Geocaching provides a very large social network with geocachers connected by finding each others caches. For this challenge just consider puzzle caches.
Suppose a pair of cachers have found at least one puzzle cache owned by the other; call such a pair of cachers friends. A group of mutual friends is called a clique. An n-clique is a clique with n members.
The challenge then is to do the following:
- Locate a clique consisting of five members and provide a list of the 20 puzzle caches that bind them together. See the sample log below.
- List the five puzzle caches you've found, one for each member of the clique.
- Find and sign the log at the posted coordinates.
Puzzled? Just ask.
Bonus. If each of the five cachers were to find a puzzle cache of yours, then you would become a member of their 6-clique.
FAQ:
- Do I need to find all 20 caches that form the clique? No, in fact you don't need to find any of them; just show that they exist. You do need to find one puzzle cache owned by each member of the clique, plus the one at the posted coordinates.
- Are duplicates allowed? Yes, although you can make it more of a challenge to avoid them.
More than you need to know: The term clique in the study of social networks was coined in 1949; whereas the equivalent mathematical term, complete subgraph, goes back to 1935. A very difficult problem is to determine the largest clique in a network, any known method method requiring exponential time in the size of the problem. Thus for the large geocaching network we probably will never know the size of the largest clique. But if you can find an efficient method for doing so you would become famous - well, at least in my clique.
