The functional equations that don't bore me, because the solution isn't just $f(x) = x$ anymore! This follows up the Monsters handout on my website.

Philosophy

Beware of pathological solutions... the usual methods apply. The problem set is mostly a collection of monsters. When you see the walkthroughs, don't be scared as the pset is less "dramatic" as Evan put it.

Notable problems

Walkthroughs

  • Shortlist 2004 A6, one of the walkthroughs, where only part of the function is benign;
  • GABRIEL, another notorious equation with a weird sol set;

Some of the featured problems include:

  • IMO 2012/4: The problem reminds of (redacted) ..... also, there were very few solves realtime, the fewest ever?
  • Taiwan TST 2017/2J/4, where you count solutions instead of explicitly finding them;
  • ISL 2013 A5, yet another infamous problem with unexpected solutions;