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a-b-c-d-e-f-g-h-i-j-are-different-nonnegative-integers-Find-all-numbers-that-satisfy-a-bc-def-ghij-




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

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