In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain solutions.
It was proved in 1965 by Charles R. Hobby and John R. Rice;[1] a simplified proof was given in 1976 by A.
: The Hobby–Rice theorem says that for every n continuously integrable functions: there exists a signed partition of [0,1] such that: (in other words: for each of the n functions, its integral over the positive subintervals equals its integral over the negative subintervals).
The theorem was used by Noga Alon in the context of necklace splitting[3] in 1987.
This fair-division challenge is sometimes referred to as the consensus-halving problem.