> The gold-medal task is to hang an inside-out dress shirt, after turning it right-side-in, which we do not believe our current robot can do physically, because the gripper is too wide to fit inside the sleeve
You don't need to fit inside the sleeve to turn it inside out...Think about a sock (same principle will apply, but easier to visualize). You scrunch up the sock so it's like a disk. Then you pull to invert.
This can be done with any piece of clothing. It's something I do frequently because it's often easier (I turn all my clothes inside out before washing).
With those grippers, though? There's a lot of difficulty in making it scrunch up a sock, and a sock does fit. Doing a long sleeve completely unanchored is probably physically possible with extreme care but I see why they mark the robot down as physically unable.