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JUXOJ Mystery Cache

This cache has been archived.

ecrane: This spot doesn't seem to be lucky for me, so on the 13th I'm archiving this, my 113th hide. Thanks to all who came a-knockin'. Sendin' out 3s and 8s to y'all. Over and out.
[b][green]~ecrane h#113

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Hidden : 9/4/2010
Difficulty:
3 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


The cache is not at the posted coordinates, and it's not accessible from the highway.

Here's a math or combinatorics puzzle, but it mostly involves counting ... that, and a made-up word. A juxoj is a natural number that has the digits 3 and 8 in it. (It could have more than one of either ... or both.) The 3rd juxoj is 138.

A. What is the smallest one? (Hint: think degrees latitude)
B. What is the smallest one that when divided by 2 results in a juxoj?
C. What is the 10th one?
D. What is the 38th one?
E. (optional) What is the 100th one?

The cache is at N 38° 3N.NNN W 121° 3W.WWW.
N.NNN = (A + B + D + 8)/1000     OR     N.NNN = (E + E + D + 36)/1000
W.WWW = ((6 x C) - 62)/1000



You can validate your puzzle solution with certitude.

Have fun!

Congrats to Dobbinsfam for the FTF!

Additional Hints (Decrypt)

"...naq fur pbhyq urne gur uvtujnl oernguvat" --Uneevfba, Olear, Jrlzbhgu, Senagm

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)