  The Poisson clumping heuristic has lead Aldous to conjecture the value of the
first passage percolation on the hypercube in the limit of large dimensions.
Aldous' conjecture has been rigorously confirmed by Fill and Pemantle [Annals
of Applied Prob- ability 3 (1993)] by means of a variance reduction trick. We
present here a streamlined and, we believe, more natural proof based on ideas
emerged in the study of Derrida's random energy models.
