For those who are having difficulty maintaining a certain number of push-ups in each set, such as doing 15 push-ups each in 5 sets, when you are doing your push-up, do not be in a rush to complete your push-up. Always take a minimum of 20 minutes to rest before you can start another set so that you will have enough strength to do the same number of push-ups you did in your first set.
I think 20mins is too much to take a rest, when you feel that tiredness while doing the push up and you don't stop that's when you get the effects more, and 30 seconds is enough for a rest. Whenever you rest for long like up to 20mins like you said, it might discourage you from continuing the task for the day, for me I do 100 every morning with some other fitness exercises, 30secs rest and I go again, like 2 to 3 times repeating same process even at night and whenever you do your exercise take a lot of water, it helps.
This challenge made some people do push-ups for the first time in their lives. If they adopt this 30-second rest before they start another set, they may want to quit this challenge because they will not have enough strength to even do up to five push-ups in the second set. If I adopt this strategy, I will not maintain my 50 push-ups in a set because my body will not get enough rest that will allow me to endure pain and still push until I reach 50 push-ups in my second set. Taking enough rest when working out is important for our bodies.
If our bodies are not necessarily young, and so if we do pushups throughout the day, there may be 3-6 hours between sets.. and depending on if there are 3 or 5 sets in a day, or maybe even more, but I have personally found 5 sets in a day scattered through the whole day to be helpful to be able to carry out the task, including that there continues to be a lot of soreness when adding this kind of activity to a routine and maybe either we had not been doing this kind of activity or that some of us are not very young, so there can be issues with recuperation time.. some older folks might have to start with just a couple sets per day, but then it probably still could be good to try to do something like 5 sets throughout the day, and just trying to figure out how many pushups per set are manageable to balance the soreness, the recuperation time and strength to do more pushups without injuring oneself or overly exhausting ones whole system (including psychology).
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I know what you are talking about because I used this type of strategy when I did a chest workout with my friend, and I must say it requires a lot of strength to keep up with it. Since we are not in competition here, we need a strategy that will allow us to have enough rest. We can even take some days off from this challenge just to get enough rest if our bodies are stressed out so much.
Another thing is doing pushups every single day for 100 days or more. The strategy needs to be more careful in order to not wear ourselves out and to be able to keep doing them day after day after day, and if we overdo how many pushups at a time or put them all together in quick sessions, we may well cause ourselves to become too sore, even though sure maybe some younger members are going to be able to accomplish those quick short sessions without having problems in being able to continue to do them day after day after day.