The island of inversion for neutron-rich nuclei in the vicinity of N=20 has become the testing ground par excellence for our understanding and modeling of shell evolution with isospin. In this context, the structure of the transitional nucleus Mg29 is critical. The first quantitative measurements of the single-particle structure of Mg29 are reported, using data from the d(Mg28, p γ)Mg29 reaction. Two key states carrying significant 3 (f-wave) strength were identified at 2.40±0.10 (Jπ=5/2-) and 4.28±0.04 MeV (7/2-). New state-of-the-art shell-model calculations have been performed and the predictions are compared in detail with the experimental results. While the two lowest 7/2- levels are well described, the sharing of single-particle strength disagrees with experiment for both the 3/2- and 5/2- levels and there appear to be general problems with configurations involving the p3/2 neutron orbital and core-excited components. These conclusions are supported by an analysis of the neutron occupancies in the shell-model calculations.