(FORTUNE Magazine) – The latest dazzling product of the Keeping Up Software Department was inspired by some articles in Discover, which is owned by the same stockholders as FORTUNE, and presumably these lucky investors will be thrilled to hear there is so much synergy going on in the Time & Life Building. Subject of the articles in question: the famous Traveling Salesman Problem. Contrary to what all you original subscribers are thinking, this problem is entirely concerned with combinatorial mathematics and not even slightly with s-e-x. Nutshell brief, the salesman's problem is to search among many alternative routes and find the shortest. The scenario laid on in the standard management science textbook tells of a hypothetical drummer who has a miserly boss demanding that he hold mileage to the absolute minimum while visiting each city in his territory once and only once before heading home to the button factory. Meeting this demand is tougher than it sounds because even a modest number of cities yields up an awesome number of combinations: eight cities, for example, means 40,320 possible routes. How the salesman wishes now that he had paid attention when the teacher was explaining linear programming! The problem is intellectually interesting, but this textbook situation always seems contrived. By contrast, the scenario envisaged in Pony Boy, provisional label of the new Keeping Up software, will be instantly recognizable to all denizens of the real-world selling scene. Scenario: the New York-based sales manager of a company with scores of regional offices is told by corporate hierarchs to get off his duff during July and inspire the troops out there. But which offices shall he visit? After holing up for several hours with the Official Airline Guide and Ryan's Guide to North American Thoroughbred Racing, he determines that 12 cities -- Boston, Baltimore, Philadelphia, Miami, Louisville, Detroit, Cleveland, Chicago, Omaha, Los Angeles, Seattle, and Toronto -- have troops worth inspiring. The nice thing about these cities is that all of them have decent Thoroughbred racing in July. To be sure, Pony Boy still needs work if it is to find more than the slenderest niche in the marketplace. One problem is that July is half over as we write these words, and while bringing out your product horrifyingly late is in the great tradition of the American software industry, it could be a definite downer marketingwise to offer this particular entry in August. Another problem for our copywriters is the excessively stately pace of the program. The most recent Discover article mentions a stunt performed by Shen Lin, head of AT&T's Bell Labs Network Configuration Planning Department, who was asked to find the shortest route hitting the capitals of the 48 contiguous states and got his mighty Amdahl 58-60 computer to spit out an answer (10,628 miles) in less than one second. This time compares all too favorably with the ! 571.39 years it takes Pony Boy's answer to glacially ooze out of an IBM PC. And yet the concept underlying our softwear is logically unassailable: repeated random runs of the 12-city route will eventually lead to the single best route. Our program tells the PC to note the total mileage for each random run and to stop running, and beep loudly, upon encountering a figure lower than the previous low. Unfortunately, you have to look at 1,426,539,200 routes in order to be 95% certain of having found the best one, and running this number of trials, at a rate of 285 per hour, is what keeps Pony Boy busy all those centuries. A real-world question we keep coming back to is who needs the absolute best route anyway? After a few thousand trials, we already have one with only 8,406 miles, which we judge to be superior to what a travel agent of average probity would give you. (The fateful sequence is New York, Philadelphia, Baltimore, Boston, Toronto, Detroit, Cleveland, Omaha, Seattle, Los Angeles, Chicago, Louisville, Miami, and New York.) And what's so terrible about a niche?