GCT9PY Fibonacci Played Tennis? (Unknown Cache) in California, United States created by RB Family

This cache has been archived.

RB Family: ...on second thought, if you need to log your find or post a note, archiving won't stop you. Enjoy!

GCT9PY ▼

A cache by RB Family Message this owner

Hidden : 2/2/2006

Difficulty:

Terrain:

Size: Size: small (small)

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Geocache Description:

Cache is not at the above coordinates.
Solve this puzzle to find the cache.

Mr. Fibonacci was comissioned to build a series of tennis courts on three strips of land.
His instructions were very specific:
- Each tennis court would be constructed so that it's area is half as wide as it is long.
(1 "span" wide x 2 "spans" long)
- Each strip of land is exactly as wide as the length of one tennis court area.
(Strip width = 2 spans)
- Each arrangement combination must start with a court situated "upright." No combo will start with two courts situated one atop the other.
- The total length of each arrangement in spans, must equal the number of courts in it.
e.g. 3 courts in the arrangement (limit 3 spans wide) = 2 possible combos
or, an arrangement of 5 courts (5 span width limit) = 5 possible combos

- The first strip of land would have 12 tennis courts arranged on it.
- The second strip would have 4 courts arranged on it.
- The third strip would have 16 courts.

The consumate mathmatician and lover of puzzles, Fibonacci set out to find how many arrangement possibilities he had to choose from, given the restrictions placed upon him. This prospect seemed staggering at first, but after a little research and a bit of math, he was delighted to discover that the numbers were not too overwhelming.

To solve this puzzle, find the number of arrangement combinations possible for each strip of land.
Keep in mind that every court is indistinguisable from the others. Ordering of each doesn't matter, only the total number of different styles of arrangements.

The number of possible arrangements for the first strip = A.
The number possible for the second strip = B.
The number of arrangements for the third strip = C.

The final coordinates are:

33° 00.A North
117° B.C West

Be sure to record the coordinates for the "Fibonacci's
Time Capsule" cache (GCT9Q3), when you find this one.

Have fun!

Additional Hints (Decrypt)

Oynpx pnc haqre tebhaq pbire.

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)