The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite plane. In this study, we explore the same problem and extend it in the context of m dimensions given n (m-1) dimensional cuts using the recursive relationship of finite cuts and enclosed spaces in lower dimensions. Once the general formula of f(m,n) was proven for dimensions, an Euler’s inspired formula was used to check the accuracy of the formula in two and three dimensions. The Euler’s formula also allowed us to derive the formula for the maximum number of unenclosed spaces in three-dimensional F(3, n). The results are as follows: