  We revisit the selection problem, namely that of computing the $i$th order
statistic of $n$ given elements, in particular the classic deterministic
algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and
Tarjan (1973). Whereas the original algorithm uses groups of odd size at least
$5$ and runs in linear time, it has been perpetuated in the literature that
using smaller group sizes will force the worst-case running time to become
superlinear, namely $\Omega(n \log{n})$. We first point out that the usual
arguments found in the literature justifying the superlinear worst-case running
time fall short of proving this claim. We further prove that it is possible to
use group size smaller than $5$ while maintaining the worst case linear running
time. To this end we introduce three simple variants of the classic algorithm,
the repeated step algorithm, the shifting target algorithm, and the hyperpair
algorithm, all running in linear time.
