 ज़ब आप शबने हैं वाँई आपाशवर्द बज़े, दब आप वाँई आप रवी आप भगए बज़े आप बगए आपवग बगए, अवी वी और पचशी बचचे आ अवी आप पची आप बचचे आप यह चाहँँँँँँँँँँँँँँँँँँ matte वाँई औरबाै को वोचर में घर nevertheless, जक्यी भी औस �彗 पुह फरे, is to lift the garbage. अगन व सके लै Regarding ٥, बौबा हाँतón, टेःो मगर रेए� sólo आफ नissementschair. बॉफकत अगे ज़ाम omega Carrada to 이게. अपके स्टींबोड का मद्शाय्ट अब के साबने है सो वारडत स्टींबोड मद्शीट से स्टींबोड का मतलप क्या है सो स्टींब का जो स्पलियग है स्ती आम अजत ठा Ahora स्टी का मतलब होता है ँथन इपनग़े प्री इनजिनरिक after a for art and m for mathematics so, we meet on Monday of each month, on Monday of the each month at 11 o'clock and This is a topic of Steam which we discuss, talk, discuss with each other or find new things or learn and we do this in a very fun way so I request that whenever you want to say anything you can put yourself in mute or you can type on the chat box सेज्डन को जादा इंटरटाउ कर सकें जादा मजे लेए सकें अप देख सकते होमारे पिछले एपिसोड टी अवेलेगल है पिछले आपपिसोड आपको हमारे यौटुट चनल के प्रेलिस्ट में लिज जाँँगे अज आज हम और ये भी हमें बताना चोंग, कि हम इसको अलग अलग भाशाव में करते है, इंगलिष, हिन्दी, मराथी, गुज्राती. तो हम ये जो आज के अईपिसोड़ हो भिन्दी में करनेवाले, बत इसको हम बाद में इंगलिष में और दुसर लंगुज में बी अपलोड़ करेंगे, तो आप जरुर वोट शेक्टर नाम न योटिब चानल दे. तो अब आज हम आज के पिसोड़ के बाड करते है, आज हमार ये सा जुदने वाले है रवी सिनहा, और हम मागkke स्झ्ट्ट्ट्ट्ट्ट्ट्ट्टट्ट्टट्टटटट地 कागी जाडूदी सा नाम है, मागक स्फ्ञेर. दोनो चाट में लिए भाखी भी जों तीमोटेः के ती मेंबस है अपने रहने का अपसे यंट्राक कर तरहे हैंगे तो या, वैसे कोन आपनी दम्मस खियसका साम पहुत लिए मैं अपने रहा है क्या अपने अपने जवान्क की लिए मैं अपी अपी रब सकते होग? वियस जुभांकी न बोलारे.े उस्बनगी सर roam kilo अलनग लिए मैंग के रब व्लाय गुत है. уGolden 56.1982. Okay. This is also 27. correct. Mayank has also replied, 10.1611. Very good. 10.1611. Okay. So you have to see that the responses up there are not match. So you have to find unique combinations. Okay, the combinations that is done, you have to type and find a new one. अबीशन दिशा आप मुझे बताते जाना, तो मैं यहाप नवबस लिए दिश्टी केरे है, 10-15-2, और बरखा शर्मा केरे है, 10-15-2, 16-10-1, तो वो हो चुके है, तो और अंवाच, मैं तोडा सा मुशकिल करतो, मैं नवबस को शफल करतों, तो मैं शफल करतों, सारी नवबस 6, 6 तो यहाप नहीं है, तो यह तो पोसबल नहीं है, अपको एं नवबस में से चुए तरपलेट स्छूएज तरन रहा है, 16-1-10, खुशन प्रीथ 16-1-10, yes, यह 27 रहा है, Okay, यहाप एक 16-1-10 के बाग्की छेए नमबस यहाप दिकर है, एन में आप उप खुशन शुएज दूंपार यो क्या? 9, 2, 17, 3, 8, or 15 मैं? उके तो रवी आप एसा कैना चाते हो कि ये नों नमबर में से ती नमबर चूँज हो चूके है, बच्चे हूँए च्हें में से हमें 27 दूँना है, एसा. उको, अखे, अखे, वच्चे हूँए ती नमबर से है, रिस्पोंस आया है, एक 15-39. 15, C and 9. बच्चे, 17, 28. असकर, सम है? एभ, वब त्च्च्चचचचचचचचचचा, गडूँ भी, आप आरी और शब के जैगा, बच्च्चचचकचचचचचन, एभ कत चोगा ळोगा रेए, तो अब हम अच्छली गेम की तरफ बदते हैं तिस में की में दिशा और आमीश को यंवाइट करोंगा की वो आई और गेम की रूल्स बताएं और हम कैसे खेल सकते हैं जेम को वो उगबर सब को दिखाएं अगे अगे, तो ये काखी मजदार गेम है हमें क्या करना है, हमने अभी पिछले साईड में ही देखा की हमें, ती नमबर से चुस करना है, जिनका सम् 27 होँजा है ती के, तो ये गेम में, आप सब अबी नहीं कभी नहीं कभी तिक टैक तो या एक सें जीरो खेला होगा जब भी हम अगर एक लाईन में, वर्टिकली, यो होरिजन्टली या डाइगनली एक लाईन में अगर तीनो सेम एक सी आ जीरो हो जाते है, तो वो परसन जीत जाता है, तीक है तो ये गेम भी काफी समिलर है, इस में अप को नीचे नहीं नमबर दिख रहे है, तो येम आप गर दिख है, तो अब आप अद्धियन साथ भी के लिए, तो दिचा अप कै बहले खेलना चाहोगे, आप क्यो में, टैन्गे बअट्वीन, अप दिशा ने ले लिया है, टैन्गे, तो अबी मैं करना चाहूंगा 3, 10 के bottom left में, bottom left, 3. यहापे? Yes, yes. Okay. सम 27 हो नचाये, तो 10 पलास 3 13 होगा. और 13 को 14 के साथ अद करेंगे, तो 27 आएगा. तो 14 वेसा कोई नमबर है नहीं होगा. तो 17 ले सकते है है, 17 को top right पे ले सकते है. अचा, 17 को top right पे ले ले ले लिया है. तो मैं लुंगा 17 के नीचे में ले लुंगा 2. 17 plus 2 19 बंता है, और फिर 8 भी है वर वर परसको. तो मैंने कर दी है गलती, अच्छा. Okay. तो दिशा क्या करोगे आप? अगर में यहा एड लिएड लिएड होगा. तो 17 plus 2 plus 8 होगे आ 27. Okay. So, clear 1 जीट गय दीशा जीट गय. तीके तो सभी को गेम समच आया है. एक बर हम खेलेंगे, audience के साथ कोन खेलना चाहेगा? कर मैं. राजू ने कहा, मैं, आम नोट शोर. Right. वोसन प्रीट लोगे आप रेस क्या है. तो वोसन प्रीट और दीशा आप खेलोगे ये गेम? आ, क्यो नहीं? वोसन प्रीट तब खेलना चाहोगे मेंगे साथ? और मैं भी. अच्छा, राजू भी खेलना चाहोगे. तीके, 2 गेम, 2 गेम खेलनेंगे आम. Okay. वीगो विद, वोसन प्रीट फ़्स तब राजू खो ते ज़ाजू, वोसन प्रीट चलेगा छीके. तो, वोसन प्रीट अब करना चाहोगे स्तात ये मैं अव स्तात कर दू. आप मम, आप स्तात कर दो. Okay. तो, मैं भीच में वान ले लितु. दो वुस्तप्रो थाझें डो ताट्रो , तो वुस्तोках आंगा आब आब चपर कंफ्ताए you can work on Ming Ji work in depending on your points that you may get..... च्सकशा भजिनि सूब पर वह बा़pture and if you want to work with Ming Jiちゃん , then you just let everything work and... अभिभसे नाएन का जरगत है अप यह गर नीचे नाएन डल गीई दुत मै जीट जाएनगी ब़वाबफ़ना Yes ma'am तो हमें गेम एसा खेलना है कि अपको मुझे जीटे नेगे नहीं अपको जीटना हैं तो आपको येचा, च्झ्षाटन जाएँस करना परगेगा 10. 10 plus 1 is 11. And I want 6 which is not here. Correct. Very good. So now we will choose another number. I will take 8 next to 10 on the right side. First one is 9. Very good. Means you won. Okay. So someone else wants to play? Maybe Raju had said. Yes. And Gautam has also raised his hand. Okay. So can Raju and Gautam play with each other? Sir, I have renamed them. Okay. Uttkarsh has also raised his hand. So Uttkarsh and Gautam can play with each other. Do you want to play? Yes. Okay. So Gautam will start first. Then after that Uttkarsh. Okay. Gautam your turn. I will raise my hand. First row, second row, third row. I will raise my hand. I will raise my hand. Okay. And in the first row, you can play 2 on the first position. And 10. Okay. Now Gautam has got a chance. Next chance is Uttkarsh. Uttkarsh, what number do you want to take? 17 after the 2. 