Can see this post is a few years old .... however as a great push up strengthening exercise, that we used to do in boxing training.
Do 1 push up, rest for a few seconds then do 2 push up, rest for a few seconds, then 3 push ups, then rest , then 4, 5, 6, 7, 8, 9 whilst resting for several seconds in between ..... all the way up to 10 push ups.
Then rest for several seconds and do 9 push ups, then 8, then 7, 6, 5, 4, 3, 2 .... all the way back down to 1 push up.
Sounds ever so easy, until you try it!