That's a pretty good program for increasing your push-up and lunge repetitions, if that's your goal. But keep in mind that it may also have some significant limitations, depending on your overall fitness goals. For example, building strength and muscle size requires that you challenge your muscles to the point of temporary fatigue within a fairly small number of repetitions, usually somewhere between 6 and 15 for most people. Once you get to the point that you can easily do 15 push-ups, doing more reps will help improve endurance, but it won't do much for adding muscle size or increasing strength, compared to a weight training program that keeps adding weight/resistance when you get to the point that you can do those 6-15 repetitions easily with the weight you're currently using. Also, push-ups don't do a great job of working some of your upper body muscles, especially some of the smaller shoulder girdle muscles. So, you may want to include some exercises for the rotator cuff muscles, for example.
The basic principal here is that the exercises you do essentially make you better at doing exactly what you do in the exercise--which is not necessarily the same thing as improving your overall functional fitness, strength, or endurance, which depends on training all your muscle groups to work together as well as strengthening them individually. That's why, for general fitness, it's usually important to have a balanced workout approach, incorporating movements that work all the muscles, and to the extent possible, work them in patterns similar to the way you use those muscles in daily life and your athletic activities.
This doesn't mean your shouldn't do the 100 push-up or lunge challenge , especially if having a specific goal like that and/or participating in a structured program helps keep you motivated. But I'd recommend not making those the only workouts you do for those muscle groups after you achieve your initial goal. Maybe you could check out some other challenging workout programs after your complete the 100 pushup challenge, like plyometric exercises, kettlebells, tabata, or others that put more emphasis on whole body movement patterns and allow you to increase the weight/resistance as you can.
Here's an article with some more info on the basics of strength training that covers some of these issues in more detail:
Hope this helps.
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