Welcome to our another Mad Kanga Webinar session. So some of the rules, I can just go really quick. Please keep your camera off and your microphone muted during the classes. You should have your handouts, paper and pencil ready to take notes and work through the problems. You can send chat to host and co-host to ask any questions. And at the end, you can focus and have fun. One another reminder guys, please make sure you turn off the camera and mute it yourself. All right. Just a quick recap about what's Mad Kanga. It's individual math competition for kiddos from one through 12th grade. Since your level is going to be like greater than five, it's going to be 30 questions for 75 minutes. There are like three categories, easy, medium, medium level and hard problems. And they have certain amount of points for you. A problem is a question that demands much thought and resourcefulness before the right approach is found. That means when we solve the problems here, like basically like pretty much we are going to do problem solving a lot. We are going to work with different ideas and discuss. When I ask you the question, I don't necessarily want you to find the answer guys. You can just even via chat, of course. You can share your ideas via chat by saying, sir, I would start with that way or this methods or anything make works, you know. Steps, some of the steps can help you to solve many Mad Kanga problems. First thing first, please make sure you understand the problem, determine what it's asking and use critical reading skills. Some of the questions may say, which of the following is not the right condition? You should check the answer choice and accordingly get the answer, right answer. Plan how to solve the problem. How can you tackle this problem? And what do you need to solve it? So plan is really important. Some of the problems or questions, you just need to read it to find some sort of relation between critical information, or if it is like kind of related geometric, critical shapes or critical part of the shapes. Carry out your plan and carefully complete your calculations or organize your thoughts and steps. Write out your work, so minimize errors and check for yourself. It's really important as well, because I see like many, many kids about like in 14 years in education and teaching my career, many kids I see that they get the answers wrong because of little tiny mistakes, you know, calculation mistakes. It's really sad because you know everything about question, you are able to solve it, but because of that little mistake, you are getting that wrong. That's sad. Look back and check and reflect. Does this answer make sense? For example, if they ask you to find like, let's say it's about one of the farmer, at the end you are going to find number of sheep that farmer has. You cannot find 45.5 amount of sheep. You know, it's obvious it has to be integer. It's also supposed to be positive number, you know. Also for some of the cases, let's say you have another work problem. It's asking you to find this distance between two different cities. You cannot find negative 80 kilometer. It's not possible guys. You know, distance has to be always positive. Some of the, you know, really critical information. At the end when you find the answer, you need to ask yourself, does it make sense or not really? If you are able to, I recommend you to just, you know, if it's kind of related equations, I recommend you just plug in the number you found and check if it is, you know, right. Okay, so today we are literally, we just started introduction. That means we are going to just cover variety of topics guys. From variety of, we are gonna check variety of questions from variety of topics, of course. That means you do not necessarily focus on one idea. It's gonna be different ideas. And again, I am open to all different solution methods as well. There is no right or wrong method here. We can just discuss anything here. Okay, problems for today, we'll give you an overview of the type of questions you might ask on Math Kangaroo Contest. Some Math Kangaroo questions will cover topics you may not yet have studied in school. That's totally fine. Stay enthusiastic about the opportunity to learn something new. In the upcoming weeks, we will explore these mathematical concepts one by one to help you become proficient problem solvers. All right, let's start with this week's first gift. This is my first gift for you guys. The question was from 2011 and number 13. Okay, this is what I need. Remember, you gotta keep the camera off. You just keep muted. Whatever answer you find or whatever you think might work for that question, please share your ideas. Then Soham is gonna check and he's gonna share with us. I'm gonna ask him, you know, how many friends has answered this? A, how many says B, and so forth. Then we gotta check together, okay? Let me start timer. I'm giving regularly one minute for each question. If we get no one, I can give you more time. All right, your time starts, Soham. All right, it has been one minute already, guys. Sovam, do we have some answers? Do they share their answer on the chat or directly with me? Let's see. Oh, OK. Guys, just a reminder. Please make sure you share your answers with the group. Because if you just send me a