Stringent Numbers 3

Logic Level 4

The above shows a long division between 2 integers, with the last box at the bottom representing the remainder of the quotient. Each box represents a single digit non-negative integer.

What is maximum possible sum of values of all the missing numbers?


The answer is 55.

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3 solutions

Saharsh Rathi
Mar 17, 2017

Very neat solution! Thanks for showing all the steps! =D =D =D

Pi Han Goh - 4 years, 3 months ago

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Thank you!! :)

saharsh rathi - 4 years, 2 months ago
Noureldin Yosri
Jan 5, 2016

lets write the numbers in the form 900 + x*10 + y , 10+ z where 0 <= x,y,z <= 9 the problem requires that (90+x)%(10+z) == 2 and (20 + y)%(10+z) == 3 , so by tuning z we get x and y , as it turns out there are only 6 possibilities , after trying them we get the answer

What are the 6 possibilities?

Pi Han Goh - 5 years, 5 months ago

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(z,x,y) : (0, 2, 3) (1, 0, 5) (2, 8, 7) (3, 3, 9) (8, 2, 1) (9, 7, 2)

Noureldin Yosri - 5 years, 5 months ago

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Thanks! Do you enjoy this question?

Pi Han Goh - 5 years, 5 months ago

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@Pi Han Goh yes ... and thanks for the problem ,keep posting interesting problems :D

Noureldin Yosri - 5 years, 5 months ago

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@Noureldin Yosri Try to solve the examples given in the Wiki page ! Enjoy!!

Pi Han Goh - 5 years, 5 months ago
Aanchal Shahi
Dec 20, 2015

Yessss I solved it in a bad long way Required divisor is 12 Divident is 987. Quotient is 82 And the required sum is 55

Yeah, can you explain why 12 must be the divisor?

Pi Han Goh - 5 years, 5 months ago

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