  Family Puzzle or Generation Problem demands an explanation of why there are 3
families or generations of quarks and leptons in the Standard Model of particle
physics. Here we propose a novel solution -- the multiple of 3 families of 16
Weyl fermions (namely $(N_f=3) \times 16$) in the 3+1d spacetime dimensions are
topologically robust due to constraints rooted in profound mathematics (such as
Hirzebruch signature and Rokhlin theorems, and cobordism) and derivable in
physics (such as chiral edge states, quantized thermal Hall conductance, and
gravitational Chern-Simons theory), which holds true even forgetting or getting
rid of any global symmetry or gauge structure of the Standard Model. By the
dimensional reduction through a sequence of sign-reversing mass domain wall of
domain wall and so on, we reduce the Standard Model fermions to obtain the
$(N_f=3) \times 16$ multiple of 1+1d Majorana-Weyl fermion with a total chiral
central charge $c_-=24$. Effectively via the fermionization-bosonization, the
1+1d theory becomes 3 copies of $c_-=8$ of (E$_8)_1$ conformal field theory,
living on the boundary of 3 copies of 2+1d E$_8$ quantum Hall states. Based on
the framing anomaly-free $c_- = 0 \mod 24$ modular invariance, the framed
bordism and string bordism $\mathbb{Z}_{24}$ class, the 2-framing and
$p_1$-structure, the $w_1$-$p_1$ bordism $\mathbb{Z}_3$ class constraints, we
derive the family number constraint $N_f \in (\frac{48}{16} =\frac{24}{8}=3)
\mathbb{Z}$. The dimensional reduction process, although not necessary, is
sufficiently supported by the $\mathbb{Z}_{16}$ class Smith homomorphism. We
also comment on the $\frac{45}{15}=3$ relation: the 3 families of 15
Weyl-fermion Standard Model vacuum where the absence of some sterile
right-handed neutrinos is fulfilled by additional topological field theories or
conformal field theories in Ultra Unification.
