We've all come across this - there's this densely populated area with a cache on each corner! Here's an example of a "power trail" in the UK, the Chiltern Hundred, consisting of more than 100 caches placed in short distance from each other but you'll find similar or even higher densities in CBDs of large cities.
Have you ever thought about how many caches could be placed in a certain amount of space to utilize this space best?
The idea for this cache developed over dinner with Lat&Long Junkie, Bedmaker and Liz and Bruce in a nice country pub in Toowoomba, Qld, close to four years ago.
What better thing to do than create a new maths puzzle cache about this problem! So here we go:
You may remember that the distance between two caches has to be at least 1/10 of a mile, or something like 161m. Whatever this minimum distance is, let's call it s, and let's say that two caches can be exactly s metres apart or more, but not closer.
Here is your task:
You are given a square area to place as many geocaches in this area as possible (we will assume that any place is a good spot, as long as the distance rules are obeyed).
Let's assume further that any cache we place in this area needs to be a distance of s away from the boundaries of this area. It can be exactly s metres away, that's ok. What is the maximum number of caches you could place in a square area of side length
- 3s: Answer = A
- 4s: Answer = B
- 5s: Answer = CD
- 6s: Answer = EF?
The cache is located at
S37 AB.E(E-2)E
E145 (C-1)(C+1).(D+1)F(D+E)
Please watch out for motorized muggles who might spot you in this semi-open location. Coordinates should be within 5m - tree cover made it difficult to get a better reading. Use the hint if you get stuck. Please replace the rock on top.
The cache contains an unactivated geocoin for the first to find, and a number of path tags.
You can check your answers for this puzzle on Geochecker.com.