Problem 3
Problem 3 with hints
Problem 3 with extended hints
Problem 3 with even more hints
The best solution awards [bonus factor exp(1/3)] goes to all those who derived the adiabatic invariant from basic laws
Marco Malandrone
Kaarel Hänni
Akihiro Watanabe
Taavet Kalda [As a non-official participant, he will not reduce the bonus factor down to exp(1/4)]Apart from these, there is a very nicely written solution by Diogo Correia Netto which earns him a bonus factor 1.1.