers to what Galileo thought that Saturn was in fact three planets orbiting together. The two "planets" on either side were its rings.
It’s always gonna end up 1089 tho cuz any three digit number of unique digits minus its reverse will get a sum that when you subtract its reverse again you get 1089. You’d be screwed if they picked any palindromic number. Really woulda thrown a wrench in there
A Irish Girl, a Scottish Girl and a Dane walk into a panel show. When English is combined with Arithmetic Giggles erupt at the sight of a Limerick Stephen will fake a Scottish slap and of course the crowd will clap At Susan's bemusement of this silly rhetoric (it's not great but I had to)
How a teacher might critique that:- Poor grammar: It should start with "An" not "A". Also girl is lower case G in both uses, limerick is lower case L and you are missing punctuation marks. Factual error: "Giggles at the sight of a limerick", she giggled when the limerick was read out so that should be "Giggled at the sound of a limerick". Plus it's technically an audience not a crowd but that one can be put down to artistic interpretation! :) And finally the limerick as a whole does not conform to the rhythm that defines a limerick. Nice try though :)
@@TanjoGalbi yes my grammar sucks it was a quick thing I did in 5 minutes if I were handing it in for marks, decades ago, I might have fixed that in a second draft of such a silly thing. Crowd and audience have a difference syllable count or I would have used it. The Capitals is an odd quark I have that may have come from studying German when I was young I don't know. I tend to Capitalize words of importance or for emphasis (It is also a common sight in marketing and what is poetry and humour if not a form of marketing ;). Girl, Limerick. The limerick was of course visually shown. Sight is a correct usage as it was both shown and heard without the visual element the laughter would have been fairly muted I suspect. (Of course when you move as much as I did growing up you learn that grammar is taught at a different pace and in different orders in different school boards. As such I missed huge swaths of it and had to learn what I could later. As it doesn't interest me I have bad grammar. Though much better than it was.)
I had "12 plus its square plus a score" but it still works. Not convinced by the idiomatic terms though. I prefer "the integral d-squared dz, between 1 and the cube root of 3, times the cosine of 3 pi by nine is the log of the cube root of e".
any number divided by 7 that has a remainder, always has the same recurring pattern of digits. for example: 45/7=6.428571428571428571... 65456/7=9350.8571428571428571... 14.25/7=2.03571428571248571248571... 22/7=3.1428571428571...
The limerick also works without the bundle terms: "Twelve plus one-forty-four Plus twenty plus three square-root four,..." In the US, McNuggets are sold in multiples of 4, 6, 10, & 20; it's not possible to get *any* odd count. I recognize every single symbol in that symbolic logic proof & could read it to you. I cannot even begin to understand what that proof means, though, as it seems to contain nothing but citations of previous results, none of which I know because I haven't read Prinicipia Mathematica.
As long as the number isn't three of the same digit (111, 222, etc), the answer will always be 1089 (or -1089 if the first number is smaller than its inverted form)
42 : the "Answer to the Ultimate Question of Life, the Universe, and Everything", calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years...and the maximum number of chicken nuggets you can buy at mcd. Coincidence?
Except 42 wasn't the answer to life, the universe, and everything. As they actually asked what is the answer to the ultimate question of life, the universe, and everything. Turns out the ultimate question was "what do you get if you multiply 6 by 9?"
@@CynBH it has already been established that the show is not correct on that fact now but at the time it was aired on TV it was correct. Facts can change!
@@TanjoGalbi 1.) 4 packs in the Happy Meal have been available for at least 20 years. That fact isn't new. 2.) I apparently failed miserably at sarcasm. Oops. Oh well. 🤷
9:19 Our maths class of 12-13 year olds were asked to figure out the formula, I was the only one to do it despite never having completed a maths test within the given time. Proving that speed and skill are not the same thing!
The first limmerick actually works by reading out the numbers too! Twelve plus one fourty four, Plus twenty plus three times root four, All over seven, Plus five times eleven, Equals nine to the two, and plus naught
@@2Cerealbox Yes, unless a + or - permeates another n or zero. In that case the 0 could contain a positive or negative charge too . Lately though I've been wondering if all the macro & micro of the Universe isn't binary. I haven't started checking that out yet. Any thoughts or opinions?
With the numbers the first number must be bigger than the last number in order to work correctly. If it's the opposite then the (-) messes it up following the logic of maths, that is unless you change the equation by sub-tracking the last figure instead of adding it. Also as stated in the comments the same Numbers all the way through (111) defeats the equation. Or rather the Magic of it.
@@zapkvr Maybe psychotherapy would help you. Feeling violent urges when you see a person having a good time is not healthy, well-adjusted, or sane. Help is out there, try looking for it.
And they do it with a smile, no not really, it has to have become quite stale by now. I wonder how many poor mcd workers have gotten orders for 43 nugget by now?
Ok so maybe they borrow weird in Britain but what is she doing at 8:50? I’dve crossed out the 2 and put a 1, then borrow 1 from the 8 making it 11-2=9.
