Scenario: You are shown a tall cylinder with a tasty nut in the bottom. How do you go about getting it out, assuming the cylinder is too tall and narrow for you to reach the bottom, and that it is fused to a tabletop (you can't dump it out)?
Could you create a strategy for getting the nut? Orangutans in one study showed amazing problem-solving skills to obtain the nut: they took mouthfuls of drinking water and spat into the cylinder, to make the nut float within finger-grasping range.
The five orangutans tested needed an average of nine minutes to realize that they could float a peanut to the top of the container, you can see an example here:
Pretty amazing, I think! Orangs are infamous for using tools and escaping enclosures in captivity (read about the legendary escapades of Fu Manchu here), which is interesting because in the wild they have not been observed to use tools to the same degree as other apes, or to captive members of their own species.
If I could pick one primate to study it would definitely be the orangutan, there is so much about the species that is unique from the other great apes. They are so imperiled right now, though, and often from places people wouldn't expect, like efforts to promote biofuels instead of fossil fuels. You can learn more about orangutan conservation efforts here, the statistics are very disturbing.