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## Zaturated Tuusula ?

A cache by arde2009 Message this owner
Hidden : 02/03/2017
Difficulty:
Terrain:

Size:  (small)

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### Geocache Description:

As the whole exercise is completely virtual, I also invented a virtual word zaturated to loosely describe what you are supposed to do:

Your task is simply to fill Tuusula  with as many caches as you can:

1. You should assume that Tuusula is completely cache-free area

2. You don' t have to worry about lakes , rivers, houses, private areas : all locations inside Tuusula borders are allowed as long as the GC- minimum-distance-rule is obeyed (use exact metric conversion for the distance D= 0.1 miles)

3. Data for Tuusula borders is given

4. You don' t need to construct e.g.  Leech lattice   - just find out the form for the optimal 2D circle packing grid, and align this optimal grid in assumingly orthogonal (E,N) coordinates :  this is easy to prove NOT to be the absolutely optimal solution for the task - but for solving this mystery it certainly is

5. One of your caches must be inside a 50 meter radius circle drawn around Bogus.

6. Write  down and remember the number Z = maximum amount of caches Tuusula can hold

7. Calculate  P= C/A , where A (km^2) is the area of Tuusula :
the area (AAA.aaa km^2 => Checker hot point: N AA A.aaa E 0 0.000) should be calculated with given borders, and you need only exactly 3 decimals in the calculations to come.
C is the total area of the circles (radius D/2) centered in your optimal set of cache-points with  :  if your P>1 you might want to check your calculations , but if it is just slightly bigger than the optimal packing ratio, no need to worry

8. Find the cache:

Calculate : ABCDEFGHIJKLMNO = INT ( Z^3*A)

Distance from bogus: JEHJ.D (m)

Direction : BDC.FF (deg)

Pnpur: Svaqvat gur pnpur znl or zhpu rnfvre sbe cvcr oenvaf ?

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)

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