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Question-208962

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Question Number 208962 by yaslm last updated on 29/Jun/24
Commented by Rasheed.Sindhi last updated on 29/Jun/24
Are all the digits in divisor,dividend and quotient different? Otherwise many many answers.
$${Are}\:{all}\:{the}\:{digits}\:{in}\:{divisor},{dividend} \\ $$$${and}\:{quotient}\:{different}? \\ $$$${Otherwise}\:{many}\:{many}\:{answers}. \\ $$
Commented by yaslm last updated on 29/Jun/24
complete from(0 to 9)
Commented by nikif99 last updated on 29/Jun/24
Please be more specific. There are 11 empty digits in the divisor, dividend and quotient. Cannot be all different.
$${Please}\:{be}\:{more}\:{specific}.\:{There}\:{are}\:\mathrm{11} \\ $$$${empty}\:{digits}\:{in}\:{the}\:{divisor},\:{dividend} \\ $$$${and}\:{quotient}.\:{Cannot}\:{be}\:{all}\:{different}. \\ $$
Answered by Rasheed.Sindhi last updated on 30/Jun/24
determinant (( , , , ,□,8,□,□),(□,(□)),□,□,□,□,□,□),( , ,□,□,□, , , ),( , , ,□,□,□, , ),( , , , ,□,□, , ),( , , , ,□,□,□, ),( , , , ,□,□,□, ),( , , , , , ,0, )) The above pattern is somewhat mismatched to that of the question. But I think it correct and my answer follows this. determinant (( , , , ,c,8,d,e),(a,(b)),□,□,□,□,□,□),( , ,□,□,□, , , ),( , , ,□,□,□, , ),( , , , ,□,□, , ),( , , , ,□,□,□, ),( , , , ,□,□,□, ),( , , , , , ,0, )) ab×8 is a 2-digit number ab×c is a 3-digit number. This follows that c>8⇒c=9 ab=12 (∵ 12×8 is 2-digit number and 12×9 is 3-digit number.) Numbers below 12 and above 12 haven′t this property Answer: determinant (( , , , ,9,8,9,0),(1,(2)),1,1,8,6,8,0),( , ,1,0,8, , , ),( , , ,1,0,6, , ),( , , , ,9,6, , ),( , , , ,1,0,8, ),( , , , ,1,0,8, ),( , , , , , ,0, )) ...
$$\begin{array}{|c|c|c|c|c|c|c|c|}{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\mathrm{8}}&\hline{\Box}&\hline{\Box}\\{\Box}&\hline{\left.\Box\right)}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}\\{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{0}}&\hline{\:}\\\hline\end{array} \\ $$$$\mathcal{T}{he}\:{above}\:{pattern}\:{is}\:{somewhat} \\ $$$${mismatched}\:{to}\:{that}\:{of}\:{the}\:{question}. \\ $$$$\mathcal{B}{ut}\:{I}\:{think}\:{it}\:{correct}\:{and}\:{my}\:{answer} \\ $$$${follows}\:{this}. \\ $$$$\begin{array}{|c|c|c|c|c|c|c|c|}{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{{c}}&\hline{\mathrm{8}}&\hline{{d}}&\hline{{e}}\\{{a}}&\hline{\left.{b}\right)}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\Box}\\{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\Box}&\hline{\Box}&\hline{\Box}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{0}}&\hline{\:}\\\hline\end{array} \\ $$$${ab}×\mathrm{8}\:{is}\:{a}\:\mathrm{2}-{digit}\:{number} \\ $$$${ab}×{c}\:{is}\:{a}\:\mathrm{3}-{digit}\:{number}. \\ $$$$\mathcal{T}{his}\:{follows}\:{that}\:{c}>\mathrm{8}\Rightarrow{c}=\mathrm{9} \\ $$$${ab}=\mathrm{12} \\ $$$$\left(\because\:\mathrm{12}×\mathrm{8}\:{is}\:\mathrm{2}-{digit}\:{number}\right. \\ $$$$\left.{and}\:\mathrm{12}×\mathrm{9}\:{is}\:\mathrm{3}-{digit}\:{number}.\right) \\ $$$$\mathcal{N}{umbers}\:{below}\:\mathrm{12}\:{and}\:{above}\:\mathrm{12}\:{haven}'{t} \\ $$$${this}\:{property}\: \\ $$$$\mathcal{A}{nswer}:\: \\ $$$$\begin{array}{|c|c|c|c|c|c|c|c|}{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{9}}&\hline{\mathrm{8}}&\hline{\mathrm{9}}&\hline{\mathrm{0}}\\{\mathrm{1}}&\hline{\left.\mathrm{2}\right)}&\hline{\mathrm{1}}&\hline{\mathrm{1}}&\hline{\mathrm{8}}&\hline{\mathrm{6}}&\hline{\mathrm{8}}&\hline{\mathrm{0}}\\{\:}&\hline{\:}&\hline{\mathrm{1}}&\hline{\mathrm{0}}&\hline{\mathrm{8}}&\hline{\:}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{1}}&\hline{\mathrm{0}}&\hline{\mathrm{6}}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{9}}&\hline{\mathrm{6}}&\hline{\:}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{1}}&\hline{\mathrm{0}}&\hline{\mathrm{8}}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{1}}&\hline{\mathrm{0}}&\hline{\mathrm{8}}&\hline{\:}\\{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\:}&\hline{\mathrm{0}}&\hline{\:}\\\hline\end{array} \\ $$$$…\: \\ $$
Commented by nikif99 last updated on 30/Jun/24
this is quite different from initial post. Initial post has no solution for any digits, according the position of the cages. I will try this option.
$${this}\:{is}\:{quite}\:{different}\:{from}\:{initial} \\ $$$${post}.\:{Initial}\:{post}\:{has}\:{no}\:{solution}\:{for} \\ $$$${any}\:{digits},\:{according}\:{the}\:{position}\:{of} \\ $$$${the}\:{cages}. \\ $$$${I}\:{will}\:{try}\:{this}\:{option}. \\ $$

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