17 after the 2. Okay. Gautam again. Okay. Some people are telling in the chat that what to take. So you can tell your responses by taking the help of the chat. Look, I have 2 names. Yes. I forgot to say this in the beginning. I think you all should bring a pen or a pencil with you. So if you don't have it, you can go and get it. Next 30 seconds. 10. Okay. Where is it? It is in front of 17. Okay. Can you see my mouse pointer? Okay. Yes, I can see it. Okay. Okay. I will tell you. I will tell you again. 15. 15. 14. I will tell you again. I will tell you again. Okay. Okay. Okay. Okay. Okay. Okay. Okay. लग राग की कुए आप नहीं की आप नहीं की कुए आप देखान। एक को आप देखान। आप वेग की फ़ाशम इस लेगी किन। शुबाखी ने के सजट कर रहे है. तो में भी उदिखर शाब देख चाँक तेो की... अपनी लेगी सेडंच कर है!糖, अंभी ञाँा, सीळसब रिए from wears along withceğim Strander urgency to places like it in 사 199, ही�acka to places like it in länger, थ nationale, उमांु. बचलते कमािगा. � knife is there. सहोभग और तो सहोभग ताली, क् duo to rahin, ka pictogramau. था औ सहोभग तो बचलते क्रें कोनों टीत हो ना मैं. ताली, ताली. 8-9-10 player 2 winner in this particular round you must have understood the game we will come back in this game in the last game we will take a little pause for this but you can also do this in copy or pen i hope everyone has cleared this how to play this okay thank you amish and thank you Disha we will come back in this game there is a loophole in this game do you think it is a loophole there is a bug but we will discuss about that bug for now what is today's topic today's topic is magic square let's talk about it okay i hope you can see my screen okay so so this was the poster and in this poster if you have noticed there are some numbers in this square these numbers i have written it a little bigger 22, 9, 14, 7, 15, 23 16, 21, 8 so this grid these numbers there is a special thing can anyone tell that they can not see any patterns you can write in chat so now basically you reply in chat i am in chat and amish and other team members we will keep monitoring the chat so according to that we will read so you have to search for patterns in these numbers can you see any pattern okay so total 45 okay so if you add 22, 9, 14 then you get 45 if you add 7, 15, 23 then you get 45 if you add 16, 21 and 8 if you add bottom row then you get 45 are there any patterns in this if they add rows then they will get 45 okay so if we add columns if we add columns if we add 22, 7 and 16 then it will get 45 if we add middle column then it will get 45 and if we add last column then it will get 45 sir we will add diagonals diagonals very good so we have 2 diagonals which one is diagonal this one and this one and if you add left and right these two diagonals sir 14, 23, 8 14, 23, 8 yes so these are all 45 so whenever you can arrange a set of numbers in this way all the numbers have not been repeated all the numbers are unique we have arranged in this grid that the sum of row, column and the sum of diagonal is 45 so from this we say it has become a magic square it has become a perfect magic square okay so now we will see where we have seen these numbers these numbers it will be difficult to identify them so what I do is I arrange them in ascending order just 7, 8, 9 14, 15, 16 and 21, 22, 23 so we have rearranged these numbers and if you notice these numbers here we have our ascending order and in this if I select the grid 3 x 3 so these are the same numbers we have rearranged in this way so that we have a magic square so that the sum is 45 till here we have understood that we have taken the grid of 3 x 3 okay and we have rearranged the numbers so that the sum is 45 so this has become a magic square so what is this 7, 8, 9, 14, 15, 16 and what is this that we can make other grids so for example we can choose 5, 6, 7 we can choose 5, 6, 7 or we can choose the starting combination of 8, 9, 10 so you can convert all these in the magic square so in today's session we are going to see a simple combination which was of 1, 2, 3, 8, 9, 10 and 15, 16, 17 we played this in pre-game and in the game along with these numbers so I think along with these numbers our familiarity has increased so it will be easy to understand but before going here one question from you is how many ways we can rearrange in this grid so if you have 1, 2, 3, 8, 9, 10 and 15, 16, 17 you have numbers so how many ways we can rearrange total possibilities how many so for example in this grid any of these numbers any of these numbers can come then in this grid the remaining 8 will come then in this grid the remaining 7 any of these numbers can come so if you calculate 9 factorial combinations in this if you take this out then you can think that more than 3.5 lakhs of combinations are possible and here I have written that we can take rotation and reflection at this point we will come later so all these combinations are possible to arrange these 9 numbers in this grid and among them we will get only 8 such combinations only 8 how many? 8 which is a magic square so this means that we have to find a certain way so we have to find a strategy we have to make an approach so that we can solve a 3 x 3 grid everyone has a problem statement that what we are going to do we are going to see how to systematically figure out the configuration of magic square okay so this is the problem statement we have to rearrange these numbers so that they become magic square so what do you think what should be the first question to solve this problem we have only this much information we have given these 9 numbers and we know that we have to rearrange them so what does it mean it means that as we saw in the first row all the rows should be the same so the first question should be what can be the row sum right what is the sum which is true for this particular set of 9 numbers so that when we make it a magic square so the column sum and diagonal sum are the same so we can easily figure out how we can figure out we know that when you take 3 numbers in the first row 3 numbers in the second row and 3 numbers in the third row then all these 9 numbers will be covered so if you sum all these 1 plus 2 plus 3, 8, 9, 10, 15, 16, 17 so who will be equal to that R plus R plus R will be equal that means that each individual will be