  The Higgs-like signal observed at the LHC could be due to several mass
degenerate resonances. We show that the number of resonances is related to the
rank of a "production and decay" matrix, $R_{if}$. Each entry in this matrix
contains the observed rate in a particular production mode $i$ and final state
$f$. In the case of $N$ non-interfering resonances, the rank of $R$ is, at
most, $N$. If interference plays a role, the maximum rank is $N^2$ or in the CP
limit $N(N+1)/2$. As an illustration we use the present experimental data to
constrain the rank of the corresponding matrix. We estimate the LHC reach of
probing two and three resonances under various speculations on future
measurements and uncertainties.
