so can you tell me that how would you start that one guys what was your first thought about the question heal it a bit every 10 minutes each of those candles burns for 40 minutes total then they goes out how many of those are alight 55 minutes after he lit the first candle what was your first thought about it do you think we should just kind of create some timeline to be able to show you let's start with that i'm gonna put at the beginning represents by zero minute guys since he lights a candle every 10 minutes okay let's just go with increments of 10 all right more participants are joining 30 40 50 and let's just go with 60 anyway so each of them burns after four minutes okay and then goes out how many candles are alight 55 minutes after alex lit the first one well we all know that 55 minutes is going to be covered here am i right as you see so and we also know that each of those candles are going to warm for 40 minutes their lifetime is 40 minutes okay another participants also joining that's good to be able to find how many candles were still are alight i recommend you to guys kind of find the difference between those 55 minutes and 40 minutes what do we get you get 15 minutes am i right so what do you check out then because some of the friends says it would be four if you check for four guys okay more and more people are coming that's good if we check for answer four guys well well each of them are going to light 40 minutes when i when we are in the minute 50 the first candle oh boy okay people keep coming okay thanks guys all right if you just join us please read the question i already start so because we cannot just wait you know there is a time limit anyway i cannot start over hopefully you read the question try to understand what's going on here if you have some ideas some answers share with us just a recap one of the friends says answer should be c i'm not sure about others maybe they are still thinking if you get answer please put your answer in the chat you can just let soham knows and then he can just let me know okay thank you guys so think about that if the answer is for well we will know when we are in the minute 50 the first candle is gonna be gone okay by minute 55 since each of those candles life basic life span is for the minute i am going to count back to the 40 minute here because they say how many of them are like 55 minutes after he lit the first one all right in that case we need to ignore first 15 minutes here here or we gotta take out those first two channels guys as you see first 15 minutes they are already gone so then what's the number we got here what do you think well i will assume that you are counting with me here guys if we change the color we have one of the candle which he lit by minute 20 then this one then minute 40 a minute 50 then it would be four of them guys our first candle is going to be then this one then minute 40 a minute 50 then it would be four of them guys our friend whoever said four that was correct thanks so much any question for this one if you have something to share please do that via chat say how why what's going on i don't get it hopefully you get it but you know okay guys i'm gonna move all right so i always mention just for new arrivals we gotta talk about clocks and calendars today guys guys all right i assume you already remember that those four step problem solver strategy let's just review we got a mention about clocks today not necessarily on the topic clocks but what type of questions you will see in that met kangaroo okay we have another friend joined thank you so much guys i'm gonna clock 12 hours on the clock face we for most cases we got we just get 1 to 12 the difference of opposite numbers is going to be 6 in general for a clock with n number of numbers the difference is n divided by 2 guys angle between two consecutive consecutive numbers is basically 360 divided by 12 because i am talking about the you know the common clock which is with the 12 numbers we are going to see 12 numbers guys here that's the reason since full circle is 360 degree we just divide by 12 to get 30 as you see the angle between each of those consecutive numbers are 30 and between each minute we know that there are 60 minutes in one hour that's the reason we gotta divide 360 by 60 we are going to get 6 degree the hour hand moves 30 degree per hour and which means basically 0.5 per minute while the minute hand moves 6 degree per minute so the minute hand relative speed is going to be 5.5 degrees per minute the two hands are perpendicular to each other 22 times and they are going to be straight angle 11 times in any given 12 hours after this little reminder we can move on we have also digital clock beside analog clock so as you see this is how they shows some of the examples displays the time in numbers directly may have 12 hours or 20 hours display it depends some problems are about the digital clock maybe all about the digits such as palindromes digit digit sums or other digit relations others are going to include missing digits or kind of mirrored image etc for some of the case we're gonna see guys fast or slow clock when a fast or slow clock slow analog clock shows a correct time again it has gained or lost 12 hours we gotta mention about that in the problems no worries when both a fast and slow clock show the same time the total difference from