The Discretizable Molecular Distance Geometry Problem is a subset of instances of the distance geometry problem that can be solved by a combinatorial algorithm called "Branch-and-Prune". It was observed empirically that the number of solutions of YES instances is always a power of two. We perform an extensive theoretical analysis of the number of solutions for these instances and we prove that this number is a power of two with probability one. © 2011 Springer-Verlag.6831 LNCS 322342Lavor, C., Liberti, L., Maculan, N., Computational experience with the molecular distance geometry problem (2006) Global Optimization: Scientific and Engineering Case Studies, pp. 213-225. , Pintér, J. (ed.) Springer, BerlinLiberti, L., Lavor, C., Maculan, N., Marinelli, F., Double variable neighbourhood search with smoothing for the molecular distance geometry problem (2009) Journal of Global Optimization, 43, pp. 207-218Saxe, J., Embeddability of weighted graphs in k-space is strongly NP-hard (1979) Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480-489Huang, H.X., Liang, Z.A., Pardalos, P., Some properties for the Euclidean distance matrix and positive semidefinite matrix completion problems (2003) Journal of Global Optimization, 25, pp. 3-21Hendrickson, B., The molecule problem: Exploiting structure in global optimization (1995) SIAM Journal on Optimization, 5, pp. 835-857Eren, T., Goldenberg, D., Whiteley, W., Yang, Y., Morse, A., Anderson, B., Belhumeur, P., Rigidity, computation, and randomization in network localization (2004) IEEE Infocom Proceedings, pp. 2673-2684Krislock, N., Wolkowicz, H., Explicit sensor network localization using semidefinite representations and facial reductions (2010) SIAM Journal on Optimization, 20, pp. 2679-2708Gunther, H., (1995) NMR Spectroscopy: Basic Principles, Concepts, and Applications in Chemistry, , Wiley, New YorkSchlick, T., (2002) Molecular Modelling and Simulation: An Interdisciplinary Guide, , Springer, New YorkSantana, R., Larrañaga, P., Lozano, J., Combining variable neighbourhood search and estimation of distribution algorithms in the protein side chain placement problem (2008) Journal of Heuristics, 14, pp. 519-547Lavor, C., Mucherino, A., Liberti, L., Maculan, N., Discrete approaches for solving molecular distance geometry problems using NMR data (2010) International Journal of Computational Biosciences, 1 (1), pp. 88-94Lavor, C., Liberti, L., Maculan, N., Mucherino, A., The discretizable molecular distance geometry problem Computational Optimization and Applications, , doi: 10.1007/s10589-011-9402-6Liberti, L., Lavor, C., Maculan, N., A branch-and-prune algorithm for the molecular distance geometry problem (2008) International Transactions in Operational Research, 15, pp. 1-17Mucherino, A., Lavor, C., Liberti, L., The discretizable distance geometry problem Optimization Letters, , To appear inLavor, C., Lee, J., John, A.L.S., Liberti, L., Mucherino, A., Sviridenko, M., Discretization orders for distance geometry problems Optimization Letters, , doi: 10.1007/s11590-011-0302-6Lavor, C., Mucherino, A., Liberti, L., Maculan, N., On the computation of protein backbones by using artificial backbones of hydrogens (2011) Journal of Global Optimization, 50, pp. 329-344Liberti, L., Lavor, C., Mucherino, A., Maculan, N., Molecular distance geometry methods: From continuous to discrete (2010) International Transactions in Operational Research, 18, pp. 33-51Lavor, C., Liberti, L., Maculan, N., Mucherino, A., Recent advances on the discretizable molecular distance geometry problem European Journal of Operational Research, , accepted / invited surveyBlumenthal, L., (1953) Theory and Applications of Distance Geometry, , Oxford University Press, OxfordConnelly, R., Generic global rigidity (2005) Discrete Computational Geometry, 33, pp. 549-563Brady, T., Watt, C., On products of Euclidean reflections (2006) American Mathematical Monthly, 113, pp. 826-829Lavor, C., Liberti, L., Maculan, N., (2006) The Discretizable Molecular Distance Geometry Problem, , Technical Report q-bio/0608012, arXivDong, Q., Wu, Z., A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data (2003) Journal of Global Optimization, 26, pp. 321-333Coope, I., Reliable computation of the points of intersection of n spheres in Rn (2000) Australian and New Zealand Industrial and Applied Mathematics Journal, 42, pp. C461-C477