I'll indicate the squares on the board by Cartesian coordinates. For instance, C is at (4,2) and A is at (3,5).
In the broadest terms, our strategy will be to get B to lie flat at (5,3) and (5,4), then move A to (4,3) or (5,2) so C can roll onto B, then move A to (6,4) so that C can roll to X. I'll break this into five stages.
Stage I: Getting B to (1,5) -- A(sswnen) B(enw)
Stage II: Getting B to (2,5) -- A(sw) B(sen)
Stage III: Getting B to (5,3)-(5,4) -- A(eswnenn) B(ees)
Stage IV: Getting C to (5,4) -- A(sswswnee) C(nen)
Stage V: Getting C to X -- A(wsseeenwn) C(ee)
This is a total of 46 moves. My first-order analysis is that getting A to (5,2) instead of (4,3) in Stage IV would take much longer in both Stages IV and V.
Notes: I solved this during the test, and it took me a little less than 15 minutes. My solution during the test was two moves longer (I had A moving nwswsseeenn during Stage V), so I didn't get the bonus points.
I hadn't attempted to solve a rolling block maze until the day I saw the instructions for this test, so I spent most of the night before practicing at mathpuzzle.com and other related sites. I am extremely grateful that the organizers decided to put out instructions before the test because this puzzle would have been impossible instead of merely challenging if the solvers hadn't been able to prepare for it.