the gain and loss is basically 12 hours 12 hours all right almost there what about calendar we have a lot of questions related calendar you will see that too a leap year has 366 days any year that is divided by four is a leap year basically except for years divided by 100 but not 400 like for example uh remember those years close to us like for example year 2000 the year 2000 was also 366 days but the year 1900 was 365 days these are the how they divide you know the years in 365 days there are basically 52 weeks and one extra day just think about when you multiply 52 by uh seven you would get 364 guys okay that means we are going to have extra one day that means first day of the year which is one one and the last day of the years is going to be same day of the week which which is non-leap besides February all months have either third or 31 days that will be four full weeks which is 28 days plus two or three extra both days so some days of the week will occur five times basically and days in a month knuckle trick as you see here January starts with 31 February 20 and so far you can just keep counting and see in that diagram you can see which month says 35 days the greater the birth year means the younger the age as you see greater and younger there's inverse operation inverse relation basically between number of year and number of age all right after the summary i hope there is no question i mean so far no one says anything in the chat okay i am gonna move on to first question this is from 1998 and question number eight as you see 1998 is a is leap or non-leap come on okay think about figure out divide 99 98 by 4 and you will find that okay it says in that year in a certain year basically there were four Mondays and four Fridays in January what day of the week was first day of the January of the year let's start timer and so on please tell me how many of our friends says a how many of them says b and so far okay We have been talking about that. Remember, gender has 31 days. Besides, if we have 4 full weeks, that means 4 times 7 is 28 days. So what? Like, what about those extra days? Think about it. And we have one minute, Soham do we have some answers or not yet? You can annotate Soham if you like, you can just, you know, underline which answer they give us or stuff. Okay, we have so far, one friend says it should be Wednesday. All right, what about others? Guys, I'm going to give you more time, I cannot just go with only one answer. Use your time wisely. Again, think about January has to have 31 days. They say in that year, there were four Mondays and four Fridays. Interesting. Think about if there were only four Mondays. Is it possible that that month start with Monday? Think about it. All right, another friend says it should be Wednesday. okay third person says Wednesday okay you say the January start with okay we have another participants come yay okay you said we start with Wednesday let's just check guys what day of the week was January 1st of that year we start with Wednesday and the first day day number one also day number 29 should be Wednesday am I right if this is correct Wednesday day 30 this is Wednesday day 30 should be Thursday you know and day 31 should be Friday think about it they said there were four Mondays also four Fridays if the last day is Friday I'm gonna have four Fridays or no what do you think Would you like to switch the answers? Okay, not Wednesday anymore. I really wonder how many friends are going to switch their answers. So, Suvam, you are saying no one switched their answer yet? Come on, man, B is not the right answer. They still say answer would be B? Okay, explain to me then. Because, look, after this, I believe it's not going to be Wednesday, guys. Think about it. Think about that 28 days of cycle, which is a full 4 weeks. That means we have to have already 4 of those days. Okay? They keep adding 3 more days. Day 29, day 30, and day 31. So, it should be Friday. That means it would be 5 Fridays in general. If Wednesday is correct. Wait, I am glad to see that there is no answer choice here either for Monday or Friday because you know, it wouldn't make sense if we start with those days, it wouldn't be four days. Okay, we are good. No one thinks that. What about Thursday? Do you want to try Thursday with me? Look, if we start with Thursday guys, it's the same logic. But if first day is Thursday, then 29th day should be Thursday, then 30th day should be Friday. Is it going to be four Fridays? No. Well, that doesn't work. I'm just saying, better say it wouldn't work. But what's Saturday? Try Saturday, Sunday, Tuesday, come on. I talk a lot, create a chart and give us an answer, whatever you think. So will we get more answers or no? No, they are still thinking? No. Okay. All right, guys, look, I'm not going to give you an answer. We can just go one by one. Since we are together, I'm going to go with Saturday. Okay. Finally, someone says A. Yes. Yes, but I really want to say thank you so much whoever that person is. All right, look, let's check Tuesday. Look, imagine the first day is Tuesday. Okay. That means day 29 is Tuesday as well. Think about the whole week cycles. That means next day, day 30 should be Wednesday. And day 31 is Thursday. Do you think we are going to have any overlap or any extra Monday or Friday here? No. That means they have to have