Question Number 72093 by naka3546 last updated on 24/Oct/19
$${a},\:{b},\:{c},\:{d},\:{e},\:{f},\:{g},\:{h},\:{i},\:{j}\:\:\:{are}\:\:\:{different}\:\:{nonnegative}\:\:{integers}\:. \\ $$$${Find}\:\:{all}\:\:{numbers}\:\:{that}\:\:{satisfy} \\ $$$$\:\:\:\:\:{a}\:×\:{bc}\:×\:{def}\:\:=\:\:{ghij} \\ $$
Commented by prakash jain last updated on 24/Oct/19
$${abcdef}={ghij}? \\ $$$$ \\ $$$$ \\ $$
Commented by naka3546 last updated on 25/Oct/19
$${a}×\left(\mathrm{10}{b}+{c}\right)×\left(\mathrm{100}{d}+\mathrm{10}{e}+{f}\right)\:=\:\mathrm{1000}{g}+\mathrm{100}{h}+\mathrm{10}{i}+{j} \\ $$$${all}\:\:{different}\:\:{numbers}\:\:{namely}\:\:\mathrm{0},\mathrm{1},\mathrm{2},\:...\:,\:\mathrm{9} \\ $$
Answered by MJS last updated on 26/Oct/19
$$\mathrm{1}×\mathrm{26}×\mathrm{345}=\mathrm{8970} \\ $$$$\mathrm{2}×\mathrm{14}×\mathrm{307}=\mathrm{8596} \\ $$$$\mathrm{these}\:\mathrm{are}\:\mathrm{all}\:\mathrm{I}\:\mathrm{found} \\ $$
Commented by naka3546 last updated on 27/Oct/19
$${ok} \\ $$