In a staring contest between Aragorn and Sauron; Sauron wins, of course, because he's a giant eye: probably doesn't even
have eyelids.
In a beauty contest between Gimli and Boromir; Gimli wins because
he actually washes his hair.
In a tree-climbing contest between Sam and Gollum; Sam wins, despite his inbred fear of heights, because Gollum says the tree smells like Elves and leaves to wash his hands.
In an arm-wrestling contest between the Witch-king and Merry; Merry wins by distracting the Witch-king with a sword to the back of the knee.
In an archery contest between Legolas and Lachwen; Lachwen wins because Legolas plucks like a biznatch.