four, only four of those days, which means when you start with Tuesday, guys, you can have four Mondays and four Fridays. I hope it does make sense. No worries. I mean, it takes some time, but we are just discussing the questions. Keep discussing, guys. Keep reviewing. You got this. Okay. Before I move on, is there any question about number one? I believe there is. Okay. For those, I would just make it visual or make some sort of chart. Charts kind of help you organize information. I would do that if it's easy for you. All right. Number two, I'm going to start timer. This is from 2004 and question number 14. And your time starts. Someone is asking on number one, how did you find the days of January 31st and January 29th? Okay. We can move it really quick. I haven't seen that. I can start the timer. I'm going to respond to this person in the chat. Can you do that? Yeah. Okay. Thanks so much. Thank you. All right. Number two, guys, I'm going to start the timer just for you. I'm going to give you 23 more seconds. Use it wisely. Okay. well well well time is up so if we get any answers can you just you know give us some ideas about how many people says which one should be answered and so forth then if you just you know use your pencil and annotate i believe no one says anything yet okay i should give you more time to think then let's just maybe if there were more thursday thursdays than tuesdays in the first two consecutive years which day of the week appear the most in the second year if neither of these years was leap year remember guys leap year means 366 days we have 365 days i recommend you to try to remember from the previous slides think about this there are 52 weeks this is what we expect this is what we just say 52 times 7 should be 364 look i gave you enough hint come on do the rest if regularly we have to have 364 days passed how many days we have extra what does that mean think about it they say they are saying if there were more thursdays than tuesdays how come there is more thursday what's going on here they are just regular years it means we have 365 days do we still have zero answers so long okay yeah one someone says friday okay here we go what about others i'm not necessarily saying this friday is right answer i just need some participation come on man if you can guess it's fine i'm not gonna give you zero or something or great one friday versus one tuesday so far what about wednesday saturday and sunday hey and another friend says saturday look at that we all spread the answers no one want to say when it's your sunday they're gonna be cry come on or maybe some more votes for friday saturday or tuesday no you can guess remember it's all right to guess oh you guys imagine look we just start with the oh someone take out saturday this is never mind okay okay friday is two so far friday beef tuesday let's see what's gonna happen with the tuesday all right so guys uh we have seven days of those this one week is seven days if i start with like for example actually you know what if i can make it one two three four five six seven this is the how the sequence works this is a week as you know that means guys if i started monday basically that means day number eight should be also monday with the same logic i just told you 52 weeks there are in any year 52 times 73 64 we just do the same cycle 52 times no one cares if you start with monday you're gonna end with monday in 365 days think about it okay we just have same repeating cycle so i am saying if there were more thursdays in the first year that means this is first year guys that means that year has to start with thursday there is no other explanation thursday because remember either one week or 52 weeks it's the same thing cycles and and this is 364 day and one extra day i'm gonna just plus one represents that one one extra day also thursday as you see well the year first year ends with thursday what about second year oops what about second year guys we have same exact number of days it's same exact logic after thursday we get friday you already know that so um which day of the week appeared the most it started friday keep going with same cycle after 364 days we still finish the cycle then one extra days which is also friday for second year of those consecutive years that's it any questions so far whoever said tuesday it was a good try thanks so much buddy but well we are still finding different answers no worries next time maybe any question for that sometimes no never ever okay we are good i can move on all right what about number three this is from 2005 i'm coach number 17 let's see what's wrong with that cat and your one minute starts It has been 45 seconds. Well, well, well, it's one minute guys. I assume there is no answer. So how since you don't say anything yet Okay, guys, I'm gonna give you more time But since we are done with one minute older, let me give you a hint. Look it says For all one answer says eat. Thanks. It says guys from noon until midnight Then it says from midnight until noon. Well, I would kinda divide a day into two parts Think about it in one part, which is noon to midnight The cat do the same cat does the same thing also from midnight to noon The same cat does another same thing Hope it doesn't make sense His first 12 hours That bars in the second 10 hours and You don't necessarily get it's noon midnight or