How do you solve a puzzle whose pieces you can't touch?

Gravity, they say, is a harsh mistress. It's an old Klingon proverb. So is "revenge is a dish best served cold." Khan said it, and he knew what he was talking about. But, why was he so mad at Kirk? Was it that he was marooned on a doomed planet by the Captain of the Enterprise? Was it that Khan's on wife was killed shortly thereafter? Or was it that Kirk had Scotty beam a case full of these puzzle spheres into the cargo hold of the Botany Bay?

See, what really drove Khan Noonien Singh mad wasn't the neverending sands of his prison, or the loss of his loved ones. No, it was that a seemingly simple puzzle was so vexing, even for a genetically superior being like himself. See, these puzzles have 5 moveable pieces, but so encased in a sphere, they're untouchable by human hands. To move the pieces, one had to rotate the entire puzzle and let gravity pull the pieces into place. Ah, but there's the maddening part! Once Khan rotated the sphere, the pieces were no longer in the orientation in which they once were.

He thought he knew where all the pieces were in his mind, super-genius he was, but he found it easy to lose track. Once he thought he grasped the technique of rotating a colored tile into the right position, he lost it again and would have to start over. It drove him crazy-bonkers, so he commandeered a starship and blew the crap out of the Enterprise out of revenge.

So, if you choose to pick up one of these wonderfully vexing puzzle spheres, make sure you leave the starships alone? KTHXBYE.