How to pinpoint specific date from limiting ranges

hello. i am writing a historical novel. i need to set it in a year that overlaps with multiple historical events. ie. i want to find a specific year in which all of the historical events are occurring.
example:
george bush is president from 2000-2008
a talk show host has televised from 1990 to 2020
the antarctic war takes place from 2001-2015

I need to pinpoint an exact year in which all of these events are occurring. the problem is, with my novel, the dates are much longer and there are MANY, MANY more events.
In the case above, a possible date would have to be between 2001 and 2008, because all 3 events take place during this period of time.
Please, please PLEASE help! You would be a savior! I will send money!

Hi again! I've been working very hard on my spreadsheet, and I think I've got it down, except I can't get the spreadsheet to give me the answers when I press Ctrl+shift+enter. I'm a newbie at excel, so I'm probably neglecting something really simple. Here's what I have. Thanks so much for helping me!

Oh my god! Thank you so much! You are incredible! Thank you! You have NO IDEA how much this is appreciated! Thank you!!!

@ narbit

Based on your last post it seems that you are satisfied with the solution(s) you've received but you haven't marked your thread as SOLVED. I'll do that for you now but please keep in mind for your future threads that Rule #9 requires you to do that yourself. If your problem has not been solved you can use Thread Tools (located above your first post) and choose "Mark this thread as unsolved".
Thanks.

Also, as a new member of the forum, you may not be aware that you can thank those who have helped you by clicking the small star icon located in the lower left corner of the post in which the help was given. By doing so you can add to the reputation(s) of those who helped.

well, I don't exactly understand how you end up getting the final "answer." here it is again. and if not. here is a google docs link. thank you so much for continuing to help me!

https://docs.google.com/spreadsheet/...EpBNmdsQ2tOMXc

Okay, I have deleted the non-overlapping event. The rest of them do, in fact overlap. But I'm still getting no results. After I input the values are the corresponding dates just supposed to show up in column B, or do I have to do something to make the appear?
https://docs.google.com/spreadsheet/...G9ReDhhbE5KSkE

thanks so much! everything is fine now!