midnight to noon. It's fine Think about it. We have only one answer says E. What about others? Okay, whoever says E, let me tell you something buddy You are close, but I would think something else because you are missing little tiny stuff here For Two hours ago and in a one-hour case you got the concept We have some sort of two plus three three hours. Yes But think about we are talking about two different 12-hour Brides, so What's gonna happen between those segments You No longer anything else I can meet Again our friend says E. You are close You get the right logic. I will just do the calculation mistakes But I would think twice That means E is not right. Come on change it and others you only four answers left You have 25% chance Okay, one person 18 also think about do you think answer is going to be either A or D It's gonna be that small numbers So between 12 and 18 you have 50% chance And we have two friends says 18 already What about peer pressure? Do you feel that it should be 18 because two of them says 18? How do you feel? You I want to get non biased probably man. So if them says 18, but what's bad? No, what's SB? Okay. I Am asking those friends who says see how do you find see? Why do you know? How do you know? It's 18? Can you give us some explanation then so on we don't give us some insight about that why others are still thinking You Look, there is a reason I gave you those time charts or whatever you call, not necessarily you will only visualize, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12, okay, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12, okay, one person says D, one person says D actually, interesting, but it might be wrong, might be a little mistake, I said 3 and 6 are really small numbers, maybe you are checking if I am not sleeping or what, okay, look, we have 12 hours here, think about they say 2 hours ago Clevercat was doing the same thing, if we are in the first hour range from that 12 hours, 2 hours ago would be in the previous activity, do you think the cat is going to do the same thing? No! Then what about second hour? Until that second hour passed, the cat is not doing the same thing because cat is going to move on to another 12 hour, you know, another activity, either sleep or tell stories, I don't know what's wrong with the cat, tell stories, anyway, and it says the cat was doing the same thing that he will be doing in an hour, think about last hour, in last hour of that 12 hour segment, do you think the cat is going to do the same thing after 1 hour? No! Then we cannot include that last hour, guys, 2 hours gone from here and last 1 hour gone from here, we have left over 12 minus 2 minus 1 gives us only 9 hours as you see, we need only that 9 hours, well, 9 hours comes from here, 9 hours comes from second part, the total is 18, whoever says 18 I'm going to give you a high five, whatever you say, thanks guys, okay, so answer was 18, do we have any questions so far? Or we are good? Are we good? All right, we are good, thank you so much, then we can move on, all right, what about number 4? This question is from 2014 and question number 17, guys, have fun! earliest time. There's been one minute and six seconds. Okay, since it was one minute, I will give you some hint guys. Think about guys, there are two bedrooms, not only one of them, and you would focus on splitting those times. Guys, if I just split those minutes and times boys use in the bedroom, anyway, with last three and first three, if I group that way, 17 plus 21 plus 22 should be 60, which is one hour. So if I say one group literally spent one hour and another group spent only half an hour, you see it's not gonna match because there is no even answer. Seven plus one hour is eight. No. Maybe instead of having one group, group one and group two, instead of saying group one spent 30 minutes and group two spent 60 minutes, maybe there is a way to get kind of closer time limits. What do you think? I think you can solve after that hint. You will see. You're gonna split them to those two bedrooms and give me the least amount possible time they can have, you know. So, I have no answer yet? Yes, someone says C, excellent. What about other friends? As you see guys, times are really close to each other. That means, please do not make calculation mistakes. Look at those numbers, 5, 6, 7, and 8. Starting 7, 4, and 5. If you do little calculation, adding or subtracting, whatever, mistakes, you're gonna get wrong answer. That's really sad. Even you know how to solve it, because of little mistakes, you get it wrong. It's sad, man. I don't like it. Okay, we have B versus C. All right, I'm going to start, guys. So as I gave you that hint before, we can just split them into two groups, guys. The first group and second group here. Well, oh, we have only one. Oh, we have two Bs. Maybe it is B then. As you see, guys, we do not necessarily know how many minutes each group should use. To be able to find that, I would just add those numbers, you know, 8 plus, 12 plus, blah, blah, blah. But as you see, I already add them by having last group, which is one hour. First group gives us 30 minutes. Remember those tricks when you add numbers. I wouldn't just add 8 and 10. I would add 8 and 12 to get 20. And since 1 plus 2 gives 3, and there is 7 here, I would just add those last three. Whatever, you get the point. So we have total 90 minutes, my bad, because 6 plus 30. The total is 90 minutes. Well, you know that we should just kind of make a way to divide that into two same groups. 