A model for the formation and distribution of sedimentary rocks on Mars is proposed. The rate-limiting step is supply of liquid water from seasonal melting of snow or ice. The model is run for a O(10^2) mbar pure CO2 atmosphere, dusty snow, and solar luminosity reduced by 23%. For these conditions snow only melts near the equator, and only when obliquity >40 degrees, eccentricity >0.12, and perihelion occurs near equinox. These requirements for melting are satisfied by 0.01-20% of the probability distribution of Mars' past spin-orbit parameters. Total melt production is sufficient to account for aqueous alteration of the sedimentary rocks. The pattern of seasonal snowmelt is integrated over all spin-orbit parameters and compared to the observed distribution of sedimentary rocks. The global distribution of snowmelt has maxima in Valles Marineris, Meridiani Planum and Gale Crater. These correspond to maxima in the sedimentary-rock distribution. Higher pressures and especially higher temperatures lead to melting over a broader range of spin-orbit parameters. The pattern of sedimentary rocks on Mars is most consistent with a Mars paleoclimate that only rarely produced enough meltwater to precipitate aqueous cements and indurate sediment. The results suggest intermittency of snowmelt and long globally-dry intervals, unfavorable for past life on Mars. This model makes testable predictions for the Mars Science Laboratory rover at Gale Crater. Gale Crater is predicted to be a hemispheric maximum for snowmelt on Mars. ; Comment: Submitted to Icarus. Minor changes from submitted version