direct message, I can see that. But Sovam is not able to see. At least you can send Sovam as well. You know, while, you know, checking questions, answering, you know, explaining and at the same time answering. It's got really difficult for me. If you share your answers, it's going to be better. We got one for C. Awesome. And I get four kiddos says C as well. I mean, three kiddos says C as well. So far, four friends says it should be C. I'm not sure about others. OK. If you have any ideas what you did, you can just share really quick. Or I can just start quickly, guys. He has nine pearls in which weight is given amount of grams. He made four of them. In each necklace said two of those pearls. The pearls in each necklace weighed 17, 13, 7, and 5 grams, perspective. What's the weight of the pearl that was not set in any of those necklaces? Well, when we add them, guys, we have one through nine. Basically, you know, when we add them, what would you get? One plus two plus nine. If you like, instead of adding them one by one, remember, you're not going to use calculator during actual exam. We can work with different methods. You can just put the same arithmetic sequence from backward. Plus one. Or you can just add them. At the end, you have 10 of those one plus nine is 10. You have 10 of those 10s, guys, as you see. It should be 10 times 10, which is 100. But as we all know that you cannot have 100, guys, because I am talking about two different sets here. I'm in sequences here. Oh, another friend just joined. Okay. So that means I am going to divide by two, which is 50. That means one plus two plus three plus whatever, plus nine should be 50. So as you see, that jewelry already use some of the necklaces, some of the purse in this necklaces with given weight. We have 17. It's 17 plus 13 plus seven plus five. They already used. If you add them all, what would you get, guys? 17, 13 should be 30, 37, and plus five should be 42. Yeah. Okay. So here is the first thing I am going to ask you. If you say answer should be 50 minus 42, you're going to get eight. That means I just missed something really quick. Let's see if our friends tell me, sir, you missed something. No, actually, you explained the answer to me. Oh, someone says 45. Yes, guys. Sorry. I might miss that part because we had nine numbers, not 10. This was my mistake. Sorry. Nine times 10, not 10 times 10. Okay, because one through nine, we have nine numbers. Sorry for that mistake. Then we should get 45, not 50 actually. Okay. Nine times 10 gives us 90. But since I had like those two different algebraic sequence, it should be 45, guys. All right. So after we found 45, the total amount of total weight should be 45. But we found 42. Well, what's the difference? You just get this one easily. All right. Any question we get here? I see many, many chats. I hope you're not keep sending the messages to me directly. Okay. Guys, one another reminder. Please, please send the messages to the group or just Soham directly. If you just keep sending all of the messages to me, I need to check the messages at the same time, explain at the same time, answer your questions. It's going to be a little bit tough for me. I will get the point. Hmm. There is no way. Okay. So it says one, for instance, there is no way to send it to group. Okay. Can you send directly to Soham then? You should be able to send him as well. At least. So are you getting any direct messages? Or not yet? Because you are right now. Co-host. So you should get a chance to get the message as well. Direct messages. So I cannot hear you. Are you able to. One of the students did send their answer to me. Yeah. That means you can get a direct message. Okay. This is what I was telling you guys. Instead of sending me, can you just send Soham, please? So it will be easier for us. And go faster as well. Okay. All right. I assume there is no question because you would say. You would ask your questions, I believe. Okay. We can move on then. Bye-bye. All right. It is one minute. Do we get some answers or not yet? One person says B. B, okay. All right. The one digit of a certain three-digit number. We have three-digit number guys, as you see. Because one digit is two. We move this digit to the beginning of that three-digit number. As a result, we will get another three-digit number, of course, that's smaller than the original number by 36. Interesting. What is some of those three digits of this number? As we are swapping, let me just give you something since we have only one answer right now so far. Let's see. We have this number, the rectangle, square. These are representing hundreds and tens digits, and we have two. This rectangle and square represents one number. What happened is that we moved this digit to the beginning of that number. As a result, we get that three-digit number that is smaller than the original number by 36. That means if I subtract 36 from this original number, I would get something like that. We moved two to the beginning. Then this is the tricky part, guys. When you move two at the beginning, that rectangle, I mean, that triangle is going to be in the middle, and that square is going to be at the end. I hope it does make sense because you just switch it and make it a completely new three-digit number. Then you will