Umm... what do you mean by "rest"? When I did something like this back at boot camp, we were allowed to "rest", too... on the "up" position of the pushup exercise. Can I get up, have a sip of water and do a sudoku while "resting", or what.
EDIT: I also have no way to measure distances. I guess a treadmill would be considered cheating?
I think the impression is that you can do whatever you want in those 2 minutes, just keep track of how many push ups you do in them.