Prime.

And the biggest rip off 😂

In the Results and Tactics: Large Numbers section, you stated the average difference of a given target and the best attempt is 0.2 in the 4 Large category. Do you have any calculated averages for the other 'hard' categories 0 Large and 3 Large? While we're at it, we might as well look at the easy ones for completess' sake.

Aepique, wut une urgazm.

@33:22 "... but please come straight back as we're about to get into the *thick of it* ..." Can't believe ksi got a free unintentional shout out for his song XD On another note, great video, loved all the different representations, breaking down of the lemmas and use of analogies and representations used in the video.

BBC Sherlock is the definition of "style over substance"

My experience with discussions like that is, when I talk to "amateurs" it is really hard to explain different things, because they are not so deep in the materia. For them the word "factorization" is clear as water. They have no idea what FTA really says. It starts with following. I ask for example: What is a prime number? Following answer is possible. A number p is called prime, if it is divisible by 1 and itself. In the most cases the answer is shorter. If it is divisible by 1 and itself. Classic answer. People have to understand the importance of precision. Then they have to understand the importance of reading carefully. They read: "Every natural number > 0 has a unique prime factorization" Later they say Every number can be written as a product of primes. Several details are missing, where are they gone? They are not used to be precise and they do not know that really every single character in a mathematical statement is important. Then: A typicall discussion is: Why is the Fundamental theorem of arithmetic talking about "product"? Take 2? It is prime. But I do not see a "product"? Where is mistake? They lose precision. It is easy. They don´t know, that the FTA is a very deep theorem about natural numbers and not so easy to understand for amateurs. Everybody knows what is the content of FTA, but they have not in mind, that the missing precision is the reason for later problems. The correct statement is: Every natural number > 0 has an unique prime factorization. What is the problem? People know, what "prime fact." means, but they do not know, that it has a precise definition, what would clear many problems. And they do not know, that there are cases like "empty product" or how to even define a product over an infinite set? This makes it hard to talk about mathematics to a wider audience. For more precision you have to explain more and more. Def. (Prime Factorization) If there exist primes p_i and natural numbers e_i, then the expression n = product p_i^(e_i) is called "prime factorization". Now they maybe are not familar with the product notation and so on but they "know" in some sense what is going on. For them it is enough to know, that you can write n = 2^a * 3^b * 5^c * 7^d * ... with "correct" exponents. What they do not know is about the empty product 1 = 2^0 * 3^0 * ... or cases like 5 = 5 (it is actually 2^0 * 3^0 * 5^1 * 7^0 * .... is considered as a prime factoriaztion by definition. And so on. Losing precision leads to misunderstandings. The other way around: every character is important. Do I really know, what it means?

I solved the one in the title card: (100 + 9) * 7 + 4 + (2 * 25) = 817

Thank you for having James on the channel, he’s such a fun, and passionate maths communicator. Great fit for your channel. BTW, really great channel, I haven’t been a subscriber for long having just found the channel in the last few months, but I subscribed after seeing one or two of your vids, they’ve all been interesting, informative, and well done. And, I agree, it was an entertaining film, but it was not a great film. Just way too many flaws in how they told the story.

Your toast example unfortunately does not work in German...

Just found your channel. Really love how you explained and make hard to understand concepts easy to understand. But you also loosen the atmosphere with your jokes. Your great thank you so much 😊

Wait, so detectives should actually be called abductors?

What is a target number?

I am FASCINATED that in antiquity, "one" was considered distinct from "numbers" as such. How have I never heard this before?

the opening deserves another like button so I can like the video twice

I am soooo late to this video (great subject BTW) I wonder if since this came out you saw the "Polytechnic" movie made by Denis Villeneuve. It's based on a real feminicide that happened at Polytechnic Montreal University. I think you would like it.

There is a trick to 11 x table. 4+1=5 put the 5 in the middle : 451. Do you use this trick to quickly work out which numbers are multiples of 11? Only works when the two digits sum to less than 10 obviously.

I’m glad that you mentioned that the other issue with Enigma was that a letter can not be encrypted as itself, it reduced the number of possible combinations.

What is this for in everyday life

"The biggest lottery you've never heard of" is such an ignorant thing to say. Sure, if you're from outside the EU, you might have never heard of it. A couple hundred million people across the channel however would strongly disagree with your statement...

Maybe ad this video to the second playlist MAFS - I almost missed it...

Amazing video, finally learned some cool facts about the lottery. Also what was your number in the lottery?

Table at 9:55 not quite correct. First three digits of 4th has a quantity of 198 not 99, and total of €198,000 not €99,000 as there are two numbers drawn as 4th prize. This also makes the total column sum to €14m.

I actually use negative bases in some number encoding systems! They allow for the 100% efficient encoding of all Real numbers into a singular real number! This can be used in certain higher dimensional projections.

I actually use negative bases in some number encoding systems! They allow for the 100% efficient encoding of all Real numbers into a singular real number!

