2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73694We prove that each measure $μ$ in $R^4$ admits an equipartition by 4 hyperplanes, provided that it is symmetric with respect to a 2-dimensional, affine subspace $L$ of $R^4$. Moreover we show, by computing the complete obstruction in the relevant group of normal bordisms, that without the symmetry condition, a naturally associated topological problem has a negative solution. The computation is based on the Koschorke's exact singularity sequence and the remarkable properties of the essentially unique, balanced binary Gray code in dimension 4.CombinatoricsAlgebraic Topology52A38; 52A39; 52C35; 55S40; 57R25; 57R85; 57S25; 68P05; 68P30; 68R05text