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Try this: hit LJ's 'Random Search' function. Then put the username you get, and your own, into this page and let it try to find a chain of friends-list links from you to the random user.
I've tried several, and so far I haven't hit one that took more than six hops, except for one empty journal with no listed friends. (It doesn't work on communities, which do sometimes turn up on the random-search function.)
I've tried several, and so far I haven't hit one that took more than six hops, except for one empty journal with no listed friends. (It doesn't work on communities, which do sometimes turn up on the random-search function.)