equal to the sum so what does it mean if you get the overall sum you can add all the numbers so the total sum of one third will be the sum of one row so if you want to figure out what will be the sum of one third so I will follow the chart once again everyone should understand why will be the sum of one third because in the magic square the sum of 3 rows should be the same and all the elements are covered and if we add all the elements that means the sum of one third that means the sum of one third that means the sum of one third okay okay so we are getting the answers so Monica has said 27 and this is absolutely correct so if you add the total sum then the sum will be 81 and if you do one third of 81 then the sum will be 27 so from here you have to first understand that you have to rearrange these numbers so the sum of diagonal is 27 right so the first part we have figured out now the second part should be easy the second part we have already played in the game what we did in the game we were looking for triplets the combination of 3 numbers the sum of which is 27 and you yourself told me by writing it in the chart so here I don't need to tell you what to do in this step so you have to find all the combinations for example if you take 1 or 2 then we need 23 to do 1 or 2 we need 24 but we don't have 24 so we cannot make a combination with 1 or 2 so next option we try with 1 or 3 we need 23 with 1 or 3 so this is also not possible because we don't have 23 we need 18 with 1 or 8 we don't need 18 for 1 or 9 we need 17 and 17 so we have a combination of 17 so in this way you have to find all the combinations you have to find triplets of 3 numbers which is 27 so what you want to do write in the chart and tell me which triplets are there so let's wait here for 2 minutes so you should reply in the chart with all these triplets which is 27 and then we will see what we will do next I hope you understood everything you have to write you are saying 17, 9 and 1 17, 9 and 1 so we have to note this because this is also a combination which you have told you need a new combination except for 1, 9 and 17 as Sivran said Sivran is saying 3, 8 and 16 so this is a very important point if you have chosen 1, 9 and 17 then it will be the same so we will not consider them so you have to find all the unique combinations so 15, 10 or 2 Manju is saying 15, 10 and 2 Diksha has also said the same ma'am can we use number 9 yes we can use number 9 we are getting a lot of replies on YouTube Nancy is saying 2, 8, 17 that will also be 27 let's wait a little more Nancy is saying 3, 8, 17 so Nancy if you are taking 2, 8, 17 which is 27 so 3, 8, 17 will be 28 so we cannot take that Sivran has said 8, 9, 10 correct very good ok so now I will encourage you instead of just one combination you give all the combinations with comma so we will count how many combinations you are getting so if you have 17 with 17 what is possible 9 and 1 is written then give the second combination then give the second combination you are finding the combination and write that in the chat now there is collaboration allowed so you can see what other people have found so that we can reach to the next step on YouTube many viewers have replied 10, 16, 1 Nana is saying 4, 5, 18 Satish is saying so we are getting a lot of replies from YouTube so how many combinations are there 8 ok so on Zoom Shubhangi has sent a big list 1, 9, 17 1, 10, 16 2, 8, 17 2, 10, 15, 3 9, 15, 3, 8, 16, 8, 9, 10 so 1, 2, 3, 4 5, 6, 7 7 combinations are given apart from this is there any other combinations if anyone knows 15, 8, 4 correct ok so total we are at 8 combinations 8 combinations nice can there be any other combination can there be any other combination apart from 8 on YouTube 69, 2 on Zoom 69, 2 so total 9 combinations can there be more than 9 69, 2 this is a cover in 10, 16, 2 69 69 combination 69, 2 there is a new cover ok Nana is saying interesting 14, 6, 7 14, 6, 7 14, 6, 7 we don't have 14 we don't have 14 so you can't take 14 you have to choose the numbers Nancy is raising hand yes Nancy are you saying any other combination Nancy was with us on YouTube but has been joined on Zoom yes Nancy you can also tell if you have any combination by the way I will have to verify all combinations will it work or not Harithnya has also told a lot of combinations like 1, 9, 17 3, 8, 6 3, 8, 6 yes we don't have 8, 6 or 17 but we don't have 27 we want 27 so we don't have 3, 8, 6 2, 10, 15 we don't have so we have to see after writing by cross checking if 27 is coming or not so let's move ahead we have to give a little more time what do you think shall I show you the answers the presentation yes 16 16 plus 10 1 correct so in this part I made slides in this presentation but I knew that you will figure out so here I have to tell you I thought I can fast forward these slides I will show you fast forward if you follow these steps 10, 10, 16 then these combinations will come and then you can match the right hand side these boxes are matching or not so in total we have 1, 2, 3, 4, 5, 6, 7, 8 total 8 combinations should be right so these are all combinations on the right, so you can match that the combinations are similar or not and now let's move on to the next step for example, if you took the first combination 1, 9, 17 so we have to fill them in grid to make magic square so how to fill them fill them in first row fill them in first column or in diagonal and how to keep their ordering first keep 9, first 17 first keep 1 so this is the next challenge so what do you think how do we move forward and I will give you a small clue the hint for the next step is on the screen so you have to look at the grid the grid in front and to understand the geometric properties of the magic square you can figure out the clue of the next step what should be our approach so I will wait for some responses and then we will discuss all of you have understood the problem we have to rearrange all these numbers in this grid so that we can make magic square but how to rearrange these questions we can't do it randomly so we have to think about what approach we should use to rearrange