Suppose we start at Cape Horn, at the southern tip of South America. We are challenged to travel from there to Tasmania (the big island south of Australia). We can travel freely over land, but only for X consecutive kilometers over water. How small can X be, and still allow us to reach Tasmania?
Ground rules: Anything similar to a bridge or a boat is considered to be “water”. It will turn out not to matter whether we can travel over sea ice.
Traveling via Antarctica would appear to require X to be more than 1000 km, so let’s try to find a better route by going north.
To reach the South American mainland, we only need X to be at least 15 km. Our next real obstacle is the Bering Strait between Alaska and Russia. It’s a little over 82 km (remember that number), but because there are islands in the middle of it, our longest water leg is only about 36 km. From here on, we only need to watch out for water legs longer than that.
We now make a left turn, and head south. We’d have to “swim” over 130 km if our route went through Taiwan, so our best route is almost certainly via Malaysia / Indonesia / Papua New Guinea / Australia.
Here’s what I think is the optimal solution. In order to improve it, you’d have to find a better way to cross the blue line. The crossing shown is the shortest I could find.
The blue line crossing is from a point on one of the Maluku Islands in Indonesia, across the Ceram Sea, to an island possibly called Femin off the coast of a much larger island in Indonesia. By my estimation, the water distance about 82.0 kilometers (51.0 miles).
Earlier along this path, there’s a stretch of water across the Flores Sea that’s possibly as long as 78 km. So even if you can find a better way to cross the blue line, that alone won’t improve the “best X” by very much.
Trivia #1: Suppose we go back to Cape Horn, and take a look southwest at the Diego Ramirez Islands. They are a very similar distance, maybe 82.3 km, from the nearest land, on Isla Hermite. To bad they’re not just a little nearer, or we could have started there, instead of Cape Horn. (It would be a pretty boring puzzle if the very first stretch of water provided the solution.)
Trivia #2: I wondered if my blue line corresponded to the Wallace Line (ask Wikipedia); but no, it’s not close. It is kind of a hybrid of the Weber Line and Lydekker Line, though, whatever those are.