Fibonacci Challenge (MI) Mystery Cache

Cache location and parking

This cache has both a puzzle component and a challenge component, which means it is NOT located at the posted coordinates, and it also has special qualifications beyond just finding the cache and signing the log that you have to meet in order to log it as a find.

About the Fibonacci Sequence

The Fibonacci Numbers are a fascinating sequence of integers beginning with 1 and 1, and then continuing with each successive number being the sum of the two previous numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711 etc.

This sequence is amazingly found in a variety of fields well beyond just the Math classroom. The Fibonacci Sequence is far more than just a cute Mathematical fetish - this ubiquitous sequence has remarkable connections with a wide variety of natural applications. The Fibonacci sequence is named after Leonardo of Pisa, a.k.a, Fibonacci, who is credited with introducing the number sequence to Western European mathematics in 1202.

Solving For The Final Coordinates

As you follow the growth of the Fibonacci Sequence, the ratios of consecutive terms will approach a certain number that has been named, Phi, or the Golden Number. This number has an amazing way of turning up in the real world in ways you'd never expect: DNA, music, psychology, art, architecture, and more. See the link for the Related Web Site near the top of this page for more information. And herein lies your very easy puzzle, not designed to be difficult or tedious, but only to inspire you to learn more about this "mathemagical" number. Visit the website, goldennumber.net to explore the many mysterious ways this number shows up in a variety of fields. While exploring this website, learn what the value of Phi is to the nearest thousandth. You'll write out its first four digits as A.BCD, and use these digits to get the final coordinates.

Meeting the Challenge Requirements

Now, in order to meet the requirements for the challenge, you'll need to look at your own counts of the different types of geocache finds that you have logged, using only cache types from the table shown, but in whatever order suits you. Then make a list like the one shown, with each line showing a Fibonacci Number, a geocache type, and the number of finds you have of that type at the time of posting. You may not skip a Fibonacci Number in the sequence, and you continue listing as many types as you can so that your number of finds is at least as large as the Fibonacci Number in the sequence. The number of rows you are able to complete is the level you have achieved in the Fibonacci Challenge. To qualify for this challenge, you need to achieve at least Level 12.

Here's an example of a correct posting for someone who has met Level 12:

Fib# - Cache Type - Number of My Finds
1 - Project APE - 1
1 - GPS Adventures Exhibit - 1
2 - Mega Event - 2
3 - Lost & Found Event - 4
5 - CITO - 7
8 - Wherigo - 8
13 - Letterbox - 14
21 - Earthcaches - 40
34 - Multi - 83
55 - Virtual - 90
89 - Unknown - 168
144 - Traditional - 3433

Here's an example of an inadequate listing - while the count of CITO events is enough to cover the first Fibonacci Number (1), and the number of Wherigos is more than enough to cover the second Fibonacci Number(1), etc., the count of Earthcache finds (12) is insufficient to cover the sixth Fibonacci number, and even if it was sufficient, the sequence only includes ten different icon types:

1 - CITO - 1
1 - Wherigo - 3
2 - Letterbox - 6
3 - Mega Event - 6
5 - Event - 10
8 - Multi - 11
13 - Earthcache - 12
21 - Virtual - 25
34 - Unknown - 75
55 - Traditional - 2012

Logging Requirements for this Challenge Cache

1. You must have found this cache, signed the log book with your geocaching name, and rehidden it in its hiding location.

2. Your found-it log should include your list of geocache types with the number of each type you've found, beside each Fibonacci Number showing that you have at least enough finds in each type to cover each successive Fibonacci number, up to at least twelve different cache types. Please include in your log the length of the Fibonacci sequence you were able to complete. That is your Fibonacci level, which must be at least 12 to qualify. You can do this by hand or use the challenge checker to generate a list for you.

3. Each type of Geocache Found can only be used once in the sequence. Allowable types that you may use for this challenge are the types listed here on the geocaching website in the list shown. You may not use any cache type that is not included in this list to meet the requirements of this challenge.

4. If you have found this cache and signed the log without meeting the challenge requirements, you may post a note stating that you've signed the log in the cache. This allows you to convert your log into a find once you meet the requirements by posting your qualifying find counts as described here.