GC74YG1 Collatz Conjecture III (Unknown Cache) in Oklahoma, United States created by The Snowdog

GC74YG1 ▼

A cache by The Snowdog Message this owner

Hidden : 5/1/2017

Difficulty:

Terrain:

Size: Size: micro (micro)

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Geocache Description:

The puzzle is not at the posted coordinates.
Solve the puzzle to locate the cache!

Pick a number, any number. If it's even, divide by two. If it's odd, multiply by three and add one. Then do it again, and again, and again...

The Collatz Conjecture proposes that no matter what number you choose, you'll always end up at 1.

For example, let's start with 42. The sequence is 42 - 21 - 64 - 32 - 16 - 8 - 4 - 2 - 1.

So the starting value of 42 completed the sequence in 8 steps (the path length) and the sequence reached a peak value of 64.

The Collatz Conjecture is called the "hardest simple problem" in all of mathematics. The only operations required are addition, multiplication, and division; yet no one can prove whether the conjecture is true or not. No counterexample has been found that is less than 10¹⁹ or so.

This series of three puzzles will help you investigates the Collatz Conjecture. The first is an introduction; solving the puzzle will require little (or no) math as the values you need can be found online. The second requires a little research about Collatz and the properties of the Collatz Conjecture; again, solving the puzzle will require little actual math. The third will require that you work with numbers large enough that a calculator will be useful.

Congrats to Max and 99 for FTF!

Additional Hints (Decrypt)

YCP

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)