I am sorry for replying so late to the thread I started.
By hitchhiking around the world, I really mean stading beside a road with your thumb up and hoping somebody picks you up, no hot air baloons or hiking. I also did not mean that you must go around the equator, that seems unnecessary to me.
I am not sure how to fit crossing the ocean into the equation, though. If one was allowed to flight across the ocean, the challenge would be easy - according to these maps
https://en.mapy.cz/s/fozepedohu , Prague to Hanoi is 12 000 km / 122 hrs of driving, which, with a speed of 6 hrs per day is like 21 days. Sure, with border crossings, etc., it would take longer, but it is still not much. USA is crossable in 8 days and once you get your final flight from New York to Spain/Western Europe, you are in Czech Republic in 3/4 days at max. But with ships, it might be much more difficult. There are some ways, supposedly, to cross the Atlantic and Pacific for free - you can work as a crew on some yacht and in return you do not pay for the journey. That would however require some ship sailing skills. I also thought that if one was able to get all the way up to Vladivostok, that maybe it would be ok just to take a ferry and pay for it (I would consider it to be ok according to the rules - the journey across Asia would be noticeably longer and there is still the ship, which is much slower than an airplane). Previously I thought that it would be even better to get further up and east, near Bering strait and find some ferry there, but looking at the map, it seems that that part of the world is even emptier than I thought, so that does not seem possible. Also, hitchhiking across Russia from West to East does not seem wise either (but getting through China to Vladivostok should be ok).
With ships, I think that 80 days around the world is quite realistic (waiting in the port for some time before the ship departs, a week or so across Atlantic, more across Pacific). What do you think?