them or to fill them in this grid so you can type in the chart what you think or you can also unmute so Nancy is raising hand what do you want to say 11917 and the last row is 2817 so Nancy what should be our approach in the next step how do we attack this problem if we have this total art combination now we have to fill in this grid but how do we fill to get the magic square what should be what should be our approach to fill the diagonals we can use a triplet that have a common number which can be placed in middle yes that is very close to I think how we have to proceed next so very good diksha by the way where will the common number come where will the common number come according to that we have to arrange triplet okay so Simran is placed 9 in the centre why you placed 9 in the centre sir because 9 four times are there 9 four times are there so very good so I think you figured out in the next step also you don't have to tell me so all my slides I think I I think I am not using because you are figuring out yourself so next I think I will visually understand so if you notice this this grid if you take the corner element the corner element is total 1 2 and 3 there are 3 triplets and how many corner numbers we have total 4 are there so there will be 4 numbers which will be part of 3 triplets if you take the centre number there are 2 triplets so all the numbers can come in blue positions and how many blue positions we have 4 but the centre number the last position this is total 1 2 3 4 there are 4 triplets and there is only one number which is 4 triplets so if we figure out in each triplet frequency is removed so we will get the next clue that we can place it this 3 2 and now we will see the frequency of it for example here 1 2 is in combination we can place it 2 where can we place it because 2 is coming 3 times so all the corner squares that is the purple squares where can we place 3 again in blue squares 8 also in purple squares if you notice 9 9 times and only one number which is 4 times so from here we can see 9 is a number if you check 10 then 3 times 16 and 17 so from here we got which number is the possibility to go in this position so let's fill 9 first and now we have solved the clues let's start from 1 because we need some 27 so we will get 1 and 17 together only then we can form 117 and 927 there are 2 other numbers 3 and 15 let's fill them too now let's start from 2 if you fill 2 here then what will be in this corner 16 and this corner also fixed and this corner number also fixed so if you fill this and then check now you can check so this is our combination 1638,1970 and 1052 IOP everyone understood what we did here everyone understood and you can tell me in the chat if you haven't come and if you have come then you can... okay I will explain this part again okay so till here it was clear what are we seeing we are seeing how many times individual numbers are coming in triplet so as we saw 1 okay as we saw 1 1 is basically 2 times so 1 can come anywhere in blue square because blue is the square that is the centre number please please 2 times okay then you can check 2 2 are coming in triplets 3 times so we have seen the frequency of each number the triplets we had and once you solve this you will know which numbers are playing and we can clearly see what is the number which is coming 4 times after that you can start from anywhere you may be you can play 3 so if you place 3 on top then because you want sum 27 then you will have to choose 17 because 9,3 is 12 and so 3,9 and 15 will form 27 and 1,9,7 will form 27 okay and then we have these purple numbers so I started from 2 but there is no need to start from 2 you can start from 8,10 and 16 but if you play any number then all other positions are fixed because there are 2 numbers already so this number is fixed and 15,02 is also fixed and 15,02 is also fixed so by default if 9,02 is equal to 16 to do 7 17,02 is 19 so here should be 8 15,02 yes so in this way we have solved our magic square and I am going a little fast because content means there are more things I have to tell but if you don't understand then you can explore in the video and then you can see the doubts but I hope on the second time it will be a little more clear okay so coming back to the first question we saw in the starting how many such magic squares are possible if you have set of 9 numbers then you will remember that total art is possible do you remember I told you in the beginning we have figured out one total is more than 3.5 lakh the total is there are only 8 such combinations in which we were able to form magic square so next question is what are the other 8 how to figure out so here I want to tell you a small activity you bring a paper cut a paper and write these numbers for example you can write 16,3,8 10,15,2 and 16,16 so I will give you two minutes you write these numbers on both sides as you have written these numbers next and back you have to keep this in mind where 16 is you have to write 16 where 3 is you have to write 3 where 8 is behind that you have to write 8 is everyone clear what to do Ameesh you tell me I am not going fast on YouTube there is no comment on YouTube so I think you are going right we are writing on paper I am trying to write 16,3,8 write below that 1,9,7,10 15,2 so I will show I have written this if you can see now you have to write 16 behind 16 so one thing I have noticed if you see 16 is on the left side if I turn it it is coming to the right side so I write exactly behind that 16 is done exactly behind that behind 3,8 behind 8 ok then between 17 17,9 10 if you have written this you can tell in the chat that you have reached here so you can tell me that you have to proceed yes I have written yes I have written no one has replied on YouTube Nancy is coming she is giving so Nancy has also written we will wait for the other participants ok keep in mind that 16 should be behind 3 should be behind and 8 should be behind all the numbers in the front should be in the back ok then proceed I think so what have I done go ahead ok so I have removed the same numbers 16,3,8,1,9,17 10,15,2 now tell me if it