The one they give also crosses numerous rivers and lakes. For the strict version of the challenge where you literally can't cross water it's likely that the best solution is across Antarctica. Guaranteed by temperature to contain no water whatsoever.

technically Antarctica is covered in (solid) water.

"technically incorrect the worst kind of incorrect".

> Guaranteed by temperature to contain no water whatsoever.

Depends on where and when.

Plenty of puddles form around the bases in summer.