2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186922We argue that the statistical entropy relevant for the thermal interactions of a black hole with its surroundings is (the logarithm of) the number of quantum microstates of the hole which are distinguishable from the hole's exterior, and which correspond to a given hole's macroscopic configuration. We compute this number explicitly from first principles, for a Schwarzschild black hole, using nonperturbative quantum gravity in the loop representation. We obtain a black hole entropy proportional to the area, as in the Bekenstein-Hawking formula.5 pages, latex-revtex, no figuresGeneral Relativity and Quantum Cosmologytext