The

ham sandwich theorem states that it is possible to
divide a sandwich made up of three layers (ham, butter, bread)
exactly in half with just one cut of the knife. Here's the

mathematical
formulation.

**Theorem** Given three bounded subsets of **R**^{3} there exists
a plane in **R**^{3} dividing each of the subsets in half
by volume.

The proof of the ham sandwich theorem
is a corollary of the Borsuk-Ulam theorem.