  We present results from computer simulations for diffusion-limited
$n$-species annihilation, $A_i+A_j\to0$ $(i,j=1,2,...,n;i\neq j)$, on the line,
for lattices of up to $2^{28}$ sites, and where the process proceeds to
completion (no further reactions possible), involving up to $10^{15}$ time
steps. These enormous simulations are made possible by the renormalized
reaction-cell method (RRC). Our results suggest that the concentration decay
exponent for $n$ species is $\a(n)=(n-1)/2n$ instead of $(2n-3)/(4n-4)$, as
previously believed, and are in agreement with recent theoretical arguments
\cite{tauber}. We also propose a scaling relation for $\Delta$, the
correction-to-scaling exponent for the concentration decay; $c(t)\sim
t^{-\a}(A+Bt^{-\Delta})$.
