In a recent paper [Moore, J. M. 1968. An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15(1, September).] Moore addressed himself to the problem of the title, and devised a rather simple algorithm for its solution. He also mentions a somewhat simpler algorithm suggested by Hodgson. The proof of both algorithms is rather involved. The following is a more direct, and hopefully simpler, proof.