  The structure of $^{33}$Mg was investigated by means of two knockout
reactions, one-neutron removal from $^{34}$Mg and one-proton removal from
$^{34}$Al. Using comparative analysis of the population of observed excited
states in the residual $^{33}$Mg, the nature of these states can be deciphered.
In addition, the long-standing controversy about the parity of the $^{33}$Mg
ground state is resolved using momentum distribution analysis, showing a clear
signature for negative parity. Partial cross section measurements are compared
with the results of eikonal reaction theory combined with large-scale shell
model calculations of this complex nucleus located in the island of inversion,
where configuration mixing plays a major role.
