Fill In The Long Division

Logic Level 2

Above shows a long division. What is the sum of values of all the missing digits?


The answer is 35.

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1 solution

Rohit Udaiwal
Jan 31, 2016

0 4 2 1 7 \enclose l o n g d i v 7 3 0 6 8 0 0 5 0 3 4 1 6 \LARGE{ \begin{array}{rlll} \phantom{0}\ \boxed{\color{forestgreen}{4}} \ \boxed{\color{forestgreen}{2}} && \\[-3pt] \boxed{\color{forestgreen} {1}} \ \boxed{7} \ \enclose{longdiv}{\boxed{\color{forestgreen}{7}} \ \boxed{\color{forestgreen}{3}}\ \boxed{\color{forestgreen}{0}}}&& \\[-3pt] \underline{\boxed6 \ \boxed{\color{forestgreen}{8}}\phantom0 \phantom0} && \\[-3pt] \boxed{5} \ \boxed{\color{forestgreen}{0}}&& \\[-2pt] \underline{ \boxed{\color{forestgreen}{3}}\ \boxed{4}} && \\[-2pt] \boxed{ \color{forestgreen}{1}}\ \boxed{\color{forestgreen}{6}} && \\[-2pt] \end{array} }

Therefore sum of missing digits = 4 + 2 + 1 + 7 + 3 + 0 + 8 + 0 + 3 + 1 + 6 = 35 =4+2+1+7+3+0+8+0+3+1+6=35 .

Nice.. Politely saying, I genuinely doubt its uniqueness. There can be many such solutions... Say for example, that last third row can take any value in 50-59 and the corresponding remainder will vary from 16-25..

Rishabh Jain - 5 years, 4 months ago

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Yes,this troubles me as well. Sir,can you provide a solution to this ?

Rohit Udaiwal - 5 years, 4 months ago

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I am terrified.. Don't call me sir I am not that old (only two years elder than you :D), BTW I am also facing same problem with all these recent phantom problems ... These require a lot of hardwork before designing them and having a insight at all the cases. Maybe @Pi Han Goh can help. He has gained expertise in these problems:)

Rishabh Jain - 5 years, 4 months ago

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@Rishabh Jain @Pi Han Goh !!!

Rohit Udaiwal - 5 years, 4 months ago

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@Rohit Udaiwal Wow! Nice question! Well, if it's any number larger than 50, then the remainder is larger than 16, but the divisor must be 17 only. Because the remainder must always be less than the divisor, then it (the number in the 3rd last row) can't be larger than 50, so it must indeed be 50.

Pi Han Goh - 5 years, 4 months ago

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@Pi Han Goh Thanks for the wonderful explanation :)

Can you provide a solution to this .

Rohit Udaiwal - 5 years, 4 months ago

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@Rohit Udaiwal Hint: What are possible values that can represent the box directly below 9?

Pi Han Goh - 5 years, 4 months ago

@Rohit Udaiwal You should try to explain that in your solution. And explain why the divisor must be 17 only, and it cannot be 27, 37, 47, ... 97.

Pi Han Goh - 5 years, 4 months ago

@Rohit Udaiwal @rohit udaiwal I have posted the solution you can see it.

A Former Brilliant Member - 5 years, 4 months ago

Can you explain me how you take last digit of divisor zero

Yashkrit Gupta - 5 years, 4 months ago

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