rotates 90 degree if it rotates 90 degree then what did you get you have to do it in the right or left ok in this way maybe clockwise you can see clockwise so if you rotate clockwise then 16 will be in your right 3 will be below it and 8 will be in the bottom right I am also looking in front of it I am rotating it now 16 is in front of me 3 is here and 8 is here which is visible on the screen so let's fill the rest of the numbers hopefully you can see 10 here in the first row in the second row you can see 15,9 and 3 and in the third row you can see 2,17 and 8 can you see it ok so don't do this that this is magic square if you search 10,1,16,15,9,3 2,17,8 all this will be 27 of the individual you can check the column 27 and the diagonal essentially we haven't done anything we have rotated the numbers in the card so there shouldn't be any difference on its property because we haven't rotated the numbers we have rotated the numbers right yes so we got this second combination second combination now let's rotate it one more time 90 degrees more so you will get this third one so it will come up to 2,15,10 and in front of you you can see the slide bus is made for support but in your hand you must have written it the numbers are not rotating because the numbers are not rotating there was an option to write it in the slide so I wrote it here but you might have understood yes is there any doubt till here so I I feel that we have rotated it twice so it is 2,15,10 above wait a minute what about Vedika yes I have done it sorry Vedika if you want to say something now we have flipped it twice so it is 2,15,10 above I think we should ask the audience to do it one more time what do you think ok this is a good question let's flip it once more let's flip it once more ok I got it 10,1,15 10,1,15 16 10,1,16 10,1,16 is done it was in the second square 8,17,2 ok ok 8,17 8,17,2 ok awesome let's flip it once more once more 15,3,8 we will get the first one we will get 4 magic squares from the front look at the front numbers if you look at the backside flip it if you flip it you will get 4 more you can rotate it we will do it 4 times so we will get different combinations we will get different combinations and what does it mean to flip it it means that for example in front side you have kept this card like this you bring a mirror next to it and look at its reflection for example the first one we will consider 10,17,10,15,2 if you keep a mirror at the bottom for example if you keep a mirror after keeping a mirror what will be the reflection 10,15,2 then 11,17 and 16,3,8 so we will get 4 more 4 more squares which are all magic squares so in this way 8 combinations are possible so you can flip it or you can take the reflection of the individual so basically you have to take the reflection and if you do this then you can understand it there are so many numbers so I get confused so if you have not made a grid then make a grid and then do your activity and you will understand the meaning of rotation and the meaning of reflection and in fact what is flipping flipping and rotating so we will get the same combination I hope you all are with me till now understood what we have done okay Ravi I have a question as you said I have made a grid we have rotated it we have reflected it so I was trying to understand that when we are rotating or reflecting it then the position of numbers is changing but if we add the sum then the same is coming so I have a question that is there any number that the position is not changing it is the same in all I have a question in the audience 9 9 is always in between we will flip it or we will flip it 9 is always in between and it is also visible in the slide in the 8th combination 9 is always in between this is a little unique thing I think people have replied I assume that everyone has done the activity then everyone understood correct but here we have got a total 8th combination but if you notice all these numbers the grid is the same when I want any combination for example if I want the first combination I am here and if I want the first one then what can I do I can reflect and rotate and come back to the first one so I can rotate the square and get back to the first square so we will call all these combinations as equivalent but they are not all unique so what is the combination when we reflect and rotate we cannot bring the first one to the square actually this square is the same this is the same because 16 is not written behind 3 is written behind so the total answer the distinct answer is only 1 but you can reflect and rotate and generate 8 more squares which hold the property of magic square but actually the unique solution is only 1 and you can see that because all these numbers are the same 16 is behind so we have not made a different grid we have rotated and reflected the grid to generate these 8 combinations so you remember in the beginning I wrote including rotation and reflection so that means that you can rearrange 3.5 lakhs of combinations including rotation and reflection and in that there is only art which will form magic square and this art is actually the same because we rotate and reflect it so all these equations are the same there is no distinct so I will show you 4x4 for example this is 4x4 magic square if you see the column scale will be the same the lower and upper squares and if you write these 2 squares in the paper and if you rotate and reflect then if you write the lower one then you will not be able to generate the first one think for yourself I will remove the zoom notification notice here 15 and 14 are not in the corners but they are in the corners there is no distinct these are different squares but if you sum up everyone will get 34 16, 3, 2, 13 I hope 34 15, 15, 30, 34 so 34 is above 34 is below so 4x4 now I have shown you 2 combinations which are distinct and you can generate 8 more from these 2 rotation and reflection but total has a distinct solution how many are there 4x4 8 80 4 if you take the numbers and if you write the magic square total 880 possibilities are formed ok now what is 3 3x3 we have seen one solution 8 possibilities