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Collatz Mystery Cache

Hidden : 9/22/2021
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


Cache not at posted coordinates.  Solve the puzzle below to get the coordinates of the cache.

The final coordinates are: S41 21.0AB E173 10.CDE

AB is the length of the sequence starting at 111,911.

CDE is the length of the sequence starting at 9,973,919.

Each term in the sequence is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. Continue generating terms until the sequence reaches 1 which is the last term in the sequence.

Here is an example to help you solve the puzzle.

The sequence starting at 6 is:

6, 3, 10, 5, 16, 8, 4, 2, 1

Which has a sequence length of 9.

The first term is 6 which is even, so the second term is found by multiplying 6 times 1/2.

The second term is 3 which is odd, so the third term is found by multiplying 3 times 3 and then adding 1 to get 10.

And so on until your reach 1.

Starting at any positive integer, will the sequence always reach 1?  For more information, see Collatz Conjecture.

Additional Hints (Decrypt)

Ab arrq gb trg lbhe srrg jrg. Cyrnfr or fgrnygul jura frnepuvat sbe gur pnpur. Ab uvag arrqrq. Cyrnfr pbire jvgu gur gjb ebpxf whfg gb gur evtug bs gur raq bs gur srapr.

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)