- Difficulty:

- Terrain:

Size: (micro)

#### Watch

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### Geocache Description:

The cache container is not at the listed coordinates.

I first learned about **balanced ternary** doing a cache in the Bay Area. I find it a fascinating topic.

Balanced ternary is a base-3 digit system with three values: -1, 0, and +1. Those values are sometimes represented as ` False`,

`, and`

**U**nknown`, or with a special symbol for the -1 digit.`

**T**rueI choose to use the system with:

- = -1

0 = 0

+ = 1

because I think it looks cool. So in my system,

decimal 66 = +-++0 = 3^{4} - 3^{3} + 3^{2} + 3^{1}

A couple of interesting tidbits about balanced ternary: first, there is no need for a negative prefix to specify negative numbers. In my system, if it starts with a - it is negative. Second, there is no such thing as roundoff in balanced ternary; truncating a fraction automatically does the roundoff!

There have been attempts over the years to use balanced ternary logic in computers. Ternary logic gates are be very powerful. Unfortunately, not everyone defines the ternary gates in the same way. For the purposes of this puzzle, here are some gates:

Be careful! The `WHAT` gate does not commute; that is, `A WHAT B` is not equal to `B WHAT A`.

To find the coordinates of the cache, perform ternary logic on the values below to get z and then "add" the result to GC8JJ5X using an intuitive but mathematically ridiculous method.

a = 4500000 b = 6155913 c = 1338256 d = -14419 z = ((a BUT b) WHAT c) XOR d

You can validate your puzzle solution with certitude.

**
Additional Hints**
(Decrypt)

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