Curiosity.com describes the Ham Sandwich Theorem best:
"In mathematical terms, the ham sandwich theorem states that given n objects floating in n-dimensional space (in our case, that's 3 objects floating in 3-dimensional space), there exists a single [n - 1]-dimensional (again, in our case, that's 3-1, or 2-dimensional) plane that simultaneously cuts all n objects into two pieces of equal volume.
In mathematical terms, the ham sandwich theorem states that given n objects floating in n-dimensional space (in our case, that's 3 objects floating in 3-dimensional space), there exists a single [n - 1]-dimensional (again, in our case, that's 3-1, or 2-dimensional) plane that simultaneously cuts all n objects into two pieces of equal volume."
They even offer you a video so you can see how it works for yourself! Now you and your friend know how to perfectly split a ham sandwich at lunch!