work with the numbers to figure out what you can find. I hope that hints give you something. I shouldn't get only one answer, only one answer. I mean, come on. do we have more answers or I'm gonna solve guys come on no one one person says B and another says D all right okay look at you guys no one says C what about a should I say E guys you are doing like regular subtraction after if you figure out this piece 2 minus 6 doesn't work we got a 12 minus 6 that's 12 minus 6 so you got the box put that value here you know All right, I'm going to start, guys. I want to show you as many problems as possible. So 2 minus 6 doesn't work, you know. We get one of the 10s here. We have 12 right now. 12 minus 6 should be 6. That means that square shape should be 6, guys. I would say 6 minus 3 is something here. But we already move one of the 10s here. We have left over 5 here. 5 minus 3 is 2. And that also makes sense. At the beginning, we should have 2 anyway, all right? Because we just carry out. Well, just add the numbers. 2 plus 2 plus 6 is what? I guess you got it, hopefully. Any question about this one? Look, this one from 2006 and number 20, this was kind of a relatively difficult question. It's not that difficult, but I believe many kudos messed up here. When you move that 2 to the beginning, you just messed up what you have left over, maybe between that triangle and square or whatever. That should be the case. I assume there is no question, because no one sent so many chats. OK, I am moving on now. All right, what about number 3? This is one of the interesting ones. Checked it before. The British mathematician, that person claimed that he was x years old in the year x squared. What? You got to find year of x squared. Careful with squares. He is known to have died in 1899. When was he born? Let's start the timer. Remember, you cannot use calculator on the actual exam. You got to find some easier ways to find square of the numbers, by the way. All right guys, it has been one minute and five seconds. Any of our friends says anything? Not yet, Soham? No one says anything? That's sad, man. I'm gonna cry here. Since it has been all at one minute, I'm going to give you some hints, guys. Think about something squared is approximately 1,800 something. It doesn't have to be 1,900 because that year, he has been dying. We know that 4 times 4 is 16, you know, if you have those four digits, we can think if 4 times 4 is 16, then 40 times 40 should be 1,600. You can say, sorry, we still have like 200. I am aware of that, but since you are improving by squares, you are actually close. You can check with 41, 42, 43, and so forth. And let's see what's going to make sense, okay? Let me give you 30 more seconds. all right another 30 seconds passed i believe no one get an answer so don't tell me anything okay i'm gonna move on now i mean i'm gonna start solving guys if we i am about to explain something i hope someone didn't send me direct message hey we got one person says e okay three say a and another says d okay you said three person says a one person said b one person said e okay yeah do not send direct message because we are kind of you know wasting time anyway uh you can send message to so on here we know that 40 times 40 is 1600 but we are kind of close about 200 to 300 let's start with 42 what would be 42 square you can either multiply them like that 42 times 42 or if you like since i believe you all know that a square minus b square is equal to a plus b times a minus b or you just learned that if you didn't know i don't know if you cancel that b square you gotta add b square both sides this is how you find a square this is how we find any number square you gotta say sir what are told about let me explain instead of finding 40 times 42 you can just make this number by adding 2 and subtracting 2 because 40 is 4 and 0 you know it's easy to calculate you can make it 44 times 40 which is 16 16 1760 so since you had only 2 times 2 just add that 2 times 2 which is 4 it's it means 1764 which is 42 square i mean either of case works for me however you want to do i'm just using different method if we say this person was born in 1764 and died in 1899 no like how many years did he live like 130 140 years it's really still small number what about 43 instead of my finding 43 times 42 i'm gonna do 46 times 40 you know and at the end i'm gonna add 9 because 3 times 3 is 9 so do the same thing 4 times 4 16 24 18 4 but it should be 1840 then add 3 get 1849 that means 43 times 43 is 1849 this might be the answer let's see uh what about 44 we're gonna find 44 times 44 i'm gonna make this number since it's still close to 40 40 times 40 and at the end i'm gonna add 16 because 4 times 4 is 16 that's for 16 32 one 936 if i'm not mistaken yep it should be 1936 so if that number is 1936 and if he already have died in 1899 44 shouldn't work guys well in that case the only makes sense answer is 43 and 43 square was 1849 they say he claimed that he was x years old in the year 42 he was 43 years old when it was 1849 when was he born so you know in that year 1849 he was 43 years old then let's just do the subtraction oh six it should be 1806 guys whoever finds a i am proud of you thanks so much i'm not gonna ask you how old was he when he he has been died he has been