of rotation and reflection but distinct is just one 4x4 880 next slide I hope you have seen 5x5 if you want to guess total solution will you write in the chart if 4x4 is 880 then how many are there you can type the numbers total distinct solution what is 5 means you have taken total 25 numbers and you are making magic square 1000 9 numbers is 16 total 880 distinct possibilities are there if we take 25 numbers and create magic square then how many possibilities are there if all the numbers are unique any guesses whatever you think you can type this fact is very fascinating when I saw this I also found this interesting ok total in total 1700 ok are there any replies on youtube on youtube there are no replies but I want to guess if 4x4 is 880 then I think if 1 is 880 then 880 plus 880 then I think approximately 1700 I think ok now let's see it is around 27 crores there are so many distinct possibilities of 5x5 6x6 yeah it has escalated total possibilities what do you think of 6x6 if you have 36 numbers and all are distinct and you want to create magic square then how many distinct magic squares are there I don't know now you can type the numbers on chat you have to type a little more because you might be able to guess that the number is going to be very big but how big Yashav Ardan is saying 27 digits Muradul is asking how to calculate this is interesting how to calculate I have given you the source you can explore it in the link if you want to know more details how people calculate basically you use computational techniques because if you do it it will be very difficult you have to use computers you have to take help of calculations to find and figure out what is it so ultimately till now after 18, there are 18 zeros there are so many distinct magic squares and we don't know because this is also an approximation after 6x6 if you go to 7x7 8x8 we don't know how many distinct magic squares are there we are not able to calculate probability, statistics all these things with the help of statistical techniques you compute from there you estimate how much should be there so we have estimated which is very fascinating it's an unsolved open problem that how many distinct magic squares are there so this was from my end what we did we saw that 15, 16, 17 these numbers how we converted them into magic squares we saw an intuitive approach after that we saw all these are the same because with rotation reflection we can generate 8 combinations and in today's session that was enough from my end but now we can come back to the game and what I told you in the beginning that Ameesh do you want to tell about the game that loophole that we left in a cliff anger that there is a loophole in this game so let's see whether the audience figured out what loophole is so this is the same game that we played in the beginning so did the audience understand what loophole is so we started this game after that we tried to understand what loophole is so if we can use the magic square knowledge what we learned then we can apply it here so is there a loophole loophole means is there a trick the trick that you can use you can always win is there any audience who is thinking Uthkarsh may have raised his hand Uthkarsh do you want to say something yes ma'am ok ma'am I am for the trick ma'am boli hai sir in the first row we have to put plus 1 in the second row also plus 2 first row we have to put minus 3 and in the other side plus first minus 3 and in the middle row minus 2 and in the last row plus 1 and in the upper side plus 4 and in the lower side plus 4 and if we put the middle number of these then we have to put the minus 3 ok Uthkarsh you have told minus 1 minus 2 minus 4 and 4 we don't have all these numbers and we have to use these 9 numbers and sum it up to 27 so try to think again ok Uthkarsh and this chat yes boli in the chat Monika Rudul is saying that 9 will always come in the centre is this correct but this loophole yes this is correct but this loophole can be what will happen if 9 will always come in the centre what can happen once we try to play or if you have said Monika or Rudul then you will want to play actually I have got a message of Shubhangi if you put 9 at the centre the first player will always be the winner so Shubhangi has also noticed so these 3 3 people have noticed so what can happen ok come on Disha you play 9 in the centre so let's see if you can win ok so you have taken 9 so I will take 1 on the right side of 9 I will take 1 on the right side of 9 1 on the right side of 9 ok so 9 plus 1 10 and if I take 17 then I will lose ok 9 plus 1 correct correct correct ok so this is the trick that if I would have added any number if I would have taken 10 then what would you have done 9 on the right side of 9 so 10 plus 9 then I would have taken 8 then I would have taken 20 8 is there and not only on the right side if I would have taken 9 on the right or on the upper right column then you could have taken 27 ok so the person who will choose the first number and will keep it in the centre can be the winner there is not much chance of winning correct there is not much there is 100% but how do you understand the trick how do you know how do you know if you want to unmute if you check all the magic squares all the 9 is always in the middle because that is about magic digital also you can say because we started with that 9 should always be in the centre so basically if we are doing this the 9 should be in the centre going back by our strategies ok that is correct that is correct so this strategy if you play this game with your friends then you can use this trick and they will also get worried about how you are always winning yes you told us how to get the magic square I think it will be will it apply to all the magic squares whatever the middle number that we get put in the magic square with those numbers will it be possible for all what do you think if we take any other magic square and that middle number we decided this will be the always middle number and we played a tiktok with others so will it be possible for all other like that because the middle number comes out a lot in