Maybe if you tried doing 5 sets of 15? That would be 75 for the day. And you could do 20,15,20,15,20 - and that would be 90 for the day.
I'm just joining this challenge today, I just did 20 right now and I believe I'll be able to do 4 more sets of 20 before the end of today. Honestly it's not gonna be easy because I can't even remember the last time I did some push ups, but I'm pretty much enthusiastic about this challenge.
I've been looking for some kinda boost to hit the gym and start exercising and this is undoubtedly the best boost I can think of, 5 sets of 20 push ups per day wouldn't be such a bad idea and I'll start reporting my progress as well from tomorrow.

I welcome you to this challenge, and we are happy to have you onboard. Since hitting 100 push-ups in 5 sets will be a little bit hard for you to achieve, I suggest you reduce it to 15 push-ups in each set so that you can do it without too much struggle. It is not compulsory that you do 100 push-ups a day; just do what your strength will allow you to do. If you are consistent with it, you will improve the number of push-ups you do in a set because your strength will increase.increase.