There has been a recent
occurrence where up to 100 caches were squeezed into a park of
limited size. Easy I hear you say? Let’s look at the
mathematics behind this optimization problem.
Let’s say you’ve found this great park land, heaps
of hides for new caches (in fact, you can freely choose where to
place them), The Ump is in a good mood and has reserved a weekend
or two (or ten) for review – and you are about to hide as
many caches as possible in this park.
You will obviously need to do this without getting into trouble
with The Ump (and the GC rules).
- If the park has dimensions 1610m*1610m, how many caches maximum
could you place?
Let this number be ABC.
- How far at a minimum would a cacher have to walk if they wanted
to find all of these caches? Assume the cacher is able to walk
directly to each cache. The total distance is measured from the
first to the last cache.
Let this distance be DEFGH(metres)
The rules:
- Minimum distance between two caches is 161 metres
- In addition, you will also have to keep a distance of at least
161m from the boundaries of the park.
The cache can be found at
S37 5A.D(E+F)C
E145 0E.(B-D)(G-F)(H-D)
The cache location can be checked here:
Geochecker.com.
I would like to thank Alansee for beta testing this puzzle!
Credit goes to quiet1_au for improving on my solution - cache
prize to be awarded!