dead anyway any question for us for this one it was number 15 but i saw that from past classes many many kids get this one wrong anyway i don't know for some reason that might be tricky as well let's move to next one then okay number 25 from 2006 let's start your one minute All right, one minute is up, so I wonder if any of our friends are able to solve that. All right, one friend said C, another friend said, two friends said B. All right, one friend C, two friends B. Oops. All right. I wonder about others. I believe so, I've got some technical problems. Anyway, so if I get one more answer, I can start. Or if you want to share your ideas, I'm open to that, too. Look like I really need to check the chat as well. Another friend said C. Another friend said B. All right, guys, that means majority of us either says C or B. For that type of questions, guys, as it is kind of speed problem, and we don't have too much information given it's kind of broad question. If he increases his speed by 3 meters per second, he will arrive at town Q, whatever town Q is, three times faster. That's it. How many times faster will Peter arrive at town Q? If he increases his speed by 6 meters per second. So here is the deal, guys. We all know that distance is equal to speed times time, or velocity. Let me just erase those. Or we can say that velocity is equal to distance divided by time. This is the basic physical formula, or the math formula for this type of questions. If we try to apply this rule, it's going to take a lot of time, at least like 15 minutes. You know, add T something, add V to do something, find X, but X is the same, X cancel out, and stop. Because we have one, two, three different variables as you see. And we haven't given any of those quantities by a number. They just say increase by 3 or whatever, you know. So in that case, guys, we need to compare those given speed by adding speed. Like, what's happening here? They say, I want you to check that second sentence. They say, if he increases his speed by 3 meters per second, he started with V, and he make it V plus 3. That means he's going to arrive at town three times faster. Guys, think about for any of the speed problems. To be able to arrive, or to be able to take the same distance three times faster, that means you are literally multiplying your speed times 3. You know, this is what that means, because we are talking about the same distance, the same distance between two cities. Anyway, I can make it V plus 3 is 3. Then it should work with finding some of the something about V. We can solve it really quick. Take out V from both sides. As we get 3 is equal to 2 times velocity. Well, you divide by 2. That means we can say that his speed was 1.5 meters per second. This one was his initial velocity, initial speed. OK, at least we found something. How many times faster will he arrive at town if he increase his speed by 6? OK, he started 1.5. Increase means you got to add. I believe you all know that. Then his new speed becomes 7.5. They say, how many faster he's going to arrive? That means, guys, they are asking us to compare those two speeds, 7.5 and 1.5. Compare means you are going to divide them, 7.5 over 1.5. I know we all not necessarily like the decimals. We can just multiply each side by 10. 75 over 15 gives us 5, guys. That means answer was 5. Whoever find B, I am proud of you. Thank you so much, guys. Of course, I am proud of others as well, because you at least tried to do something. That's cool, too. Thanks so much, guys. All right, answer was 5. Any questions about this one? OK, I got some chat, but as you see, guys, I cannot really check the chat directly while I am. Oh, yeah. Yes, definitely, that works. So it should be. Anyway, I believe his device has some issues. Anyway, guys, any question? Being quiet means no question, OK? You can move next one. Cool. So I ordered to make you cause a couple of times. I'm not sure what's going on. It's almost permissions now. What was that? Have co-host. I have co-host permissions and one person answers D for number five. Oh, we can order it. Okay. Someone says that's cool. Start time. Maybe I can just give you only 30 seconds this time. Okay. All right we are done with half a minute so anyone else give us any answer besides d we have only d that's it all right someone keeps direct messaging me okay okay one of our friends said it should be c all right very good i believe we gave you enough time i'm gonna start really quick so so finding average means you need to remember first how to find average of the you know given group of numbers in this case guys we are finding average age of the players on a certain certain team with 11 kilos so finding average means you are going to add all of those ages of those 11 players we don't know them yet let's just say the total is x divided by what i did was since that team consist of 11 players i just divide by 11 and at the end i found average which was 22 this is the first case what i did okay i can find their total age easily here by cancel 11 since 11 is division here i can multiply both sides by 11 to get you know what's x when i multiply 11 times 22 should be 242 i believe x is two so please do calculations if i make a mistake you can just tell me okay because 11 times 11 is 121 i just