SIERKSMA’S DUTCH CHEESE PROBLEM

K. S. SARKARIA

Abstract. Consider partitions, of a cardinality (q − 1)(d + 1) + 1 generic subset of euclidean d-space, into q parts whose convex hulls have a nonempty intersection. We show that if these partitions are counted with appropriate signs ±1 then the answer is always ((q − 1)!)^{d}. Also some other related results are given.