The goal of this set of notes is to improve our problem solving and proof writing skills. You are encouraged to submit a solution to any of these problems, and join in the discussion in #imo-discussion on Saturday 12 at 8:30 pm IST ,0800 PDT. For more details, see IMO Problems Discussion Group.
It has been a lot of time since the Last note in the series. Examinations really took over and I couldn't concentrate here... Any ways happy Problem Solving!. For all the Brilliant community here who are scared of IMO Questions try Q1 and Q2. Post any ideas you may have, doubts you come across or solutions you get!
1. (POL) Find the smallest natural number with the following properties:
(a) In decimal representation it ends with .
(b) If we move this digit to the front of the number, we get a number times larger.
2. (HUN) Find all real numbers x for which
3. (CZS) A cube ABCDA'B'C'D' is given. The point is moving at a constant speed along the square in the direction from to . The point is moving with the same constant speed along the square BCC'B' in the direction from to . Initially, and start out from and B' respectively. Find the locus of all the midpoints of .