Last Saturday I went to NUS for SMO Senior Section special round. 3 hours to attempt 5 questions (no part a part b all those). Haha. Not bad eh.. in the end I only could do 2 questions.

Then yesterday I went to NUS again for SMO Open Section special round. This time, it was the same number of questions but 4½ to do! So it averages to 54 minutes a question. Haha. I also only knew how to do 2 questions, and spent around 2 hours on one question but in the end, I still didn't know how to do.

There were 2 questions which I did not attempt at all. One of them was:

Let a₁, a₂, ..., a_n be n real numbers whose squares sum to 1. Prove that for any integer k ≥ 2, there exists n integers x₁, x₂, ..., x_n, each with absolute value ≤ k - 1 and not all 0, such that