9 over 2 gives us 45 minutes. But the question is, think about this mad kangaroo, man. It's not going to be that simple. We cannot just say 7, 45. Is it going to match with 45 minutes? If you add some of those numbers, you're going to get 45 minutes. It shouldn't be that simple. So when you add, I checked a variety of ways. You're not getting 45. Here, with 1 and 1, you can only get 5, as a one-digit 5. But if you add 12 by 21, 12 by 21 by 22, you should get 65 minutes. No, 55. Not 45. Remember, guys, we are looking for 45, not 55. This is also another trick. They are choosing numbers in that way to be able to trick you. Maybe we cannot get 45. But what about 44, 46, something really close to 45? Well, you can still check other variations. I will try to find 46. Let's see. 17 plus 8 gives us what? If I say 8 plus 17 plus, 17 plus 8 gives us, guys, 25. When I add also 21, it should give us 46. If I choose 7, yeah. If you add other numbers to be able to check that, check your answer, we have left over 22, 10 and, which one? 22 left over, 10 left over, and 12 left over. It should give you 44, guys. In that case, as you see, there is no better way than splitting them, 44 and 46. Remember, we cannot have 44. There is no 744 anyway. After 46 minutes, answer would be 746. The question here is, does it make sense, guys, or no? Look, since no one is going to know your name or who is asking, I hope we can ask pretty, you know, we can ask easily without any hesitation. All right, so I believe there is no question. I'm going to move on. Yeah, we can move on. All right, thanks so much. Then question number five. Look at us. Even the question topic is really odd. We are fast. OK, this is from 2020. Yes, OK, this is from 2022, and number 15. Have fun, guys. Let's start timer. All right, it has been one minute, guys. Let me give you some hints here. As you see, yesterday, I set them both to correct time. But when I come back today, one of them shows 11 AM. Another one shows 12 noon. That means there is a one hour difference. You need to figure out, how come we get that one hour difference? What's going on? I will check the first two, three sentences to get some hints. OK, this is another question. Not necessarily give us answer. How would you start solving this question? What is going to be the first step you are going to take? Can you just put them in the chat, please? One friend already says, answer should be C. All right. Is there any more friends? Are there any more friends saying C or B or D or none? Again, guys, if you couldn't find the answer, please share what is going to be your first step here. What would it be? What do you do? Are you going to draw a picture of clock or what? You can do that too, if you like. Is this going to help you? OK, so would you like to give us some hints? Or how would you approach the question? I mean, anything. So we know that the two clocks are a one hour difference. So suppose you have the two clocks that are set to the same time. And one hour later, how many minutes apart would they be? That's your hint. Thanks so much. That's going to work. Come on, guys. OK, literally give the answer. No one besides our friend says C. Come on. I'm going to wait a little bit to get more answers. I'm not going to do my lesson with the screen here. Or only Soham. He's not my student. You know that already. And we get only one answer. We can do better. Do you want me to motivate you? Do you want me to sing for you? I have a terrible voice. It will motivate you, believe me. Look like no more answer besides C anyway. Okay, yeah, one more answer. One more friend says answer should be B. What about other friends? We all know there are more than two kiddos in this classroom. Okay, other friend says C. So far, C is winning over B. Maybe someone else says B. Or even other answers, A, D, and E. All right, you guys, let's start then. It's going to take some of your time. Look, like Soham says, guys, in one hour, I literally underline those words for you and circle some of them. If one clock gains one minute and another clock loses two minutes in just one hour, with that gaining and losing minutes in one hour, the difference between those clocks is going to be three minutes. Am I right? Think about it. All right. Think about it, guys. In one hour, the differences are going to be three minutes between those two clocks. Well, they said that person, it says, I didn't do that. I don't know who said I, but whatever. The person set the time sometimes, then the person look at them today, and that person saw that the time shown one was 11 and another one is 12. That means there is already one hour differences. Instead of putting here one hour, I am going to make it 60 minutes, guys, because it doesn't make sense if I just put one hour, you know, 60 minutes. To just think about it, in one hour, actual time one hour pass, there is going to be three minutes between those two clocks. How many hours pass, then there is going to be 60 minutes difference between those clocks. Well, you can say one hour over three minutes. You can set the proportion however you like. X hour over 60 minutes. If you do those little tiny butterfly method, cross