Unlocking An Irrational Location: Solving a Geocaching Puzzle

[waterdroplet]

This might not be the usual kind of question posted here, but I am trying to solve a geocaching puzzle. The puzzle is called "An Irrational Location", and the only information provided is more or less the following:
~~~~~
No rational person should attempt to visit the posted coordinates

Cache can be found at:

N: 315239

W: 42159949 (or 80453732)
~~~~~

I know the following - that not much complex math knowledge is needed to solve, that the title is the key to solving, and that somehow the numbers above need to indicate the latitude/longitude for the geocache location. I'm not asking for help to solve, persay, but just in understanding what kinds of mathematical things I could be overlooking.

 

[MarkFL]

I would look at the fact that you are given two different numbers to refer to the same longitude...this will give you a way to convert from these numbers to degrees. ;)

 

[waterdroplet]

Thanks for the tiny hint... I suspected something like that but I still feel super clueless as to how to do that! I've tried looking for online tools that will automatically plot things on a grid for me in the hopes that it will somehow turn into degrees or something that looks like degrees but I feel like I'm taking stabs in the dark... will keep trying in that direction!

 

[MarkFL]

Thanks for the tiny hint... I suspected something like that but I still feel super clueless as to how to do that! I've tried looking for online tools that will automatically plot things on a grid for me in the hopes that it will somehow turn into degrees or something that looks like degrees but I feel like I'm taking stabs in the dark... will keep trying in that direction!

What I did (and I may be way off target here) was to state:

\(\displaystyle 80453732-42159949=360^{\circ}\)

\(\displaystyle 38293783=360^{\circ}\)

Note: I am assuming the two numbers given for the western coordinate are one cycle apart, when in fact they could be any natural number of cycles apart.

And so, if we are given some coordinate $C$, to convert to degrees, we would use:

\(\displaystyle C\frac{360^{\circ}}{38293783}\)

Does that make sense?

 

[waterdroplet]

Hi! No it doesn't make any sense to me whatsoever :-( Maybe I should make it clearer that I do not have the slightest math background at all... anything beyond the standard addition/subtraction/multiplication is a bit beyond me. Can you explain it in a way that a 5th grader might understand? I mean I know that a circle is 360 degrees so maybe that's why you used that number, as the world is a sphere which is kind of like a circle, so if I'm plotting latitude and longitude on it, it might be a necessary number in a formula... that's as far as I can understand of why you did what you did!

I should maybe add that I know the result of the puzzle will have to be coordinates that are within a 3.2 km radius of the following "posted" coordinates of the puzzle, as per standard geocaching rules: N 43° 41.115' W 079° 21.980'

 

[MarkFL]

Hi! No it doesn't make any sense to me whatsoever :-( Maybe I should make it clearer that I do not have the slightest math background at all... anything beyond the standard addition/subtraction/multiplication is a bit beyond me. Can you explain it in a way that a 5th grader might understand? I mean I know that a circle is 360 degrees so maybe that's why you used that number, as the world is a sphere which is kind of like a circle, so if I'm plotting latitude and longitude on it, it might be a necessary number in a formula... that's as far as I can understand of why you did what you did!

Suppose you are at the intersection of the Prime Meridian and the equator (0° N. 0° W.) and I tell you to go due west 90° longitude. You will then be at (0°N 90°W). Now, suppose you go back to the origin, and I tell you to go 450° due west longitude...you will wind up at the same location as before, but you will have gone all the way around the word 1.25 times rather than 0.25 times as before.

I should maybe add that I know the result of the puzzle will have to be coordinates that are within a 3.2 km radius of the following "posted" coordinates of the puzzle, as per standard geocaching rules: N 43° 41.115' W 079° 21.980'

I know nothing of standard geocaching rules, and this would have been good to know up front, because it renders everything I've stated thus far as moot. :)

 

[waterdroplet]

Thanks for clarifying... I think that makes a little bit more sense! I'm going to have to sit with it and see if I get anywhere by using this line of thought. Thanks! Will post back if I'm still stumped.

 

[waterdroplet]

A friend of mine's partner solved it. They showed me how, but I still don't understand exactly what their online tool did. I don't want to post the solution here just in case future puzzle-solvers are searching the internet and come across me giving away the answer! If you're really curious you can send me a private message and I can explain.