double it 242 i guess anyway uh during a game one of the players was injured and had to leave the field that said the average age of the rest of the players was then 21 we are just we just know that right now we have only 10 players left you know so nif total divided by 10 because we had 10 kilo left or players left and at the end i get the average of 21 as you see well to be able to find nif total i need to multiply both sides by 10 because it was division that means nif total becomes 210 guys as you know guys there is only one difference between the actual the previous total and nif total one of the players just injured and they just took him out of the you know game well to be able to find that we can just look for the difference 242 minus 210 give us the answer guys you should get 32 as an answer answer was d whoever gets 23 maybe our friend just made messed up with you know digits or i don't know what any question about this one i still get some chats okay all right guys any question about how to solve number five or this type of questions relates average by the way any part you got stuck you feel stuck or you are good okay i assume you're good we got a move look since i'm not going to tell any of yours name don't worry about asking questions guys it's fine i'm gonna say one friend asked why and how we get d or one friend says he or she i don't even know like you are he or she whatever so one friend said that person couldn't get that piece you can ask that's totally fine no worries okay anyway we can move on to the next one then number six and your time your one minute starts We have 50 seconds so far, and one friend said D, two friends said E. Okay, we have D got one point versus E got two points. One and two. All right, let's start guys. For those type of questions, you need to remember all of those properties of the triangles. So which of those angles in triangle ABC can we find the measure if we know the measures of angles one and two? Look, if you feel confused, or if you see, sir, we have A, B, alpha, beta, gamma, theta, whatever, all of those numbers and everything, and it's really confusing to me. It's fine. Let's just plug some angles, you know, for those numbers. Since we know those angle measures, let's say angle one is 30, and angle two is hundreds. Why not? In that case, guys, if you remember the vertical angles rule, which applies pink color here, that angle should be equal to 30 as well, because they are vertical angles. We found that one of the interior angles should be 30. Well, we can say that straight angles here, the total is 180. We call them supplement angles, guys. So a hundred plus angle A should be 180, since they are supplement angles. Okay. Then we can just take out hundreds from both sides easily to get A equals 80, guys. Supplement angles, guys. Well, right now we know two of those interior angles in the triangle. One of them is 80, another one is 30. I believe you remember that there is another rule that represents some of the interior angles of any triangle is 180. So A plus B plus this one should be equal to 180 from some of interior angles. Then we got to keep working. We already know A and B, which is 80 and 30. No, not this one. 80 plus B plus 30 is 180. If you do the calculations, guys, you should get these equal to 70. As you see, we are able to find the measurements of every single angle. Okay. I have been getting some chats. Let's see what we got here. Okay. Yes. Excellent. Our friends get, a majority of our friends get E. Thanks, guys. I assume there is no question. If it was, you could just send me via chat, you know. You can still ask. All right. Clear all of those. And go to the next one. And number seven. When you divide the circle with four chords, like based on those straight lines, you know, how many parts can you not get? Remember, I have been telling you, make sure you read the question carefully, which one you can not get. That means out of those five numbers, four of those answers you can get. Okay. Let me just start timer and give you some hints. And you should, guys, draw the circle. It's about circles. Remember. Two, three, four, and five. And you can just play around, like, using those straight lines. Let's see what we get. Okay, it has been one minute and one of the friends says answer should be E. All right, let's see about others. E got one vote so far. Another friend said also E. Oh no, wait, actually three different friends says E. Look at you guys. Look like answer should be E. We don't know that yet. Oops. Plus two. Okay, one more. Let's see what we got really quick and I can stop showing that for you. Okay, one more friend says answer should be E. Wow, all right. Okay, answer is E. I'm not gonna solve that. I know. I will. I just keep getting chats. Okay, one more person says also E. Look at you guys. All right. So I believe you get the majority here. If we just, you know, draw the lines really quick, guys, without taking too much of your time. One, two, three, four. You know, you can just get five of them. Seven should be something like that as far as I remember. One, two. Yep, four plus three is seven. Nine should be like that. Let me see. So far we have six. If I put another like that, that should give us nine. Am I