Solution: First thing to notice is that all the words on the right are compound words made up of two smaller words. You must break these apart and then match the up again in the "tournament" to form a bunch of new compound words. For example, the words "eye", "black" and "ball" could be placed in one of the brackets of the diagram to make the new compound words "eyeball" and "blackball" (See below).

Once all the given words have been placed, it is just a matter of finding a word that would match up with all four finalists (ball, back, head, board). This word, and thus the solution, is "room".