  The $^{111,112,113}$Sn isotopes have been studied with ($p,d \gamma$),
($p,p^{\prime} \gamma$), and ($d,p \gamma$) reactions to extract the nuclear
level densities (NLDs) and $\gamma$-ray strength functions (GSFs) of these
nuclei below the neutron separation energy by means of the Oslo method. The
experimental NLDs for all three nuclei demonstrate a trend compatible with the
constant-temperature model below the neutron separation energy while also being
in good agreement with the NLDs of neighboring Sn isotopes, obtained previously
with the Oslo-type and neutron evaporation experiments. The extracted
microcanonical entropies yield $\approx 1.5$ $k_B$ entropy of a valence neutron
in both $^{111}$Sn and $^{113}$Sn. Moreover, the deduced microcanonical
temperatures indeed suggest a clear constant-temperature behavior above
$\approx$ 3 MeV in $^{111,113}$Sn and above $\approx$ 4.5 MeV in $^{112}$Sn. We
observe signatures for the first broken neutron pairs between 2 and 4 MeV in
all three nuclei. The GSFs obtained with the Oslo method are found to be in
good agreement below the neutron threshold with the strengths of $^{112,114}$Sn
extracted in the ($p,p^{\prime}$) Coulomb excitation experiments.
