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Few years back at IIT KGP, it so happened that 7 friends of electronics department were studying the same course. One of them was a first semester student, one a second semester student, one a third semester student, one a fourth semester student, one a fifth semester student, one a sixth semester student and one a seventh semester student. One night they discovered that there was an assignment submission next day. The assignment consisted of 57 questions and it was impossible for all of them to solve all the questions themselves in the given time. In EC department students were required to solve their assignments independently as they professors had devised ways to identify copied assignments. So, in all they were required to generate 57*7 solutions. As the time was limited they decided to solve the assignment once i.e. generate just one set of solution and then divide the solutions amongst themselves. One example distribution can be, 5-17-9-6-2-10-8 amongst the 7 friends.
Once the assignment was solved, they decided upon a certain distribution protocol. The eldest friend (one in the seventh semester) would divide the questions. For the distribution to be accepted he should have atleast 50% people (including himself) agreeing to the division. If less than 50% people agree then he will have to leave the place and the next eldest person (the sixth semester friend) will be called for distribution and now the person who has left (the seventh semester friend) will be out of the distribution and would not be given any solutions.
Now if the eldest one is to distribute then what is the distribution which would get accepted and the eldest friend gets the maximum number of solutions for himself? Explain your answer briefly.
Sudipto Sannigrahi
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