The Buffon noodle problem is an extension of the Buffon needle problem: curves of unit length are dropped randomly onto a plane marked with lines one unit apart. If crossing multiplicities are taken into account (i.e., a noodle crossing a line times contributes to the total crossing count), then the expected number of crossings is , where is the number of noodles thrown. This is the same result as the classic needle problem, where the probability of a crossing is .