I would be lucky if I could do 10 push ups these days never mind 100 I remember around 10 years ago when in school I had to climb up the rope and touch the roof now that was an exercise.
Being a former member of the armed forces, what worked for us hitting the 200 bench mark was: Break it down into manageable sets ie: If you want 100 but can only do 10 at a time. do 10 x 10sets a day. Increase this number in week two to 20 x 5 sets a day. and so on. Push ups are not as much a strength exercise as they are a muscle endurance exercise. Work on your sets and by week 4-5 you should be hitting 80-100 consecutive. Good luck.
It's possible - I did 92 pushups when I did my final PT test for army basic training in the 80's - and each of those had to be perfect form (with a 2 minute time-limit) so I would have gotten a lot more if I could have done them like most people do. The secret to doing a lot of push-ups is to do a lot of well-formed push-ups. No great mystery. Nothing else will help you any better if that is your goal. We were doing over a thousand a day back then but you don't have to go to that extreme. Just do some several times per day until muscle failure and give yourself every other day off or so to recover.
I don't think there is any point in doing 100 pushups. What you should do is add resistance so that you can get a better workout from about 15
Doing 100 pushups is hard work. 1. You have to have a love for exercise. During the summer I slowly build up my body by doing pushups and challenging myself to the core. I could do 500 pushups and squats in under 30 minutes at peak. I would do 60 pushups in 60seconds sometime. I never tried to do 100 pushups straight but I am sure I could as long as it was just one time to test my strength. It will depend on your current shape to determine if you can do 100 pushups by 6 weeks. I dont think it really matters though as long as you're healthy and willing to exercise. At the end of the day there will always be someone bigger, faster, stronger, then you.
When i was trying out for the army i did 65 in a minute. If you do them regularly u could do it in 6 weeks i recon.