Sufficiently long long division

Logic Level 3

Above shows a long division. If the product of all the missing digits is non-zero, what is the sum of the values of all of the missing digits?


Inspiration .


The answer is 98.

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1 solution

Rishabh Jain
Jan 26, 2016

0 6 7 8 1 1 \enclose l o n g d i v 7 4 6 7 6 6 0 0 0 0 8 6 0 0 7 7 0 0 9 7 8 8 9 \LARGE{ \begin{array}{rlll} \phantom{0}\ \boxed{\color{#D61F06}{6}} \ \boxed{\color{#D61F06}{7}} \ \boxed{\color{#D61F06}{8}} && \\[-4pt] \boxed{\color{#D61F06}{1}} \ \boxed{\color{#D61F06}{1}}\ \enclose{longdiv}{\boxed{\color{#D61F06}{7}} \ \boxed{\color{#D61F06}{4}} \ \boxed{\color{#D61F06}{6}} \ \boxed{\color{#D61F06}{7}} } && \\[-4pt] \underline{\boxed6\ \boxed{\color{#D61F06}{6}}\, \phantom0 \phantom0 \phantom0 \phantom0} && \\[-4pt] \boxed{\color{#D61F06}{8}} \ \boxed{\color{#D61F06}{6}} \phantom0 \, \, \phantom0 && \\[-3pt] \underline{\boxed{7} \ \boxed{\color{#D61F06}{7}} \,\, \phantom0 \phantom0 } && \\[-3pt] \boxed{\color{#D61F06}{9}} \ \boxed{\color{#D61F06}{7}} && \\[-2pt] \underline{\boxed{8} \ \boxed{\color{#D61F06}{8}}} && \\[-2pt] \boxed{9} \end{array} } Hint:The choice for divisor is between 11 and 12. For 12 second block of third row is turning to 0 Hence divisor must be 11 \small\color{forestgreen}{\text{Hint:The choice for divisor is between 11 and 12.}\\\text{For 12 second block of third row is turning to 0}\\\text{Hence divisor must be 11}}

Hhaah! You really do love these types of problems don't you? Maybe I should post more ahahaha

Nice work!!

Pi Han Goh - 5 years, 4 months ago

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Yup.....I'm loving this variety of problems :). BTW Thanks.

Rishabh Jain - 5 years, 4 months ago

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