Problem

Source: Bundeswettbewerb Mathematik 2021, Round 1 - Problem 1

Tags: 3D geometry, inequalities



A cube with side length $10$ is divided into two cuboids with integral side lengths by a straight cut. Afterwards, one of these two cuboids is divided into two cuboids with integral side lengths by another straight cut. What is the smallest possible volume of the largest of the three cuboids?