- Difficulty:

- Terrain:

Size: (small)

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How Geocaching Works

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### Geocache Description:

We all learned the general solution of the quadratic equation at school. But did you learn how to extract the roots of a cubic equation? There is a general solution for the cubic. Read it and weep.

Quartic equations are, of course, even worse - you have to convert to a depressed quartic, and then use Ferrari's solution. Feeling depressed yet?

When you move up to quintic equations, it starts getting really tricky, they're only solvable if the Galois group is a solvable group. It's a mess. Galois died when he was 20, in a duel.

But don't worry about any of that. Because I'm not giving you a quadratic, a cubic, a quartic or even a quintic. What I'm giving you is so horrible, it doesn't even have a name, although if it did, it would be a hexic or maybe a sexic? I like "sexic". So, here's your sexic equation.

x^{6} - 32x^{5} + 415x^{4} - 2780x^{3} + 10084x^{2} - 18608x + 13440 = 0

If you remember the fundamental theorem of algebra, then you'll know that this gives you six solutions. Arrange them in increasing sequence, and call then abcdef. Then the cache is at N 51° 43.caf W 000° 39.bde

But before you rush off to retreive it, you'll need some Special Equipment - a Phillips head screwdriver.

## First to find - Bob Smith

**
Additional Hints**
(Decrypt)

[Cache]Zntargvp

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