Well, capitalism need not apply (and isn't the only reason people do things for money, of course). If the only people who can cast wish in the setting are the Good Archmage and the Evil Archmage who are mostly concerned with stopping each other's machinations, then it's probably not worth their time to do anything about this. Sure, the Evil Archmage Society will enter a team in the prize (and they'll cheat like crazy) but they won't be able to use the big magical guns. It really depends on how the setting works for magic, and it's very easily sorted narratively.This needs some expanding.
My first thought was Wind Walk. It's not in any of the above categories. By my rough calculation it would let you travel around the world in about 45 days. I'm sure there are other options for an easy win.
Maybe I'm just jaded, but this is not my experience with how capitalism works. If the reward is significant enough for the adventurers to care, it's also enough to make it worth some high level NPC to care.
I recommend putting a story-based limitation in to address it. Maybe the traveler needs to be the first person from Mist's home town to travel around the globe (and there are no high level adventurers there). Or there's a pre-race contest to become part of the race. Or maybe simply an age limit.
Wind walk could work well. It lets you fly at 37mph for 8 hours = 300 miles at a time. If you cast it twice a day (you still need to sleep and rest) and travelled in a straight line perfectly without hindrances, it would take you about 40 days.
But you need to rest while flying over the ocean, and most large oceans are rather more than 300 miles wide, so you can't travel the perfect route - like a goose, you'll need to stop on land regularly. On our world, that means flying via Siberia/Alaska and Canada/Greenland/Iceland, which both take you a long way out of your preferred flight path, and you still need to get to the way stations* and stop for supplies. The other point is that wind walkers are very affected by the weather, which could be a problem (but could be an asset for someone who's very sure they know how the prevailing winds work).
*It depends where the way stations are, of course. If we use the book for reference, the way stations would be in the equivalents of London, Paris, Turin, Suez, Bombay, Calcutta, Hong Kong, Yokohama, San Francisco, and New York. This setup, since it dips a lot around the equator, is quite unhelpful for wind walkers.
But I agree it looks like the easiest D&D magical way to have a chance of doing the route in the time allocated. You could argue it's a form of polymorphing but eh, it's up for discussion.
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