Google This! Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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Here's another puzzle for mathematically minded geocachers. In my previous attempt at this type of puzzle, a few geocachers unexpectedly found the solution using Google. Well my response to that is "Google This!"
Analyze the dots in the image below and determine the length of DF rounded to 7 decimal places.
Let DF = a.bcdefgh.
The digital root of abcdefgh is 1.
The diagram is not drawn to scale and the position of the dots is approximate.
But knowing the following 6 angles and 3 lengths, fixes the length of DF exactly:
Lengths CE = 1, AF = 2, BD = 3.
Angles FDA = DFB = FEC = 90 degrees.
Angles ACF = BCD = DEF = 180 degrees.
The cache not at the posted coordinates but at: N47 39.[c-2e][f+d][g-3f], W122 19.[c+2e][f-c][h-g]
When calculating digits for the coordinates:
If a result exceeds 9, use only the rightmost digit.
If a result is negative, flip the sign to positive.
The puzzle can be solved in a variety of ways. Using algebra all the way to get an exact solution is a messy slog. However, I've discovered an approximate solution, using just a little algebra and a simple algorithm. The result can be generated either by a 8-line computer program or a 4-column spreadsheet. If that seems like too much work you can always flail away with Google.
Good luck.
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Note: 9/4/07
It took fishiam coming out of retirement to solve this. Congratulations to the old master. Now Fish Soup, after a little refresher course in high school algebra, appears to have the solution. It looks like the rest of you are going to flunk the math part of this assignment. As I said, there are a variety of ways to solve the puzzle. Surprisingly, the easiest way is the one mentioned in the title, Google! That is of course, if you know the correct search words.
So here is some help that will get the rest of you back on track. Go to N 47 39.912 W122 19.013.
At this spot name two objects that are in clear view. Get them both and Google will bring up a web page with the solution, correct to ten figures, to the top. *** This is not true in 2015, see Note 8/1/2015 below *** Get only one key word and you will still have quite a bit of work to do. Perhaps just being at this location will jog some memories.
Note 9/5/07:
Additional Hints-- Today I stopped by the spot and was surprised to discover that one of the objects had been moved and was now hard to recognize. It will probably be returned to its usual position soon. Luckily there is another of these same objects close by that is not going anywhere. But because it is not as obvious as the first, I'll add some additional hints. Although one of the things you are looking for is much smaller than the other, both are clearly recognizable as you look about when facing north. Both things have similar shapes, long, narrow and flat. One is long in the vertical direction and the other is long in the horizontal direction.
Note 9/7/07:
Another Hint-- Although both objects are long and narrow, the length to width ratio of one is much greater than the other.
Note: 9/9/07:
One more hint-- One of the objects is part of the art installation.
Note: 9/22/07:
The art object is sometimes moved out of sight. However, there is a larger, more functional version of this same type of object just a short distance west of the art installation. The art object and it's larger version are both smaller than the the second object you are seeking.
Note: 12/29/09:
I discovered that the solution using the two-word Google search can be done without leaving home. The Google Maps street level photos of the "art instillation" site clearly show both items you need to identify for a successful web search. Because of the current construction it is better to stay home and do this entirely on your computer rather than going to the location and looking.
Note: 8/1/2015: The google search algorithm has changed over the years and it now takes a third search word to bring up bring up the desired web page. Adding "solution" to the original two search words now brings the desired web page to the top. This currently works but who knows for how long.
Additional Hints
(Decrypt)
Ab arrq gb chg lbhe unaqf va gur oenzoyrf.
Hfr pner nf lbh erzbir pnpur sbez vgf uvqvat cynpr.