Independence Day Celebration
The independence day is celebrated all over India on August 15. In addition to the celebration in the capital, many cities in the province hold large celebratory shows. Akshara’s school decided to have a student presentation competition on the theme “The Future of Uttar Pradesh”. The school children are asked to talk about the future of Uttar Pradesh!! Why not, after all they are the hope of the province? They are also told about a prize to be awarded for the best presentation.
The thirteen year olds Akshara, Tipu, Pappu and Chameli are good friends and talk to each other often.
Tipu: I want to participate in the school presentation. I don’t want my father to write the speech because that is dishonest. Can we ourselves make up a presentation? It should be something no one will even think of.
Fashion or math?
Chameli: I love fashion. I will do this with you if we talk about fashion.
Pappu: Why are you making fun of Tipu with this thing about the future of the province being in fashion?
Chameli: Do you know how much money Bombay makes with fashion? Do you know how much money Bollywood makes? Why can Uttar Pradesh not have a more prosperous future in these areas?
Akshara: Chameli, I have been thinking about what Tipu says, and also about what you want.
Pappu: I am interrupting you so you don’t insult Tipu. You always do that.
Akshara: My dear friend Tipu, do you want to win?
Tipu: Of course, I want to win. Why ask this stupid question? I want to win with something meaningful – not fashion. Fashion is for girls.
Chameli: Tipu, Tipu, Tipu. Almost half the school is girls. The judges may include some of our female school teachers. Did you think of that?
Akshara took over the conversation
Akshara: All of you, we can present as our gang of four if you want to win. We will develop a presentation together if you let me.
Akshara has a commanding effect on them, and they all agree to work with her. She put together a presentation.
As it often happens, many students approached their older siblings or parents for help. Some of them were told not to worry about this topic because they were too young to think about it. Others were rewarded with speeches with the old beat up lines. They used these lines and similar thoughts just saying Uttar Pradesh will progress rapidly in the future and become the best place in the world. The students delivered the memorized speeches like robots but said nothing meaningful or to provide directions. The principal then announced that the last presentation was titled “Choice – Math Or Fashion” by Pappu, Chameli, Tipu and Akshara.
Pappu’s introduction and Chameli’s fashion
Pappu: You have heard from other students that Uttar Pradesh is the garland of India. Why is it then we are one of the poorest states in India? Should we not be more prosperous? But how? This is what we want to talk about. Our order of presentation will be Chameli who wants to talk about fashion, followed by Tipu whose passion is numbers, and then Akshara who says that this is not a choice between Math or fashion. Chameli, please start.
Chameli: Bombay fashion models and Bollywood actresses make a lot of money because everyone – rich or poor spends their disposable income on fashion. Uttar Pradesh can get more prosperous if its students can learn more about the fashion industry. More popular fabric and beautiful dresses can be made here and sold to the world if we learn more about fashion. Everybody knows about how different color combinations can be used for fashion. Tipu will take this idea further by showing the use of different arrangements of colours.
Tipu talked about Tiranga colors
Tipu: As a resident of Uttar Pradesh, and as an Indian, I would like to start by saying Jaihind and showing you the Tiranga (see picture of Tiranga). Please, excuse me for not including the Ashoka Chakra in the flag. Tiranga can also be used in fashion. Chameli may like to get a tricolor on her designer backpack. Some of the others might like the idea of the three colours but they don’t want the same backpack as the others. This is what we can do. We can give them 6 different types of backpacks with the similar but different patterns. In the Tiranga, we have the red color on the top, white in the middle and green at the bottom. We can get the second pattern with the red colour on the top, the green in the middle and the white at the bottom. For the third and the fourth patterns, we keep the white on the top but the red at the bottom in one and the green at the bottom in the other. For the fifth and the sixth, we can keep the green at the top, and the white at the bottom or the red at the bottom. So I used the three colors to make 6 different permutations. I love it but Akshara has bigger ideas.
Akshara’s rainbow colored backpack
Akshara: Thank you Tipu, and namaskar to everyone. I want to start by thanking my grandpa for giving me this backpack as a present to celebrate the Independence Day. See this picture of the beautiful backpack with the stripes of the rainbow colors. From top to bottom the colors are violet, indigo, blue, green, yellow, orange and red. Chameli is laughing because she knows what I am going to tell you next.
We all want similar designer backpacks but unique: no one else in the school should have the same exact pattern. You know what, it is not a problem. If you have two colors, you can have any one color on the top and the other one at the bottom. So, there are two possible arrangements. With three colors, there are 3 possibilities for which color goes on the top, and for any one color on the top, you can get two different arrangements like I just showed you. You get 3 x 2 total arrangements. With four colors, any one color out of four can be on the top with 3 x 2 arrangements of its own and so on. Then you have a total of 4 x 3 x 2 possible arrangements. This picture shows the number of arrangements for 5, 6 and 7 colors also. From 7 color red stripes one can make 7 x 6 x 5 x 4 x 3 x 2 which is 5040 different patterns.
Math can be used for fashion
We only have about 500 students in our school. I challenge one of our companies to make all the 5040 unique designs and advertise them. I am sure this will bring more jobs for us. You don’t need 5040 machines to do this. You need to make only a small change in your machine program so that it selects the ribbons at random. You will get all the designs. See the beauty of Math and how it can change the fashion industry. I have done this only for the ribbons for a backpack. You can apply these ideas to making different kinds of ghagras, chunarias, sarees and other things.
This is why I think that the future of Uttar Pradesh is in the girls developing the knoweldge of math to combine it with their interest in fashion. I am going to end our presentation by showing you that these ideas apply not only to ribbons but also to flowers and to the other shapes. Thankyou.
The judges agreed rapidly and unanimously that this was the best presentation. The principal asked Akshara’s parents if they helped. They say that the children thought that it would be cheating, and did not allow them to help. The four kids thought of everything on their own. The principal was still amazed because he was not taught the permutations until class 12, and even then he found the subject to be difficult. The children in class 8 had made it so simple.
The Prize
They received a cash prize and a certificate from the school. A shop keeper from the city had also come to attend. His shop sold T-shirts and chunarias. He announced that he would award two chunarias to the two girls and two T-shirts with the Tiranga to the boys. Akshara objected saying that he should treat girls and boys the same. Girls would be equally proud of showing the Indian flags on their shirts. He should not insult their patriotism. So he agreed to bring four shirts with Tiranga – one for each of the four to the school.
Upon returning home the kids find that the prize they received is a cheque for Rs.1000. They divided 1000 by 4 and figure that each should get Rs. 250. The parents decided that each of the kids should open a junior bank account with their mothers, and deposit the money in it. This way they would also learn more about banks.
Challenge
Akshara and her friends Tipu, Pappu, Chameli and Manal decide to have a party to celebrate their finishing grade 8. They will all be sitting in a row at a long picnic table. Jonny always wants to figure things out. Now he wants to figure out the number of possible seating arrangements. Please, help him. You can do this by writing names of the friends in each possible arrangement if that helps.
Solution: Let us call the seats A,B,C and D. Anyone can sit in seat A. So there are 4 possibilities. Let’s say Tanya hogs seat A. There are three seats left, anyone can sit on seat B. There are 3 possibilities. The number of possibilities would have been the same if Manal or anyone else instead of Tanya had taken seat A. So there are 4 x 3 or 12 possibilities for occupation of seats A and B. After this , only two seats are left and so are two persons out of which anyone can seat in C. So the possibilities so far are 4 x 3 x 2 or 24. There is only one person left and they can go in seat D. So there are 24 different possibilities.
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