Hi Geocaching Community,
With some sadness, I have archived a portion of this cache series and now "The Final Thing" will stand alone. Each of the series caches contained a clue to solve the final puzzle, with the appropriate information now transferred to this cache page. As this has proven to be a challenging puzzle for many cachers, I hope it will live on and be one of your favorites too.
So the background:
Back when I was a wee-old cacher, I had grand plans to hide the "most difficult and clever puzzle" in the area. Of course, that didn't become a reality (you all are too smart for me), but it was at very least tricky and had some style.
Basically, I'm asking you to account for the curvature of the Earth - yes, it exists and is relevant even within our little community. Using a method called TRILATERATION (not triangulation as we learned back in high school), you can determine a location by three distances instead of angles.
As an engineer, I assumed I'd crank right through this setup but found out quickly that this math is way beyond me. I once worked with several Ph.D. Post-Grads, one a physicist who did differential calculus for fun on his lunch breaks. They flatly declined this problem, calling it "Spherical Geometry" and that most people still can't do it. Instead, I turned to another Ph.D. (an engineer - take that Sheldon!) who tried and after 8 weeks of working on VERY large equations, resigned and provided some simplified solutions which I pumped into a spreadsheet and here we are...
So today, I re-pose a much-simplified situation of the problem, which occurs in the days of Gilgamesh (you know, when the Earth was still flat). From a certain three locations, a fourth can be found. That’s where you’ll find the cache.
As the location caches no longer exist, the information needed is posted plainly below. I will leave the difficulty of the math and hide to maintain the 5-Star difficulty, but will not be providing coordinate checks or solvers. Also, as so many of your fellow cachers have found out, and I'm sure the neighbor will appreciate - this cache is NOT located in someone's garage but in public space with easy access.
Location 1 (Previously "Thing 1")
N 45° 04.033 W 093° 03.667
H1 = 0.015611742375526
Location 2 (Previously "Thing 2")
N 45° 03.491 W 093° 04.787
H2 = 0.00836557828246395
Location 3 (Previously "Thing 3")
N 45° 04.655 W 093° 04.569
H3 = 0.0116429978957274
Good Luck Everybody!
Chris (Mr. Lazy)