Hi everyone,
The problem is one I saw on a mathematical puzzle book some twenty years ago and the solution offered seem plausible to me at the time. However, I still considered it a bit skeptical as it is so hard to believe.(See my previous post)
It was definitely not the Rupert's problem as that was easy to explain and understand.
As this has generated some controversy, I have decided to mock one up and try to get to the bottom of it, for everyone else and also myself.
Needless to say,the cube barely pass 20% of itself through the square hole, no matter how I turn it.
I sincerely apologize for misleading everyone on this. My hat off to JimB and Ron.