combination so yes it is a very lovely session you always talk about magic squares but you gave us so much detail in magic, I never thought about this so thank you for this lovely session I would like to say thank you so much I would like to tell you this trick we are using of the middle number if you take 3 cross 3 magic square then it will be possible because it has a middle number but if you are playing tiktok then you will play with that 3 cross 3 so yes middle number always if you have a starting combination for example if you have started with these numbers then you will figure out that 9 should be the target sum like the same approach so again the middle number is 3 in this case so if we place 3 first then you will always get the sum no matter what number you can place so if somebody places minus 1 then you will need 7 for 9 so again you will always win so starting combination of 9 numbers with which you are creating magic square but the same strategy is applied to all the 3 cross 3 same strategy you can use I will reset it again so 1,2,3 8,9,10 15,16,17 ok so here I want to tell you that if you want to play this game then maybe you can add a rule to this game that in this you can add this rule that the first player can not play in 9 middle numbers but you can play it and then it becomes a fun activity so that could be one rule so make your own rules make your own games so that was all about this game I don't know how much time we have left there was one more game that we can discuss but depending on the time I think we will decide what do you think what do the audience think should we play another game someone is saying something yes yes please explain yes Simran is asking what is this bug Simran, there is only one bug that if you play 9 middle 9 plays in the middle of the grid then you will always win player 1 will always win so ok so quickly let's move on to the second game Amish why don't you then explain the rules this is also a very interesting game the game is a very similar game so what we have to do in this one minute Ravi what is that in front of the screen so in this also we have set of 9 numbers the first one is 1,2,3,8,9,10 and these are the 277 lines for example look here we have to choose from each number so player one choose from each number player 2 choose from each number one of the numbers in which sum of the number you have sum 207 that wins and keep in mind 3 numbers will suggest the same number अर उन चारो में से कोई 3 का 27 हो रहे है, तो भी जलेगा. तो मैं और दिशा एक बर आपको खेल के दिखाते है. तो मैं वो त्रेक यूस करूंगा जो अभी तक हम ने सीका है. नाईन नमबर आस दे मोस पोसबलिती. तो मैं नाईन चूस करता हो पहले. तो मैं 17 चूस कर लेतिओ. अके दिशा ने चूस कर लिया है, 17. तो नाईन के बाद में 10 चूस करूंगा. 10. उ नाईन और 10, 19 बना रहा है. और फिर अगर 8 लेंगे, तो वो 27 बन सकता है. मतब आप जीट सकता है. जो में होने दुखे नहीं. तो 8. तो 8 चला गया जेसे की आपने मेरा प्लैन समच लिया. तो मैं क्या लेना चाहूंगा? ती के मैं 1 लेता हूँ. तो 2 तू. तू लेता हूँ. और मैं बहुली गया. अब भी 27 बन रहा है। तो तू जीनो ने भी काहे. मैं बहुल गया दा. अब भी और बहुला है. अगर. बहुली भी नहीं. तो 9 और 2 बन रहा है का 11. और 16 तो है बाब अप आप के पास. तो 11 और 16 को लेके ट्वेंती सेथ बना सकते हो. तो 16 या फिर 10 और 2 को लेके 12 और 15 भी बना सकते हो. तो आपके पस ढो पोसइबलिटीज है तो आखा दीः तो में, 16 लूए 16 लूए, शायट रा आप आप याप जीत होगा तो, I'll take 15 अखे ए, उचो दिशा देख स्विख्छीन में लेता हो 16 और मेरा सम हो गया तो 9 वलग स्वत्तार जीहाँ पर भी वरग कर रहा है तो अडियन्स मैसे किसी को ये केम केलना है क्या? तो 2 अडियन्स जल्दी से यें केल सकता है एक बर कोई खिलना चाहेगा अवीश सम कैसे हूँ आप ये दिंग अपने वोः 10 प्लष 2 प्लष 16 आप येदिस 28 9 प्लष 2 प्लष 16 अप आप येदिस 27 तो प्लेर वान मिद्स तो कोई अडियन्स में से खिलना चाहेगा क्या? चाहेगा क्या? चाहत पे है कोई रिपलाई लेटमी सी वुद्कर शाए और आश्वो वर्दन हैस रेजद हैं दिक्षा इस तेलिग मी दिक्षा कोई वोखा देते है, दिक्षा नहीं खेल पाए कोई गेम दिक्षा ये वोन तो प्ले? ये रब लग 스타일 दिक्षा के साट कोन खेलेगा? आस्वो वर्दन आख्विवopoly जो आखविवला जो आखविवला जो आखविवला दिक्षा लोभ रिपलाई पर साए पाए लोग नहीं अभी शे खीर कतने, यह ग क जोअ जो चाहतो है अगर हैं, हैं के अजा लगे नहीं सेगा। अजा गयट्में पहली जोगे भी रगे नहीं लगे चीथ नहीं? अगर तो लेंग तो सब प्रशा दूग सेगा अगर ख़ी कीदूं है। अगर ख़े ख़े यह नहीं के वैद करनो अगर के विई रने के जए आगते. next player takes 10 8 is force right player 1 1 player 1 will be the winner ok 2 should take 16 player 2 should take 16 ok but player 2 takes 16 then 9, 1 and 17 will be 27 right yeah but 10, 1 and 16 will also happen so here it's a so this is a strategy because this is a trap 16 will also happen and 17 will also happen ok so maybe here the second move in that should have chosen a starting combination so that player 1 doesn't win ok let's think about this but should I like because we have less time let me tell the Amish what do you think yeah I think first complete this game let us say that player 2 chooses 16 or 17 I think that number 2 is 2, 8, 16 and 10 yeah those are part of 2 roles maybe they can't be chosen means this is not a situation so you have to try should I undo it should I undo it I undo it ok 10 so player 1 will take 8 no 8 no no player 1 has any choice player 1 will take 8 so will someone choose player 1 what should we take to win player 1 2 2 so we are forced to take 16 so player 1 has to take 1 1 so player 1 has to take 1 15 no sorry sir now if we take 17 then we have a choice you have 1 now if you take 17 why how can I 17 17 17 for player 2 17 for player 2 so player 2 has 1 no no no but there are only 2 numbers we need 3 numbers no in the third round I am saying now we have 2 chances either 3 or 15 so they will choose either 3 or 15 right no they can also choose 17 17 is not gone yet so 17 is already chosen by player 2 player 2 has chosen 17 in the next round that's what I am at the end correct now whatever you choose we have 2 choices 3 or 15 for player 2 why do we have 2 choices for player 2 no no no sorry sorry sorry sorry sorry now we are doing very well because he is drawing no no no but we have to draw actually we had to draw because we have chosen player 2 that's what I was trying to okay but I think the player 