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How Good Is Your Maths? A Maximum Number Of Geocaches Challenge

Is this the future for all the world's land?

Groundspeak’s Latitude 47 weekly mailer recently commented that “more than 400,000 new active geocaches were listed on Geocaching.com” in 2011.

This now brings the total number of active geocaches to around 1,614,930 (at the time of writing). That’s a lot.

Last year’s massive increase in numbers is an intriguing development. It would be interesting to know if there was a similar rise in the number of new geocachers or whether existing players simply increased their output – or both.

It also got me pondering the sustainability of our game. How many years can this level of growth continue before we have placed a geocache on every possible inch of land  available? And how many would that be exactly?

So I pulled out my trusty calculator app … and promptly wished I’d paid more attention in maths class. It is my Achilles heal. If the world was invaded by math-phobic aliens tomorrow and the only way to defeat them was by attacking them with formulas my family would be toast (think the movie Signs, but with maths and not water).

Therefore, I present a challenge to INATN readers to work out answers to the following questions:

  1. What is the current level of geocache land saturation?
  2. What is the maximum number of land-based geocaches that could be placed?

Submit your answers in the comments section below. The best response will receive an It’s Not About The Numbers geocoin from my own personal stash.

SOME COMPETITION NOTES:

  • For the sake of consistency, let’s assume that the world’s land surface area is 148,940,000 km2 land (29.2 per cent). (Source: Wikipedia – because they know everything)
  • Let’s also assume that the number of geocaches (1,614,930) does not change on a daily basis.
  • The best answer will be judged by my maths loving geo-widow, Sarah, though she doesn’t know this yet. (And yes, I realise my family would be safe from a math-phobic alien invasion with her around 😉 )
  • Where possible, please include the workings that lead you to your answer.
  • For Question No 2, disregard the plethora of variables that could have an impact. We simply want an answer at this stage and will consider cache type, geocaching guidelines, land restriction etc at a later date.
  • We’ll close off the competition in a couple of weeks (Sunday, January 22nd) to pick a winner.
  • All normal INATN competition rules apply, plus any I decide to make up in the near future. 😛

Looking forward to seeing what people come up with!

10 comments

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  1. Luke

    An interesting article for sure! Question 1 is easy, it’s simply the total number of current caches divided into the total land area. Using the provided figures, that comes out as: 92.2 km2 per cache. Quite a distance! The frozen wastelands of Siberia and medieval North Korea come to mind as reason why this figure is so high.

    Question 2 is much too confusing to figure out, but as something necessary to factor in, this comes to mind: http://mathworld.wolfram.com/CirclePacking.html

  2. CraigRat

    Assuming we are applying Groundspeak’s 161m rule I say approx 5,745,920,296.66 caches.

  3. CraigRat

    Oh, my workings are:
    (((square root of 148940000 ) * 1000)/161) * (((square root of 148940000 ) * 1000)/161) 🙂

    Gives us the length of a square shaped land mass’ sided in meters

    We then divide one side by 161m to give us the caches we can place on one line

    Then we multiply that number by itself to get the amount we can possibly hide over the whole surface.

  4. Luke

    @CraigRat: Remember placing circles in a square or line pattern is not the most efficient packing method.

    The best way to fit lots of circles into an area is to pack them hexagonally in a honeycomb pattern.

    1. CraigRat

      Yes, that is true
      I might have to re-jig my numbers a bit

  5. I3SENII

    Surface of Earth is ~ 510,072,000 km2 but only 148,940,000 km2 land (29.2 %)
    We can place the caches in the front of a equilateral triangle to fit most.. So, 1 cache will take the area of an equilateral triangle with 161m side. that area is 0.011224 Km2
    Dived the land surface of earth to that and you get a maximum of 13,269,634,519

  6. kjwx

    Nice one, brother dearest: Tell the whole world we can’t count why don’t you? You could have at least pointed out that we make up for said numerical shortcomings with our ability to use words like a rapier. Also am now rethinking our decision to let you be INATN’s accountant …
    As for the above calculation, I think your premise is far too simplistic. Why limit ourselves to purely land-based caches when GC’s rules currently allow for placements underwater – DiveCaching anyone? – and on planets other than Earth (not to mention additional heavenly bodies like the ISS). Perhaps as available ground runs out, we’ll follow the lead of city developers by building up into what is now cache-free airspace, rather than out.

    1. Cumbyrocks

      It’s not about the numbers dear sister. And don’t get too complicated just yet, we’ll get to those bits once we’ve worked out the ‘simple’ stuff first.

  7. Tara Booth

    Hmmm…I worked out that the current density, assuming all caches are equally distributed, is 1 cache per every 92.2km^2.

    However as for the rest…I’m afraid my brain dribbled out of my ears so I could not complete the question!

  8. Larry Easler

    Don’t forget to carry the 1…

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