This is one of those puzzles I managed to solve but have no clue how I did it nor can I explain how the puzzle works!
The Push Box Puzzle came courtesy of Simon Nightingale during the IPP34 puzzle exchange. If you didn't already know, Simon was the winner of the Grand Jury Prize for the 2014 IPP34 Nob Yoshigahara Puzzle Design competition for his "Six Locks 2 Keys" puzzle.
The Push Box is made from Corian (the stuff that you would normally find on kitchen and sink counter tops). The puzzle is pretty heavy and well made in a nice light blue colour. The joint lines are well hidden and not obvious at all. It looks like Simon had dug out the insides to create the box. I am not sure how strong Corian is but I would think the box would likely crack if dropped onto a hard floor from anything more than 3 feet. The object is the push and "open the box" like a drawer.
The drawer is spring loaded and allows for some movement (several mm) inwards but there is hidden mechanism which keeps the drawer from coming out of the box. Inside there are a couple of ball bearings spinning around, which may or may not have anything to do with the locking mechanism (yes, there are some puzzles where ball bearings are red herrings; serve no function but to merely to confuse).
I fiddled with the puzzle for a while, trying to guess how the drawer is locked inside the box and how the ball bearings come into play. I pushed and released the drawer over and over again, turned the box at all sorts of angles and in all orientations, and all of a sudden, pop out comes the drawer. The drawer cannot be fully withdrawn and part of it remains inside the box. Again I am not sure if the drawer is intended to fully come out, but I don't think so. And the box also cannot be taken apart.
I managed to solve it a couple more times, more through trial and error, but not fully understanding how the hidden mechanism/trick works, at least not until I see the inside. And mind you, I have a fair amount of experience with trick/puzzle boxes. I have emailed Simon for the solution. Hope he replies soon. I am really super curious as to how it operates. I will update this post, once I have seen the solution.