We study the problem of providing multiple but identical public goods as "options" to agents with single-peaked preferences, a problem introduced by [Miyagawa, E., 1998a. Mechanisms for providing a menu of public goods. Ph.D. dissertation, University of Rochester]. For every feasible interval of locations and every preference profile, a solution chooses m locations for the m public goods. Each location is an option and each agent selects his most preferred option. For m=2 [Moulin, H., 1984. Generalized Concorcet-winners for single-peaked preferences and single-plateaued preferences, Social Choice and Welfare 1, 127-147] studies Nash's and Arrow's Independence of Irrelevant Alternatives (IIA). We show that for m=2 the 'extreme peaks' solution is the only solution satisfying Pareto-optimality, Nash's IIA, Arrow's IIA, and interval continuity. We also show that for m greater than or equal to3, Pareto-optimality and interval continuity are incompatible.