Want a challenge? Do a Russian IChO.
Actually Mao - YOU should try the Russian IChO 2007 I think it was.
http://www.icho39.chem.msu.ru/downloads/endTheoretical_task_complete.pdf
link me?
Procrastination mode ON.
EDIT:
Problem 1: I do not know of a quantum system that perfectly oscillates as the given wavefunction suggests. I haven't done much quantum modelling myself, but I don't think it makes sense that the dynamics of this proton tunnelling effect is so well defined. As far as I'm concerned, it is still governed by the Boltzmann distribution, the sinusoidal variation simply doesn't make sense to me.
Problem 2:
The formulation of free energy here is inconsistent. Why insist that the free energy of nanoparticles have a pressure term, and then assume that once the surface is oxidized it becomes a bulk-like environment? An oxidized nanoparticle is still a nanoparticle, and there will still be a significant pressure term. nevermind, jumped the gun. they eventually did it properly.
Lost interest at problem 4+. This is the kind of maths an experimentalist would encounter when trying to interpret a physical measurement. There also seems to be a particular fascination with rate equations, but my qualm with that is why should I try to deal with rate equations when I can throw it into Mathematica, and instead spend my time on problems that cannot be solved by a computer?

Problem 1 was the most fun.