Suspended between benchmarks Mystery Cache
Suspended between benchmarks
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Difficulty:
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Terrain:
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Size: 
(regular)
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in our disclaimer.
The coordinates are not for the
cache, although it is a useful intermediate waypoint
for the driving part of your quest. Solve the puzzle below
before you go, or bring a good calculator on the trail to
solve it on the go.
This cache was inspired by georapper's 3D
Triangulation cache. Thanks, georapper! We chose quite a bit
easier terrain, but the math is certainly no less challenging
here. This cache is also meant to be a plug for the
often-overlooked benchmarking section of geocaching.com.
The cache is located in 2,977 m from the summit of Mt. Aire and in
4,483 m from the summit of Mt. Raymond. These are actual 3D
distances. If you try to simplify the problem by solving it in two
dimensions, your result is going to be hundreds yards
off.
The assumptions are as follows:
- UTM locations and altitudes of the summit benchmarks are
precise
- 1 ft = 0.3048 m
- choose the solution with the lowest altitude (the other one is
on the harder terrain, too).
- the altitude of the cache was read from the map. My GPSr would
display a 10-to-20 ft higher numbers (the reception is pretty good
around the cachesite). But even if your altitude reading is off by
30 or 40 ft, you should still home in on the cache location just
fine.
If you would like to solve this problem analytically before you go,
then the added challenge (compared with 3D
Triangulation in Poci) might come from the need to rotate your
solution in 3D space. The most intuitive way of doing this, IMVHO,
is to apply two rotation matrices consequitively. E.g. you rotate
around X axis first, and then around Z axis, and in this way you
end up where you wanted, in two easier steps.
On the other hand you probably don't have to calculate all this 3D
stuff in advance. Wander around the area, keep applying the
Pythagoras thing to whatever relevant numbers you get, and it
should do.
The cache is an ammobox (as of 7/3/06) with the usual combination
of coins, toys, and useful thingies. For the first-finder prize, we
threw in a
whole extra ammobox of stuff, including DaScorpion
the Cach-U-Nut #198. Have fun!
Additional Hints
(Decrypt)
ba gur tebhaq yriry - abegu rqtr bs n obhyqre