Beats me!

Now, before you get worried, let me tell you that no one is actually getting beaten (hit) here. "Beats me!" is an expression we use when we have absolutely no idea about the answer to a question.

Another expression with the same meaning, and one of my favorites [BrEng favourites] is "I haven't the foggiest!" Again, nothing about the weather here, it just means "I really don't know."

Both of these expressions are often accompanied by a shrug (moving your shoulders up and down, as in the picture). This emphasizes the fact that you really don't know.

A word of caution, however. These are quite emphatic, colloquial expressions, and if you use them to casually they can sound rude or flippant (too casual and unconcerned).

More neutral expressions include: "I'm not (really/very/entirely) sure." and "I don't (really) know."