Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody

The Rainbow Redemption

It takes about another ten minutes to finally calm Rarity down enough that you can proceed on with your quest, but you manage to wash the mud off before your ears are wrecked beyond repair. There are only two more ponies to rescue, and with it, hopefully the mystery of the strange mountain and the unusual array of puzzles along the way may be solved.

Your next hostage turns out to be none other than Rainbow Dash, who the group encounters nearer the top of the mountain, inside what looks like a long forgotten temple. She's trapped inside an hourglass running the hour, and just to throw in a few more irony points, she seems to be coming close to drowning under Prism Poppers. And they're coconut flavoured: the absolute worst kind next to coffee flavoured. Things truly cannot be any more cruel.

Fortunately, Rarity is more than willing to step up to bat to try and free Rainbow Dash (after Applejack conclusively proves unable to break the glass with several well-timed bucks) and makes her way to a small sign. The instructions are refreshingly direct - almost disappointingly so:

Estimate 2⁶⁴.

Sadly, out of all the equipment you and Twilight packed for the expedition, a calculator isn't one of them. Twilight is tempted to break out her parchment and quill to write down the calculations, but is bluntly informed by Applejack that Rainbow probably won't last that long, and it says to GUESS the number. Even pinkie admits that she'd probably make a mistake somewhere if she tried it the hard way. In other words, the right logic thread will get you close enough to the answer to pass.

The real question is if Rarity can figure that out too. So how can it be done: estimating the number to a reasonable degree of accuracy?

Author's Note:

So outline the logic that leads you to the answer. I won't accept just a number here.

1. 2⁶⁴ is 2 multiplied by itself 64 times.
2. You may not use a calculator.

PUZZLE: Estimate 2⁶⁴.

Comments

[SisselSandvich]

Probably the simplest method is using the fact that 2¹⁰ is 1024, which is slightly over 1000, so we can say 2¹⁰ is approximately 10³. This would make 2⁶⁴ about the same as 2⁴*10¹⁸, so our estimate would be about 16 quintillion, though we know it's a bit on the low side (for what it's worth).

[Duckgame4life]

Hmmmm this might work
2^4=16
16^4 is about 65 000
65 000^2 is about 4 billion
4billion^2=16 000 000 000 000 000 000 or 16 quintillion

[The Real Anonymous Pony]

2⁶⁴ is ~18,000,000,000,000,000,000
I was writing some long winded answer involving 2⁴⁴⁴, when I noticed something.
There are six groups of three zeros in the answer and the problem is 2⁶⁴. "It can't be that easy right? Well, let's see what 2¹⁰ is."

2¹⁰ = ~1,000
2²⁰ = ~1,000,000
2³⁰ = ~1,000,000,000
2⁴⁰ = ~1,000,000,000,000
2⁵⁰ = ~1,000,000,000,000,000
2⁶⁰ = ~1,000,000,000,000,000,000
2⁶¹ = 2⁶⁰*2 = ~2,000,000,000,000,000,000
2⁶² = 2⁶¹*2 = ~4,000,000,000,000,000,000
2⁶³ = 2⁶²*2 = ~8,000,000,000,000,000,000
2⁶⁴ = 2⁶³*2 = ~16,000,000,000,000,000,000
~18,000,000,000,000,000,000 is only a little bit off.

[Brony_of_Brody]

9420813
Simplest, sure, but not the best way.