Several comparative studies have linked larger brain size to a fruit-eating diet in primates and other animals. The general explanation for this correlation is that fruit is a complex resource base, consisting of many discrete patches of many species, each with distinct nutritional traits, the production of which changes predictably both within and between seasons. Using this information to devise optimal spatial foraging strategies is among the most difficult problems to solve in all of mathematics, a version of the famous Traveling Salesman Problem. Several authors have suggested that primates might use their large brains and complex cognition to plan foraging strategies that approximate optimal solutions to this problem. Three empirical studies have examined how captive primates move when confronted with the simplest version of the problem: a spatial array of equally valuable goals. These studies have all concluded that the subjects remember many food source locations and show very efficient travel paths; some authors also inferred that the subjects may plan their movements based on considering combinations of three or more future goals at a time. This analysis reexamines critically the claims of planned movement sequences from the evidence presented. The efficiency of observed travel paths is largely consistent with use of the simplest of foraging rules, such as visiting the nearest unused “known” resource. Detailed movement sequences by test subjects are most consistent with a rule that mentally sums spatial information from all unused resources in a given trial into a single “gravity” measure that guides movements to one destination at a time. Am. J. Primatol. Am. J. Primatol. 76:410–420, 2014. © 2013 Wiley Periodicals, Inc.