Helium nanodroplets doped with argon, krypton, or xenon are ionized by electrons and analyzed in a mass spectrometer. He(n)Ng(x)(+) ions containing up to seven noble gas (Ng) atoms and dozens of helium atoms are identified; the high resolution of the mass spectrometer combined with advanced data analysis make it possible to unscramble contributions from isotopologues that have the same nominal mass but different numbers of helium or Ng atoms, such as the magic (He20Kr2+)-Kr-84 and the isobaric, nonmagic (He41Kr+)-Kr-84. Anomalies in these ion abundances reveal particularly stable ions; several intriguing patterns emerge. Perhaps most astounding are the results for HenAr+, which show evidence for three distinct, solid-like solvation shells containing 12, 20, and 12 helium atoms. This observation runs counter to the common notion that only the first solvation shell is solid-like but agrees with calculations by Galli et al. for HenNa+ [J. Phys. Chem. A 2011, 11s, 7300] that reveal three shells of icosahedral symmetry. HenArx+ (2 <= x <= 7) ions appear to be especially stable if they contain a total of n + x = 19 atoms. A sequence of anomalies in the abundance distribution of HenKrx+ suggests that rings of six helium atoms are inserted into the solvation shell each time a krypton atom is added to the ionic core, from Kr+ to Kr-3(+). Previously reported strong anomalies at He12Kr2+ and He12Kr3+ [Kim, J. H.; et al. J. Chem. Phys. 2006, 124, 214301] are attributed to a contamination. Only minor local anomalies appear in the distributions of HenXex+ (x <= 3). The distributions of HenKr+ and HenXe+ show strikingly similar, broad features that are absent from the distribution of HenAr+; differences are tentatively ascribed to the very different fragmentation dynamics of these ions.