calculation, multiplication, whatever you call, it's going to give you something. So three times x is going to be 60. Well, may you cancel? x is going to be 20 hours. As you see, guys, it's going to be 20 hours. Well, if I just count from 12, I mean, if I count back from 12, I would miss something. Think about that. They say one clock gains one minute every hour. That means after 20 hours, that same clock gains basically 20 minutes. Am I right? You know, one-to-one ratio. And if that clock was 12, because why am I choosing 12, not 11? Remember, that clock is the faster one because it's always gaining. Another one is losing. That loser should be 11, you know, but that our champion should be 12, because it's gaining something, you know, whatever you say. So in that case, at starting, that clock already get 20 minutes. 12 minus 20 minutes give us 11.40. But you're going to say, sir, there is no 11.40. I know about that. Wait, patient. So after 11.40, we know that there is 20-hour difference. We already found that. If you count back from 11.40 to 20 hours, you should get 3.40, guys. That means I am proud of you guys. Whoever says C, I am proud of every single of you. Even Sunday, you are coming to lessons. Thanks so much. But C, I am proud of others more, just saying. Thank you, guys. Any questions about this number 5? Or no? I am going to move on then, okay? Yeah, we can solve one more. Yeah, we have 5 more minutes. Come on, you got this. Where is next one? I got to click. All right, next one from 2002 and question number 23. Have fun. Okay. Let's start the time. Bye-bye. or it has been one minute. Are there any friends who want to share something now? Oh yes, it was one minute. Let me give you something else. In one month, we are talking about any month which Sundays fell on even days. Think about it. Okay, someone says Thursday. Thank you so much, buddy. Think about it. If we have 28 days, guys, because it says in one month. We don't know which one is that. Oh, okay. Maybe I should shut up so we are getting more and more answers. Thank you, guys. One more. Is that the same three friends from the previous question? Give us some answer. Hopefully not. Oh, that's good. We are different friends participating. That's nice. Hopefully, none of our friends are just looking at the question and thinking nothing about that. Okay, guys. If we had 28 days, think about it, guys. It says in one month, three Sundays fell on even days. Well, let's see. The first day is Sunday. I'm just, you know, doing some calculations. Number one is Sunday. We just go with one week and this is day number seven and this is plus one. Or when we just start in the second week. This is day number eight. This is day number 14. Whatever. Day number eight should also be Sunday. But think about it, guys. In one month, three Sundays fell on even days. Well, the first day was odd day and in the second week, day number eight is even date. And they say three of them fell on even dates. Look, if we had only 28 days, think about it. It has to be only two Sundays on even dates, not three Sundays. I hope that makes sense. Well, in that case, I would work on the first week and I would try to give some of the even days to Sunday in the first week. With that logic, I hope it makes sense. I would start with, guys, second day of the month, which is Sunday, which is even day. That means if I add also 14 days, remember that it's going to be even date. Does it make sense? Because day number two, then day number nine, we just add seven. It doesn't work. Add another seven. Day number 16. Okay. So we need more. Am I right? Yep. You add another seven. Day number two is even. That works. Day number nine, no. Day number 16 works. We have to add another day seven, which is, what's 16 plus seven? 23. Doesn't work. And I have to add another seven days, because this is how Sunday is going to fall on even dates. And day 30 is also Sunday. As you see, second day, 16th day, and 30 days are going to be Sunday in that case. And the day is having either third or third one. We don't need that. So, after that, we are going to look at what day of the week was the 28th of the month. Oh, okay. Someone switched from Saturday to Thursday. Okay. We know that, guys, date number 23 also was Sunday. We just count. Well, we can just count back. Day 22 should be Saturday. Day 21 should be Friday. And day 20 should be Thursday. What was the story? Go ahead. I think the person who answered E thought that it was what day of the week was the first day of the month. Because they knew number two was going to be on Sunday. So, they put E for number one instead of number 20. Yeah, that makes sense, man. Thanks. Guys, we know that you know a lot. Please make sure we are checking your answer. Okay? We're going to do some mistakes, and then we're going to learn from our mistakes. No worries. I'm not judging. Thanks to everyone who participated today. And is there any question for today, guys? Not necessarily from that question. Others? Something about day, month, time? Making you upset? Okay. I hope your days are going good. And I'm going to see you next time, guys. Take care. Bye. Bye.

mathematical problems

time and logic

Mathematics Kangaroo

candle problem

clock and calendar

leap years

problem-solving strategies

systematic approaches

arithmetic and algebra

collaborative learning