 How are you? Do you like riddles? From a complete pack, a small number of cards. From a complete pack, we'll read this, it looks like math, I was scared it might be a trolling factor. From a complete pack, a small number of cards has been taken out. If you deal among four people, three cards remain. If you deal among three people, two cards remain. And if you deal among five people, two cards remain. How many cards are there? Let's lay this out. I'm not sure. Let's check it out. So how will we approach this? So we don't know the number of cards in the deck, let's call it X. That's the number of cards we have. From a complete pack of small card, a number of cards has been taken out. From a complete pack, a small number of cards has been taken out. So you take a whole bunch of cards out. If you deal among four people, so are you dealing out what you took out a pack? So I'm assuming X is the number of cards. The first sentence is just throwing you off. If you deal among four people, three cards remain. So basically, if you take X divided by three or four, divided by three, Mask of Raven does it. So let's check it out. Let's see if we can do it. So I'm gonna approach it this way. I don't know if it's the right way. I just like laying it out first. The most simplest way I can, right? If you deal among four people, three cards remain. So if you divide this by four, you're gonna get a number with a remainder of three, right? If you take this and divide it by three cards remain. If you deal among three people, two cards remain. And if you deal among five people, two cards remain. So three people, you get the number r is equal to two. And if you divide it by five, you get the number r is two. The remainder is two. So what's the best way of doing this? 47. Mask of Raven, how do we do? How did you get it so fast? Literary. I like reading riddles, thinking about them quickly, and then looking at the answer. That's the way I like doing riddles. I don't really do them. I read them. So how do we do? What's the best way of doing this? Mask of Raven direct us. So if we divide it, so basically here, if you say the remainder is three, so this would be three over four, this would be two over three, and this would be two over five, right? Whatever the number is. He's right, 47. Well, the number is an equation is a multiple of 15 minus two. Notice that first. The number in the equation is 15 minus two. Is it? Plus two, rather. Notice the first. Mask of Raven. Let me see. Well, the number in question is a multiple of 15 plus two. It's a multiple of 15 plus two. Oh, because of these guys, right? Because there's two there. Cool. 15 plus two, and then how do you deal with that? So it's a multiple of four plus three. That's a cool way of approaching it. I don't have a riddle mind. It takes a certain mindset to do riddles. So basically what it is here is to get X. Well, here, let's do it this way. Let me erase this. X, right? If we multiply everything by five here, you're going to get X is equal to box, oops, five times box plus two. This is the remainder theorem, by the way, when it comes to polynomials. If you know your division, polynomial long division, it's just long division. It's what do you call it? It's just a remainder theorem, right? This one would be X is equal to three box plus two, and this one would be X is equal to four box plus three. If I did that correctly, I used my modular arithmetic. I used modular arithmetic here, but the way you're doing is a good intuitive way to think about it also. My chat got deleted. Can someone post a question again? Yeah, I didn't see your question here. Let me grab it. Here's the question. So, prime, litter, litter, prime posted the question from a complete pack of, oh, thank you for posting it. Little, little try. Oops, that's okay. So, so far I've gone to here. How would we go from here to 47? How would we go from here to 47? We could subtract the equations. We have three equations. We got two unknowns. We should be able to do this, right? Or, wait a second. These are different. These are different. This is, let's call this YZW, right? So, right now we've got four unknowns and three equations. We need one more equation to be able to solve this as far as I see it, right? Because we don't know what the numbers are here, right? These boxes are different. Let's call these. YZW, that's what we're calling it. Okay, where I'm calling it. YZW. YZW. Oops, then this is, I wrote this backwards. So, this would be WZY. Just to confuse you guys, I flipped it. So, is there any other relationship we have that we can figure out? Because we've got four unknowns, three equations. In mathematics, if you have four unknowns, you need four equations to solve it. This is five blank plus two and three blank is two plus two or both plus two. You can combine them in one equation. 15, but the blanks are different. Z and Y would be different mass over even, wouldn't it? It would have to be, no? Then the number of equations is reduced. But the Z and the W are different numbers. We just have five blank plus two and three blank plus two or both plus two. You can combine them in one equation. 15 blank plus two. So, you're multiplying them. Two times. Two cards remain. Combine those two guys. So, are you multiplying them? I don't follow the logic there. So, three times five is 15. Sure. Like, if we multiply these, then the blank becomes WZ, right? W times Z. But then that becomes four. So, I don't understand why three blank plus two and plus or both plus two. You can combine them in one equation. 