Question 112
In the coordinate space, we consider all the planes with equations of the form $x \pm y \pm z = n$ (for all integer $n$). These planes partition the space into tetrahedra and octahedra. Assume that the point $(x_0, y_0, z_0)$ with rational coordinates lies in neither of these planes. Prove that there exists a positive integer $k$ such that the point $(kx_0, ky_0, kz_0)$ lies in the interior of some octahedron of the partition.
(A. Glazyrin)
(A. Glazyrin)