This is the first time I have heard of the 100 push ups challenge. Are you trying to do 100 per day or working up to a set of 100 like this plan: https://hundredpushups.com/index.html

I did the test set to determine my starting level then decided to do a few sets to get to 100. I rested about 2 minutes after the first set then 1 minute for each set afterwards.
30, 20, 15, 15, 10, 10