Question Number 151801 by ajfour last updated on 23/Aug/21
$${If}\:{a}\:{natural}\:{number}\:{of}\:\mathrm{3}\:{digit} \\ $$$$\left({for}\:{example}\right){N}={abc}\:\:{such}\:{that} \\ $$$${N}=\mathrm{100}{a}+\mathrm{10}{b}+{c}={a}!+{b}!+{c}! \\ $$$${Find}\:{all}\:{N}\:{of}\:{any}\:{number}\:{of} \\ $$$${digits}.\: \\ $$$${e}.{g}.\:\:{N}=\mathrm{1},\:\mathrm{2},\:\mathrm{145},\:... \\ $$