The cache is not at the posted coordinates. Solve the puzzle below to find the final location.
Penguin Peter is not a numerical sort. He only deals with letters and words. Looking at the coordinate words, he realized that if you spelled out those coordinates, it would take anywhere from 16 to 23 words. For instance, the least word count could be for example:
north zero degrees thirty point five two nine west ninety degrees fifty point zero one seven
while the longest might be
south forty six degrees twenty six point seven five one east one hundred and sixty nine degrees forty eight point two zero seven
After feeling pretty charmed with his work, he showed it to his friend Paul, who had recently retired after his own crowning achievement. Paul ambled over to look at what Peter had done, and merely scoffed. "Your first encoding is super long, and your second is much more confusing! What's the point if you can't make it simple and short!" Peter replied that "you know I don't like the numbers, they frighten and confuse me. But I've been working on a new idea, and I just might be able to use some help." Paul sniffed and walked away and pretended to be busy.
So Peter called his mathematician friend mjouk, who helped him with his new scheme. He suggested that all you had to do was take Peter's word description of the coordinates, then get it sorted alphabetically within the list of all possible coordinate strings (mjouk calculated the numbers: there are 233,280,000,000,000 such possible coordinate strings). The location of the given coordinate string within the list could be given as a decimal fraction of the total. Voila: a single fractional number to represent the word coordinates! Paul was impressed, felt it was way over his head, but nodded along anyway. Peter was not so sure, and a little confused, but he went along with it. After which, they both retired in exhaustion.
0.400099153287787
You can validate your puzzle solution with certitude.
Congratulations to Team Ottlet for FTF and the FTS!
Note for the purposes of the calculations above assume that there’s neither north or south ninety degrees, nor any east or west one hundred and eighty degrees. There is however, both north and south zero degrees zero point zero zero zero minutes, and similar duplication east/west.