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Target audience: Typically the course is for undergraduate students but the course is also recommended for students who are in high school and higher secondary and quite advanced in Mathematics.

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How do I know if this course will interest me?

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If the below questions interest you, then this course may be of interest to you.

 

1. Do there exist 100 consecutive natural numbers with exactly 7 primes in them?

2. In the Parliament of Sikinia, each member has at most three enemies (enmity is mutual). Prove that the house can be separated into two houses, so that each member has at most one enemy in his own house.

3. Suppose the positive integer n is odd. First Pichai writes the numbers 1, 2,..., 2n on the blackboard. He then picks any two numbers a, b, erases them, and writes |a − b| instead. He repeats this process until only one number remains on the board. Prove that an odd number will remain at the end.