First I love your screen name, it shows you have a sense of humor. If it had been 101 instead of 11 that would sound like a college course that would be very appropriate for this forum but still a very good screen name. I see you just joined, glad you found us.
There are some different things working here. How much room do they have and how is that room set up and managed? Room is extremely important when integrating chickens of any age. It can be even more important when you are mixing chickens of different maturity levels. If you could, a photo or two of the set-up and some physical dimensions in feet or meters of the coop and run could be helpful. Also, when is that various space available? Do you keep them locked in the coop only part of the time or do they have access to all possible space all the time they are awake?
Chickens are social animals and like to be with other chickens. But if you have a difference in maturity levels the more mature can often bully the immature ones as you are seeing. I regularly integrate 5 week old brooder raised chicks with an adult flock with almost no issues (have not lost a chick to another adult flock member yet) but my brooder is in the coop so the chicks are raised with the flock, they are not strangers. I have enough room so the adults and chicks can stay well apart. And I don't have single chicks or single adults, I have several of each. Your single 20 week old pullet might create some issues.
What makes you think your 8 week old pullet is lonely? At that age she shouldn't be, not with those two cockerels. When they hit puberty you may have issues with them but it won't be loneliness. It will be her trying to avoid them when their hormones get out of control, but that's a different issue. When you are dealing with living animals you don't get guarantees on behaviors. Some people will tell you that you will absolutely have issues with 2 cockerels and 1 pullet. You certainly can but it is not guaranteed. I've raised 19 cockerels with 5 pullets with my adult flock before without any of those issues, but I've also isolated cockerels from the main flock and the pullets when I had more pullets than cockerels because of those issues. To me ratios of pullets to cockerels don't mean much but their individual personalities, how much space they have, and how they are managed do.
So what can you do with what you have? A lot of that depends on how much space you have and how it is set up. I'd separate the older pullet from the chicks so they can see each other but can't get to each other for at least a week. There are different techniques for how to proceed from there, depending on space and your set up. Maybe a panic room. Definitely different feeding and watering stations so they don't have to compete to eat and drink.
If you can I'd get another pullet about 20 weeks old to keep that one company. Until the chicks reach maturity they tend to stay away from more mature chickens. Since that 20 week old is by herself she may want to be close to the chicks but if she gets close her bullying tendencies because of different maturity levels may take over. Their logic and thinking is not always like ours.
Try not to force them to be together. Give them the opportunity but try to let them work it out at their pace.
It's very possible that if you turn them loose together in a week or so things will work out great, even with just the four. It's also possible you could wind up with dead or injured chicks. With living animals you can't tell for sure how they will react. I certainly cannot give you any guarantees either way, but maybe some of these tricks will improve your odds of success. Good luck and again welcome.