If you get a money back or “pedrea” price in El Gordo, we usually buy another ticket for “El Niño” Lottery for the 6th january, almost as important as El Gordo Lottery and even more spread in prizes.

There are only five platonic solids because you can't fit more than two regular polygon with more than 6 sides around a point. The explanation is really simple to grasp, so...I am not sure this comparison holds very well

cool video

Fascinating

@AnotherRoof I enjoy your proofs and elucidation on the history of math. I did not know and have never heard that Fermat had a coordinate system that was equivalent to and around the same time as Descartes; the Newton Leibnitz dilemma. I wonder why we aren't informed about this fact as we are of the latter. Great video and I find Descartes method interesting though more tedious to compute. It is interesting that they are essentially doing Calculus and shows that this branch was inevitable even without Newton or Leibnitz. We are aware that Archimedes attempt to approximate the area of a circle with inscribed polygons already was knocking on the door of limits and infinitessimals. Great video and continue to educate

Bro needs a new set of Haguromo for Christmas....

26:47 if the EV is -0.84, that's a 42% not 59% loss (In comparison with el gordo's 30%)

The real question now is did he win anything?

When the 4th rotor was added, how did they continue to crack it, as the bomb machine was build with 3 rotors in consideration?

Only know from Spanish class 😅

an increase from 185 to 193 factorial would change A lot. imagine the paper these tickets would be printed on. how many trees would need to be cut down for this? this represent more tickets than there are atoms in the planet. or it is possible that the exclamation mark placed next to a number did for whatever reason not mean factorial.

Thank brother Ill add this video for my sleeping music list

It's actually very slightly worse odds than stated due to the fact you can't take more than el gordo. For example, if el gordo was 12345 and 2nd place was 12346 - you only get 4 million, despite the fact your calculations give both the 12500 and 1000 results for being close to second place

i thought of a demonstration that throws the intuition in the other direction for linearity of EV than the one you did. the example you give in the video [15:25] basically assumes taking out the first place; of the scenario of 12345 -> X2345, which is obviously worse than 12345 -> 12345 but thats not the only example. theres also 12345 -> 1234X, which is better than 12345 -> 12345, as you now have a higher chance of rolling a better prize you can see then that since 1234X, 123X5, 12X45, 1X345, and X2345 are equally likely, it averages out to being the same expected value as if you just had 12345 for the second round. im not entirely sure as intuition is vague and i havent formalised this argument at all, but it might presuppose that the sum of expected values is equal to the expected value of the sum; if it does then at least it shows how that can be intuitive.

Things you'd also have to take into account when calculating the expected value: - Taxes: there may be some amount that is exempt, but large prizes are usually subjected to taxes - For large prizes, most lotteries will offer to pay you a smaller lump sum instead of the full prize if you want it "now", otherwise they'll pay you in installments, over many years (20+), which means opportunity costs

What do mean I've never heard of it? I live in Madrid.

This is nest lottery ever lol

Btw, when using the € sign, you slap it to the end of the amount like a unit in the other SI units, and you can use the standard SI prefixes to like k and M with it. (Like you already did) America is the weird one that marks the currency character before the amount. :D

damn I had thought that this might be a lottery which actually generates money for the end user which I was seriously confused at , but nope , remember people , lottery is the tax of the poor (even this , though this is twice more good than other but still all lotteries are bad) and 30% loss is inexcusable

I've been thinking about why the replacement doesn't change the EV. The proof assumes the marginal probability of the second draw being a certain number remains constant. This is maybe more counterintuitive than the linearity itself. Initially I noted that for equally distributed numbers, with replace the probability of any one event is 1/n^2. Without 1/n(n-1). Marginal probability is n/n^2 = n. Replacement scales the remaining events by n/(n-1), that is 1/n(n-1). Marginal probability is (n-1)1/n(n-1) = 1/n. So the marginal probability is unchanged making linearity almost obvious. Actually even if they weren't equally likely, marginal probability wouldn't change. The probabilites of the second draw after replacement must still equal 1, so the new probabilities must be scaled by 1/(sigma_E !=D_1 {P(E)}) that is the reciprocal of the sum of the remaining probabilities from the events in the second draw. This scaling factor directly negates the effect of removing the double draw by scaling the marginal probability up to its original value. This logic can be extended to multiple replacements.

I feel like a simple way to compute the EV would be to consider the hypothetical scenario where exactly one of each ticket was purchased. This spends a total of 200*100,000= 20,000,000 euros. Now what’s the total amount given out from the prize pool- Which I’ll leave as an exercise. But the ratio of those two numbers should give you the ev for a ticket.

Since the 22nd of december passed, did you win?

Good vid! Easy to understand. I also appreciate the correction you posted in the comments. I'm not the one to complain about pedanticness when it comes to such things, sometimes it's very important to establish precision. Otherwise the "discussion" will be meaningless and unproductive.

0:42 Reminds me of my dream where a game was called Princess Poline

FYI House intentionally lost that game in order to distract Cuddy and go behind her back in order to save her patient...