From charlesreid1

Possibly The Biggest Number You've Ever Laid Eyes On

The Story

POOKIE hijacks the video feed, and wrestles control.

Oh no! Our feed has been hijacked!

Hello kiddies! Are you ready for this week's puzzle?

The Eddington number, which approximates the number of protons in the known universe, is 10^80

Archimedes, in the Sand Reckoner, approximated the number of grains of sand that could fit in the known universe at 10^63.

But these are peanuts, and they come nowhere near the largest numbers conceivable by mankind.

Claude Shannon famously created the Shannon number, the number of distinct games of chess that can be played, at about 10^120. Taking into account various rules and invalid positions, the number is closer to 10^50. That's a one with fifty zeros after it.

A googol refers to the quantity 10^100. In case you're wondering - yes, it's the origin of the term Google.

There are a class of prime numbers called gigantic primes that includes 2^44497 - 1, a prime number with 13,395 digits.

You can also create nested exponential notation: tetration is an operation that is defined as follows.

Consider the number 4. To make a larger number out of 4, you might add 4 to 4 and get 8. You might multiply by 4 to get 16. Or you might raise 4 to the power of itself: 4^4, or 256. But what if you took that a step further: Raise 4 to the power of 4, 4 times:


4^{4^{4^{4}}}

That's 4 tetrated, or {^{4} 4}. That's a very, very, very big number:

4^{4^{4^{4}}} = 4^{4^{256}} = 4^{ 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 }

And that's just FOUR tetrated.

Imagine 10 tetrated. 20, 30, 40 tetrated. 100 tetrated. A googol tetrated.

Okay, kiddies, time for the puzzle.

What is the remainder when you divide


4^{ 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 }

by 11?

You may think that guessing one, then two, then three, until you get to eleven will be a lot faster than punching that number into your calculator. But beware! POOKIE will demand proof, and will reject any attempts by the faint of heart to guess at the answer!

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