Question Number 98077 by Lekhraj last updated on 11/Jun/20
Commented by MJS last updated on 11/Jun/20
$$\mathrm{it}\:\mathrm{only}\:\mathrm{makes}\:\mathrm{sense}\:\mathrm{if}\:{a},\:{b}\:\mathrm{are}\:\mathrm{digits}\:\mathrm{and}\:{ab} \\ $$$$\mathrm{doesn}'\mathrm{t}\:\mathrm{mean}\:{a}×{b}\:\mathrm{but}\:\mathrm{10}{a}+{b}: \\ $$$${a},\:{b}\:\in\mathbb{N}\wedge\mathrm{1}\leqslant{a}\leqslant\mathrm{9}\wedge\mathrm{0}\leqslant{b}\leqslant\mathrm{9} \\ $$$$\mathrm{now}\:\mathrm{try}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{pairs} \\ $$$$\mathrm{1}!+\mathrm{0}!=\mathrm{10}^{\mathrm{2}} \\ $$$$\mathrm{1}!+\mathrm{1}!=\mathrm{11}^{\mathrm{2}} \\ $$$$... \\ $$$$\mathrm{9}!+\mathrm{9}!=\mathrm{99}^{\mathrm{2}} \\ $$
Commented by Lekhraj last updated on 11/Jun/20
$$\mathrm{Thanks}. \\ $$
Commented by mr W last updated on 11/Jun/20
$${only}\:{one}\:{possibility}: \\ $$$$\mathrm{7}!+\mathrm{1}!=\mathrm{5041}=\mathrm{71}^{\mathrm{2}} \\ $$
Commented by MJS last updated on 11/Jun/20
$${yes} \\ $$