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He puzzled and puzzled till his puzzler was sore Mystery Cache

Hidden : 8/15/2004
Difficulty:
3.5 out of 5
Terrain:
3 out of 5

Size: Size:   not chosen (not chosen)

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Geocache Description:

Betty, Jane, Andrew, and Karl all have numbers taped to their back. None of them can see their own number. However, they can all see everyone else's number.

Betty notes that Jane + Andrew + Karl = TotalB
Jane notes that Betty + Andrew + Karl = TotalJ
Andrew notes that Betty + Jane + Karl = TotalA
Karl notes that Betty + Jane + Andrew = TotalK

Your job is to figure out what numbers are taped to who's back, which in turn, will lead you to the cache. Your first step is to travel to

WPT1 = N44 41.008 W063 34.786

What year was the monument placed in this location? Based on the answer, you should be able to solve the following equations.
TotalB = the last 2 digits of the year, plus 20
DiffA = TotalB minus 18
DiffB = TotalB minus 76

Then goto WPT2 = N44 39.[DiffA]6 W63 [DiffB].057

What year year the plaque was dedicated? Based on the answer, you should be able to solve the following equations.
TotalJ = the last 2 digits of the year, plus 13
DiffC = TotalJ minus 46
DiffD = TotalJ minus 62

Then goto WPT3 = N44 40.[DiffC]0 W63 [DiffD].998

What year was the plaque was erected? Based on the answer, you should be able to solve the following equations.
TotalA = the last 2 digits of the year, plus 25
DiffE = TotalA minus 65
DiffF = TotalA minus 75

Then goto WPT4 = N44 40.[DiffE]3 W63 [DiffF].797

What year was the expedition sent from France? Based on the answer, you should be able to solve the following equation.
TotalK = the last 2 digits of the year, plus 90

You now have all of the values for all 4 totals.

Now comes the tricky part. You must figure out the values of each of the signs which are taped to each individual's back. Once you have those values figured out, you can now attempt to find the final cache. Fill in WPT5, and go find the cache!

WPT5 = N44 [Betty].[Jane]3 W63 [Andrew].[Karl]1

(Example: If all of the signs were 10, then WPT5 would be N44 10.103 W63 10.101. Obviously this is not the case, because the first formula would not work.)

Good luck!

Additional Hints (Decrypt)

Jvguva 5z npphenpl. Ybbx va gur ebpxf sbe gur svany pnpur

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)