##### This cache has been archived.

dgauss: Post time to let this one go. It's been fun reading the comments tho.

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## Just Fix It

A cache by dgauss Message this owner
Hidden : 01/02/2012
Difficulty:
Terrain:

Size:  (small)

#### Watch

How Geocaching Works

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### Geocache Description:

The cache is NOT at the posted coordinates.
Rather it is at

### N A°B.C W D°E.F

where

A = ×4+56
B = /×452
C = ×2×5-×561
D = 45×5×7-
E = 56×2/
F = 999×65×+×

Jan Lukasiewicz (1868-1956) was a Polish logician who made an early contribution to the development of computers. In his studies on mathematical logic he introduced and promoted a notation for logical expressions which was unambiguous, parenthesis-free and could be evaluated in a single left-to-right scan. These were exactly the qualities desired for the fast evaluation of arithmetic expressions by computers. For arithmetic expressions as well as logical expressions there are two such forms depending on whether the operators come before or after their operands; these are known as prefix and postfix expressions, respectively. Prefix is also called Polish Notation because that was the notation Lukasiewicz first used and many people had trouble pronouncing his name. (The correct pronunciation can be heard by grabbing a long piece of tin by one end and giving it a good shake.) Postfix is called Reverse Polish Notation or RPN despite the fact that postfix is not exactly the reverse of prefix as we'll see below. RPN was commonly used on many calculators and is at the heart of most computer compilers. In fact entire programs, not just arithmetic expressions, are compiled into a postfix form for ease and speed of evaluation.

Examples: Consider the expression a-b/c in infix notation which usually means a-(b/c), as / has priority over -. However on some calculators entering a,-,b,/,c might return (a-b)/c! To remove such ambiguity the two expressions completely parenthesized would be (a-(b/c)) and ((a-b)/c) resp. In prefix notation a-(b/c) would be written as -a/bc and in postfix as abc/-; whereas (a-b)/c would be /-abc and ab-c/, resp. As desired these expressions are parenthesis-free and can be evaluated left-to-right, employing temporary storage called a stack because items are placed on the top of the stack and also taken off the top. Postfix is preferred as it only stacks values. In postfix evaluation, whenever an operand is scanned it is simply placed on the top of the stack; whenever an operator is encountered it is performed on the top two values on the stack and the result is then stored on the stack. The rules for prefix evaluation are slightly more complicated.

You can validate your puzzle solution with certitude.
Acknowledgement: Thanks to JustJackMN for suggesting this topic.

Haqre n ghegyr.

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)

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