In alkaline medium, the reduction of permanganate anion involves a gain of ____________ electrons.

In Faintly alkaline medium potassium permanganate changes to manganese dioxide in its oxidising action.

${\mathrm{MnO}}_4^{-}+2{\mathrm{H}}_2\mathrm{O}+3{\mathrm{e}}^{-}\stackrel{}{\to }{\mathrm{MnO}}_2+4{\mathrm{OH}}^{-}$

The oxidation state of manganese in ${\mathrm{MnO}}_4^{-}$ is +7 and in ${\mathrm{MnO}}_2$ is +4.

Hence, it transfers 3 electrons during the oxidising action in alkaline medium.