I am just starting and am feeling dizzy already now I know why, that suggestion of resting for 20minutes seems perfect, because working so hard without rest, wear off energy in our body tissues, ligaments, tendons and leave us with so much stress shown on our faces and body especially for new members like me, so I make adjustments until I find a perfect solution that will propel me to do push up better everyday.
Since you joined this challenge late, do not be in a rush to do a lot of push-ups today; just maintain the 100 push-ups a day if you can handle it, or do less so that you will have a lot of time to rest your body. You must not complete 100 push-ups a day; you can do what your strength allows you to do, and as time goes on, you will keep improving in your push-ups.