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X (the 24th letter) Mystery Cache

This cache has been archived.

Rich_Life: The recent road construction on E. Woodmen Road finally claimed this cache. Taos Drive once came to a dead end before it reached Woodmen. There was a nice quiet meadow and a tree in the corner of the meadow where the cache was hidden. I went by today to see if I could find the cache in the pile of tree rubble to no avail. Another one of my caches had been bulldozed into oblivion in the name of progress.

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Hidden : 4/13/2010
Difficulty:
3.5 out of 5
Terrain:
2 out of 5

Size: Size:   micro (micro)

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Geocache Description:

Need an X for anything? The cache is NOT at the above listed coordinates. It is a busy enough boulevard without you standing in the middle of it. Please solve the following puzzle to find the cache.

Lots of words begin with this much neglected letter of the alphabet. Here is just a small sampling. You will need the number after each word to form a larger number:

Xhosa (0); Xenophon (1); Xanadu (2); Xenia (2); Xinhua (2); Xipe (3); Xylem (3); Xyster (3); Xerophyte (4); Xanthus (5); Xerus (6); Xylitol (7); Xyst (7); Xu (8); Xylene (8); Xanthan (9)

Knowing the definitions of these words will help you solve this puzzle. I dislike (hate is such a strong word) math just as much as the next guy (okay—there are some math lovers out there—but not many) but I couldn’t construct a puzzle about the letter X without also using this definition: “X, Symbol. An unknown quantity or a variable.” So here’s the deal, solve for X to find X (the cache)!

Calculate the cube root of a number made up of seven digits as defined below: a city in W Ohio; the Aztec god of sowing or planting; an ancient city of Lycia, in SW Asia Minor; the official press agency of the People’s Republic of China; an African ground squirrel; a surgical instrument for scraping bones; and a covered portico, as a promenade. This number is seven digits long, one number for each definition. Are you with me so far? Do not add or multipy these numbers, just use the seven-digit number!

Calculate the square root of a number made up of six digits as defined below: a water-soluble natural gum produced by the fermentation of sugar with certain microorganisms and used as a binder, extender, or stabilizer in foods and other products; a compound tissue in vascular plants that helps provide support and that conducts water and nutrients upwards from the roots…; a naturally occurring pentose sugar alcohol, used as a sugar substitute; a member of a Nguni people of eastern Cape Province, Republic of South Africa; a place of great beauty, luxury, and contentment; a plant adapted for growth under dry conditions. This number is six digits long. If you got the number above then this one should be a little bit easier!

A special thanks goes out to Mr. Webster for helping supply the definitions for this puzzle.

The cache is located at:

N38° 56.cube root of X; W104° 45.square root of X.

You can check your answers for this puzzle on Geochecker.com.

Congrats to mtn-goat for FTF honors.

Additional Hints (Decrypt)

.fxpbe av xpvgf erqah

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)