right? One, two, three, four, five, six, seven, eight, nine. Yep. And we can check 11 and 12. It's gonna be either 11 or 12. Like that. And when I put another one, should be something like that. Let's just count. One, two, three, four, five, six, seven, eight, nine, ten. That means I missed something. Okay. Is it gonna be? The thing is, you draw the four lines. Yes, I am gonna draw four lines. So I have only three lines right now. I put number four here. And just to check. And if I'm not missing it, give me ten. One, two, three, four, five, six, seven, eight, nine, ten. I am looking for 11 or 12. That's the reason I took out one of the lines. So it should be something like that. Draw your fourth line. There are three lines. What was that? I'm gonna put one more line. So this is what you're saying. If I put line like that, let's just count. One, two, three, four, five, six, seven, eight, nine, ten, 11. As if you just keep playing, you're gonna get 11. So we know that we got five. The first one, we got seven of them. We got nine. And we got 11. That means, guys, there is no way you can find 11. Since many friends get this one anyway, I'm gonna just skip without even asking if you have any questions. All right. The next one, we can solve one more. Yes, we have six more minutes. Come on. Let's see. Oh, someone ordered a text. You get the answer? Even you just see the question in a couple of seconds? Interesting. Okay. Let's see if our friend find the answer or what. Okay. Thanks so much. But I said about six minutes. But, yeah, you are right. We have five minutes left. Okay. Thanks for the reminder. Two messages. Two of the friends says it should be C. Okay. Who knows? We get more messages. And one more friend said C. Another friend said A. Look at that. C get three points versus A get only one point. And one more friend said C as well. Okay. C get four points. All right, guys. Let's just keep moving. Well, here. What's the most number of rectangular blocks with sides two, six, and one need to make a cube? Okay. What I'm talking about, guys, least common multiple of two, six, and one. We can see LCM. LCM of two, six, two, six, and one. Is what's the number? It's going to be six. Am I right? Okay. Since LCM of two, six, and one is six, guys, what we need, we know that one side of that bigger cube or that cube is going to be six units. You're going to get six. So how many of those rectangular blocks do you need? We can just find the volume of the cube divided by volume of that blocks, basically, because we are putting in or we are just generating, you know. So we have six times six times six divided by we get two times six times one. As you see, I am kind of comparing the volumes. Volume of cube over volume of the small item. As you see, guys, I didn't calculate because I don't need that. If it is possible, guys, you can keep the answer like that. And you can simplify. So we have six and two. Simplify to get three. And six times three gives you 18. Since many of our friends says 18, I believe there is no question. We have only one minute and some sort of seconds. Maybe we can just take one more question. Let's see. If there is any question, just ask me really quick, please. We are almost done with the class. All right. they shook hands exactly once. With everyone they already knew. Not necessarily with each other, you know. These are the people, guys. It might give you some ideas to generate unorganized information. All right. Two of the friends says B. All right. You get two votes. What about others? I get one more answer. It's almost time. I can just start solving, too. Come on, one more. One more answer, one more friend also says B. Then maybe it is B. Let's see. All right, guys, if you just keep sending me messages, I might not be able to check it because it's a little bit of time. I will just solve this one really quick and we can end the session. All right, so Ellen shook hands only once. Okay, Beth twice, Claire three times, and Dora shook hands four times. Look at Dora, guys. That means our friend Dora shook hands with everyone, basically. Am I right? You know, and Dora is gone right now. We are looking to find how many times did Eric shake hands. We don't know that yet. At least we have just one with Dora. Anyway, we know that Ellen shook hands only once. Oops, and Ellen gone as well because Ellen already shook hands with Dora. Dora shook hands with Ellen. That means Ellen shook hands with Dora. That's the same thing. Oops, my, yeah, you see that. You already cannot. Yeah, like that. Anyway, Beth shook hands twice. So Beth shook hands with Dora already. This is one. Beth cannot shook hands with A because Ellen is gone. Cannot shook hands with Dora anyway. What about C? And Claire shook hands with three times. We have only Beth and Claire we got to think of. So if I say, guys, Beth and Claire, you know, basically shook hands, it's reasonable. Beth is gone, as you know. And Claire needs one more because Claire shook hands three times. Well, I can just match Claire with Erin or Eric. And that's it. In that case, Eric shook hands twice. Any question with this one? All right, that means no. I enjoy our webinar class today. I hope you enjoy as well. And I am going to see you next time, guys. Take care.

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