15 blank. I don't see it, the truth. I don't see it. I mean, the only way you would get 15 if you multiply those guys. And if you multiply this, you got an X squared. And that one you got, but you can't just multiply these guys. It doesn't make sense. Unless you foil it out or you don't want to foil it out. No, I don't see it. Well, riddle me this, riddle me that. Gicho doesn't know the answer. What would, what did Mask of Raven do to figure it out? You did modular, I use modular arithmetic. I don't know what modular arithmetic is. Modular arithmetic. Nice question. It's got to be a way around this. Yeah, I don't know. I don't know. If someone does know where to go from here, our Discord page would be awesome to post it up, right? To see where it takes us. I don't get it either. I don't get it either, Dante. I don't know how you would combine them to get 15. I mean, we could subtract them, get rid of the X's and those guys. Oh, the relationship we could have would be this. If you just subtract equation one and two, let's see where that takes us. X is equal to 5W plus 2, and X is equal to 3Z plus 2. Subtract this from this, right? So equation one and equation two, subtract them. So this kills this. This becomes zero. This becomes 5W minus 3Z minus 3Z and the two kills the two. So we have this relationship. How's that going to help us? I don't know if it is, right? So 5W is equal to 3Z. Did you try that too, Dante? Modular arithmetic is using remainder, but I don't know how that's relevant. Oh, is that what it is? So that's exactly what we're doing. So over here, here, let me race, give us some more room here. So over here, we would just have 3Z is equal to 5W, right? But that's just combining these guys. We need an original equation. Hi, been lurking, but imagine you take those two remainder cards away and you get a number of cards divisible by both three. Oh, so they're for 15. Also, not sure if that's helpful. That is helpful, Mr. Because what it is, oh, that's of course, we can't just think of it as a standalone thing, right? Are you laughing? Of course, of course. Didn't even think about it, right? Crazy. If in both scenarios, two cards remain, the amount we look for must be a multiple of three, and it must be a multiple of five. So it must be a multiple of 15 as well. That's right. Crazy. I can't believe we didn't think about it. So if you zap this out, then they must be this. So if it's a multiple of 15, so there's got to be two remainder, so X is equal to 15 blank plus two. So how did you get 47 then? So the blank is three, 40, 45 plus two. But how do we narrow it down to 47? All right. How do we narrow it down to 47? It's a small amount of cards that I took out all from a 52 deck. Is that what it is? All good with you, bro. Hey, Nicholas, how are you doing? Just in front. Yeah, all good, brother. Thank you very much. By the way, Nicholas, check this out. My snack, one of my snacks for today, cuckoo and avocados. Cuckoo and avocados. Right? Super delicious. I made the cuckoo like two days ago, so this is a 30. I'm just eating it as snacks. Very good. This combination is fantastic as well. So there's only three options. That's right. We narrow it down. It's by elimination. It's by elimination because if it's got to be divisible by three, multiple of 15, the only choices is there's either 15 cards, 30 cards or 45 cards. Right? So if it was 15 cards and there's two cards remaining, so that's 17. If you divide 17 by four, you get a one remainder. So it's not a three remainder. If it's 30, you add two. That's 32. 32 divided by four is straight up eight. So there is no remainder. If it's 45 plus two is 47. 47 divided by four is 11 and three over four. That's the three we want. So it's got to be 47. So it's by elimination. That's the riddle part. Right? You have to eliminate eight questions and great collaboration trying to solve it. Awesome. Now that's a snack. Now that's a snack, Nicholas. You should try lemon juice and pepper on your avocado. Oh yeah, lemon juice. Yeah. Right now I'm staying away from peppers so no peppers, but lemon juice for sure. And if lemon juice would go, what do you call amazing with the cuckoos as well? Chad is amazing. Little tribe for sure. We've got a nice group of people here, man. Thank you. Thank you. And thank you to everyone in the chat. It's fantastic. Don't make, don't make, this is a great question. That was a great question. Why are we wearing it? Wearing a tuk? I'm staying warm. Also no bell peppers. Bell peppers. The red ones are okay. I don't mind eating the red ones and the yellow ones are okay. The green ones, heart and tummy. Right? This was a great question. This was a great question. And I like doing the remainder theorem laying out like this because you get a visual sort of, it's just ratios, fractions. Glad I could help you entertain us for sure. And you guys too and educate. We're learning. Right? Fantastic. There's nothing better in life really. Well, there are a few things that are really awesome, but one of the great things in life is learning while being entertained. Like, and Manchin and Kuko and Avocado. Right? A great question. Great question. I liked it. I couldn't do the jump straight to this. It didn't make sense to me, but it had to be a multiple of 15 with the two. Yeah, it made sense. The variables threw me off. We have three equations and then you, the way you solve it without the fourth equation, there's only three choices and you reference going to show this to my students tomorrow. Awesome, Mr. Moss. Yeah, for sure. Great question. Great question. And you don't need high level mathematics really. You need to know long division. Remainder theorem would be good. That's sort of grade 11 in my part of the world. So you would have to explain the remainder theorem to people to say that you can lay out the problem like this. Right? Fantastic question. Nice. Very good.