Pirates have buried treasure on a very unusual perfectly circular desert island, with no trees or obstacles of any kind. The map takes me to the island but doesn't tell me where to find it on the island.
It only tells me that it's buried under a small x marked on the ground.
The tide is coming in fast so I have to find my treasure as soon as possible, or risk drowning.
The island is 1km across in any direction.
I can only spot the small mark from 10 meters away (pirates were often short sighted).
What's the most efficient way to search the island? Should I walk around in a spiral? Cut the island into segments and cross the center many times? What's the best search pattern?
Edit: I should probably mention that I can use the treasure chest as a boat and won't drown if I find it.