Turning a simple mech. problem into an olympiad one

[wrobel]

There is a nice sheet of mechanics problems: Kalda
I once shared this link on the PF.
Consider problem pr33. Since this problem is very simple let us modify it a bit. Namely assume that the left block has the same initial velocity:

The question is the same. I suspect that now it is an olympiad problem indeed. :)
My guess is to write down the Lagrange equations for the system with three degrees of freedom and expand the corresponding solution using the Taylor formula up to at least $O(t^4)$ .

 

[anuttarasammyak]

My guess. The pulley would turn counter clockwise by conservation of angular momentum. It would make the right block higher as it does in the original problem, even if mass of the purely is negligible.