2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120918We present an exact enumeration study of short SAWs in two as well as three dimensions that addresses the question, `what is the shortest walk for which the existence of all the three phases - coil, globule and the {\it theta} - could be demonstrated'. Even though we could easily demonstrate the coil and the globule phases from Free Energy considerations, we could demonstrate the existence of a {\it theta} phase only by using a scaling form for the distribution of gyration radius. That even such short walks have a scaling behavior is an unexpected result of this work.Three page RevTeX4 double column manuscript with four .eps figuresStatistical Mechanicstext