The most "Old School" QuikSand/FOFC puzzle ever

[QuikSand]

Inspired by favorites from days gone by like:

FOFC Game: Guess the Median Number - Front Office Football Central

OT - Monty Hall resurfaces in Parade magazine - Front Office Football Central

(I fear the original FOFC Monty Hall thread was lost in the site migration many moons ago... but people offering "2/3" as an answer to any QS puzzle lived on for a long time arising from that...)


Here's a 40m YouTube video that scared up some real ghosts for me...

[QuikSand]

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)

[Passacaglia]

Originally Posted by QuikSand

Anyhow... I have yet to watch the video, but have talked the puzzle over with two of my kids.

Two of your three kids (I hope)?

[QuikSand]

Originally Posted by Passacaglia

Two of your three kids (I hope)?

i only deal with the offspring in increments of 2/3

(yes, two of three kids, fantastic)

[QuikSand]

Alas, by not watchign the video, I ended up on a wild goose chase with my unbounded framing. A fairly interesting one, but nonetheless not related to the puzzle in the video.

In the video it's confined from 1 to 100.

The theory is that logic tells you to never stop contracting the range of possible answers:

-the highest possible average is 100, to the winning number can never be more than 2/3 of that, so nobody would ever submit 67 or higher...

-but given that nobody would ever submit higher than 66, now the highest possible average is 66, so the highest winning number is 2/3 of that, or 44 so nobody would ever submit higher than that...

-but given that nobody would ever submit higher than 44, now the highest possible average is 66, so the highest winning number is 2/3 of that, or 30 so nobody would ever submit higher than that...

...ad infinitum, and ad absurdum.

So, it becomes less logic and more human nature. Fun to mull over.