Question Number 20298 by mondodotto@gmail.com last updated on 25/Aug/17
Answered by Tinkutara last updated on 25/Aug/17
$$\mathrm{45}\:=\:\mathrm{36}\:+\:\mathrm{12}\:+\:\mathrm{18}\:−\:{n}\left(\mathrm{medals}\:\mathrm{in}\:\mathrm{two}\right. \\ $$$$\left.\mathrm{categories}\right)\:+\:\mathrm{4} \\ $$$${n}\left(\mathrm{medals}\:\mathrm{in}\:\mathrm{two}\:\mathrm{categories}\right)\:=\:\mathrm{25} \\ $$$${n}\left(\mathrm{exactly}\:\mathrm{two}\:\mathrm{categories}\right)\:=\:\mathrm{25}−\mathrm{3}×\mathrm{4} \\ $$$$=\:\mathrm{13} \\ $$