11th National Mathematics Competition at UTAR

On 18 June 2016, I participated in the 11th National Mathematics Competition at UTAR Sungai Long Campus organized by Universiti Tunku Abdul Rahman (UTAR).

There were many students from different universities joining the competition, totalling 300 students. There were students from National University of Singapore, UTAR, USM, MRSM, Sunway, etc.

Competition categories

There were 3 categories, A, B, and C. I joined category A and B (individual categories), so I had no idea what category C is about, I only know it is a team based category.

For category A and B, participants are separated and guided to their own computer labs.

Category A consists of 20 questions from topics such as discrete mathematics, probability and statistics, linear algebra, algebra and number theory, and calculus. The participants are given 30 minutes to answer them, 1 mark for one correct answer, and -1 mark for one wrong answer.

Category B consists of 100 questions. The participants are given 30 minutes to answer them, 1 mark for one correct answer, and -1 mark for one wrong answer. The questions are simple arithmetic question requiring only +, -, *, and /. Example: 6783 – 8939 * 9102. You can win the Superman Trophy if you answered all 100 questions correctly.

Category C, I had no idea. But, I know from talking to one guy from Sunway that the organizer can choose team mates for you if you cannot find 2 people to join you during registration. I could have opted for that! Argh.

Category A – analysis of some questions (the ones I remember)

  1. Find all non isomorphic 5 vertex tree (connected with no cycle)
    Answer: http://math.stackexchange.com/questions/537295/how-to-find-non-isomorphic-trees
    Comment: I learnt this in discrete structure subject. Learn what is graph, isomorphism, isomorphism.
  2. You are to catch some flies, there are a delay before catching each fly, catching a fly happens at an instant. The delay to catch the first fly is 1 second. The delay to catch the 2m-th fly is the same as that of m-th fly. The delay to catch the 2m-th fly is less than 1 compared to that of 2m + 1-th fly. How long does it take to catch the 98th fly?
  3. Sum to infinity k^2/k!
  4. Two circles r inner radius, 1 outer radius, another circle o tangent to this circle, find ratio of both area as r approaching 1-

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