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Well, I hate the idea that this forum just dies and my last "contribution" is a puzzle thread with zero responses.
Anyhow... I have yet to watch the video, but have talked the puzzle over with two of my kids. My leaning is to basially think of the puzzle as effectively becoming a series of one and zero answers, where the biggest entry is so massively oversized that all the rest become trivial in contrast, and the average ends up effectively being MAX/n.
But (in this scenario) while MAX manages to skew the results with his absurd number, he won't win because 2/3 of the average will remain far closer to the second highest entry than his.
So, my approach is to try to guess what the MAX number will be, and submit my entry seeking to be second highest and in the ballpark of the correct result.
Among all the impossibly large numbers, it's hard to pick one so my reckoning is the two that make the most sense are the impossibly huge numbers that have some familiarity. So, among them I can think of three:
Avogadro's number, 6.0223 x 10^23
a google, 10^100
a googleplex, 10^(10^100)
Putting myself into the shoes of the wiseass who would (1) play this game, and (2) come up with the angle to try to break the game with the impossibly large number, I choose the googleplex as his answer.
So I'm going to work with the assumption that we will have n=100 entries, and I plan to submit a number designed to win if one person enters a googleplex and no other numbers are anywhere near that magnitude:
2/3 x 10(10^100-2)
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