Isosceles: Hermione's S.P.E.W. Elf Shelter Mystery Cache
Isosceles: Hermione's S.P.E.W. Elf Shelter
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Difficulty:
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Terrain:
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Size: 
(micro)
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The cache is NOT at the posted coordinates. You need to solve a geometry problem, and then look for the container about 40 feet southeast of the puzzle solution coordinates in the skirt of a light pole.
The cache is a small tin. It is one of several in a series called "Isosceles" and themed for characters and events in the Harry Potter series of novels.
In the Harry Potter stories, the character Hermione is determined to treat all creatures equally. She even creates a society to protect elves, called S.P.E.W. This cache location reminded me of the Hermione character because the cache lies very near the apex of an equilateral triangle...all sides equal. To my amazement, when I originally scouted this cache location there was a small doghouse structure in the woods near these coordinates that just had to be a shelter built to assist some creatures that frequent this site. It was easy to imagine that someone sympathetic like Hermione placed it there. The woods have since been cleared and the structure has been removed. The cache container has been relocated to a nearby light pole.
All of the caches in this series are puzzles that involve solving for the location of the apex of an isosceles triangle. The base of the isosceles triangle is the line that connects two water towers in Kingwood. The cache is located at the apex that satisfies a condition that is specified below.
Tower #1 is located on Kingwood Drive near East End Park.
Its coordinates are: 30° 3.5293 -95° 9.3855
UTM coordinates: X= 292115 Y=3327263
Tower #2 is located on Woodland Hills Drive near the High School Agricultural Sciences Barn.
Its coordinates are: 30° 1.9972 -95° 13.0668
UTM coordinates: X= 286144 Y=3324545
The puzzle solution is located at the apex of an isosceles triangle whose sides are exactly the same length as its base. This special case of an isosceles triangle is called an "equilateral" triangle. The cache is SOUTH of the baseline.
The puzzle solution will place you in a small grove of trees. The cache is inside the closest light pole skirt ABOUT 40 FEET SOUTHEAST of the puzzle solution. This area was recently cleared of brush, so you will be very conspicuous to Muggles from all sides.
Additional Hints
(Decrypt)
Na vfbfpryrf gevnatyr unf gjb fvqrf gung ner gur fnzr yratgu. Gur guveq fvqr vf pnyyrq gur onfr.
Gur ncrk bs na vfbfpryrf gevnatyr vf nyjnlf rknpgyl gur fnzr qvfgnapr sebz gur bgure gjb pbearef.
N yvar pbafgehpgrq ng 90 qrterrf gb gur onfryvar guebhtu gur zvqcbvag bs gur onfr jvyy cnff guebhtu nyy cbffvoyr fbyhgvbaf sbe vfbfpryrf gevnatyrf jvgu gung fcrpvsvp onfr.
Gur zvqcbvag bs nal yvar vf fvzcyl gur nirentr bs gur raqcbvag pbbeqvangrf.
Gur Clguntberna Gurberz eryngrf gur fvqr yratguf bs evtug gevnatyrf. Na vfbfpryrf gevnatyr pna or gubhtug bs nf n evtug gevnatyr wbvarq jvgu vgf zveebe vzntr nybat gur zvqcbvag ovfrpgbe yvar.
Nyy pnyphyngvbaf fubhyq or qbar va Havirefny Genafirefr Zrepngbe zrgref. Gb genafsbez pbbeqvangrf orgjrra YngYba naq HGZ zrgref, lbh pna hfr lbhe TCF nf n pnyphyngbe ol fjvgpuvat lbhe TCF orgjrra qrpvzny zvahgrf naq HGZ. Perngr n jnlcbvag va bar pbbeqvangr flfgrz, gura punatr gur flfgrz naq ivrj gur jnlcbvag qrgnvyf va gur bgure flfgrz. Irel pyhaxl, ohg vg qbrf gur wbo. Tbbtyr Rnegu pna qb vg, gbb.
Vtaber gur Rnegu'f pheingher sbe qvfgnaprf guvf pybfr.
Gur fybcr bs n yvar vf Z=(L1-L2)/(K1-K2)
Gur rdhngvba bs n yvar vf L=Fybcr * K + Vagreprcg
Gb fbyir sbe na vagreprcg, erjevgr gur yvar rdhngvba jvgu bayl L ba bar fvqr bs gur rdhnyf fvta naq fhofgvghgr gur inyhr bs gur fybcr naq gur K naq L bs n cbvag xabja gb yvr ba gur yvar.
Tvira n yvar bs fybcr Z, gur fybcr bs nal yvar crecraqvphyne gb gung yvar vf -1/Z
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