2 does not want player 1 to win so he is going to draw or he is going to win or we can take what can we take just give me a chance sure you can think 16 yes no then it is difficult you have to you can only draw in that case okay so let's draw and then let's understand logic with another analogy so it will be interesting so should we draw it yes no but see that was 17 you put 17 there and now suppose 9, 10, 12 and we take 15 so player 1 wins where is the draw now player 2 can take either 3 or 8 but he has already won 9 no no no we have to take in a line in a line you have to take from your cards so think of I think what player 2 player 1 is saying that a 9 plus 2 plus 1 plus 15 is 27 so you have to make only using 3 cards only use 3 cards not 2 cards exactly 3 let player 2 win now I am in play yes player 2 go ahead so what would be the player 2 choice meanwhile I am just drawing a grid this is going to this is so intense intense cricket match chess match I am also thinking what should be no but I will draw 8 okay so should I choose 8 8 yes okay and then there is 3 and this is draw because no 3 cards have any individual players that is 27 can you give me a combination of magic square player 1 player 1 has 15, 3 and 9 that makes it 27 15, 3 and 9 so here you have to choose 8 so then there is 8 then it would be draw last moments you have to be attentive so you have to think exactly which cards are going to the second player and which cards you have to choose so that you have and the other block so this was the game all about let's see this game in a different way so I will create magic square from each side so 8, 9, 10 so 27 15 will come this would be 70 and 24 3 so this is magic square right now what we will do we will follow the first move so let's play the first player in tic-tac-toe and let's allot the second player so wherever there is 9 I will put cross there and wherever when the player 2 move I will put 0 there so what was the first move in the center so player 2 moved player 2 moved 10 where is 10 bottom left so 0 then player 1 moved player 1 moved 2 so which was this player 2 moved 16 so to block this 16 then player 1 moved 1 because this is 27 then player 2 what will have to be done because you have to block this oh so 17 yeah so 17 will come so this is 17 then player 1 chose 15 so this was being made with 3 but if you do 8 sorry if player 2 chooses 3 so this blocks and then player 1 is left with 8 which is cross and that's a draw tic-tac-toe ok so I hope this connection will be interesting actually you were playing tic-tac-toe on magic square playing we choose 15 17 3 or 1 second player's first choice second player's first choice ok instead of 2 8 16 and 10 if we choose 15 17 3 or 1 it will be little different yeah it will always be similar to playing a tic-tac-toe and tic-tac-toe on magic square so so many combinations are possible and you always have to win yourself but you have to block the other player so it was a similar game so what you have to do is create a magic square play this normal game and see how the grid is formed so that will be a very interesting connection once again I hope Amish what is there some audience on youtube like which saying something that we should do it again public thumbs up is giving tic-tac-toe this connection between tic-tac-toe and magic square I think I understand and on youtube on zoom a sur is asking what will this class always run so this steamboat we meet every second sunday we meet every second sunday live session but on youtube the channel of hbcse homey baba center for science education if you type on youtube you will get channel you will get all our previous videos if you want to see and on second sunday you can live with us okay okay so shall we wind up I think audience have understood this game so I think you can play after that and this is on youtube and if you are developing a new game like by choosing different numbers if you have a different strategy you can write us you can email us or you can check on our website you can comment on youtube I type my email on chat box yes sir on chat box youtube channel of hbcse has been added so yes sir ravi you go ahead okay so before we move towards last part in this slide you can see some interesting magic square which you can explore but for example there is a possibility that you form magic square with integers so here all sum is zero you can form product magic square that you can multiply these numbers that you have the same number across row across column across diagonal you can form magic square with fraction so the possibilities are limitless this is on our creativity how we use this as an interesting learning tool depending on our goal which topic you are studying as a teacher and in the bottom there are some interesting magic squares for example there are all prime numbers in 1979 it was generated and this is the smallest number whose product comes 216 so these are natural numbers so if you cross row across diagonal or cross column if you do product then 216 sum will come for the magic constant so this also came in 1913 it was figured out people discovered it people not I think it was Selies and there are a lot of other interesting magic squares 4x4x5x4 in 4x4 a durar magic square is quite popular and it is even connected with engraving अप विकिपीडा में उसके बार में भी जागर क्या आप हिस्ट्री थोड़ी सी पड़ सकते हो कि आप कनिक्षिन स्वोड़ सकते हो फर इस पेंटिंग के तोप राइप में आपे ये ये सेम मादिक सक्वेर है जो अमने एक आप फोख्रोस फोर में देखा था तो तिस वस ज़स फुट वर को और विकिपीडीग क्या दोपे बरहो ओर सकता हो था और इतना दीप वो सकता है आप गगी रुगु लेग है तोब एक आप थी नहीं तो वोगे लीद मोड अगे टेड तो जी था आप लच़्िया में था थाए देखा लक्ता है, अद विकिप e-mail-id steamboat-ad-the-rate of hbcc.di or rs.in. This is my e-mail-id. If you created games with your own way , as Amish said , you can also tell us in the comments on YouTube or you can write to us , Amish. And thank you so much for joining. And thank you Ravi , for bringing such an interesting topic. It was a lot of fun, you played many games and learned a lot too. अगर मुजे कुछ सवाल होगे तो मै आप को पूछ हूँँँँँँँ.