  In this paper, we perform fits to $B \to PP$ decays, where $B = \{B^0, B^+,
B_s^0\}$ and the pseudoscalar $P = \{\pi, K\}$, under the assumption of flavor
SU(3) symmetry [SU(3)$_F$]. Although the fits to $\Delta S=0$ or $\Delta S=1$
decays individually are good, the combined fit is very poor: there is a
$3.6\sigma$ disagreement with the SM. One can remove this discrepancy by adding
SU(3)$_F$-breaking effects, but 1000\% SU(3)$_F$ breaking is required. The
above results are rigorous, group-theoretically -- no dynamical assumptions
have been made. When one adds an assumption motivated by QCD factorization, the
discrepancy with the SM grows to $4.4\sigma$.
