The Sum of the Digits of a Number

Number Theory Level 4

Given that M M and N N are both positive integers, the sum of the digits of M M is 34 and the sum of the digits of N N is 32.

If M + N M+N involves exactly 4 carries, what is the sum of the digits of M + N M+N ?


The answer is 30.

Paul Fournier by Paul Fournier , 70, Canada

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2 solutions

Nagabhushan S N
Dec 3, 2015

When a carry is generated, the sum is decreased by 9. For eg, 5+6 is 11. The sum of sum of digits in 5,6 is 11 but the sum of digits of the result is 2,so sum is reduced by 9. In the given problem, 4 carries are generated, so subtract the sum by 4x9

32+34-4x9=30

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Awesome solution! Love this way of thinking. I used trial and error sadly.

Shubham Bhargava - 5 years, 6 months ago
Faisal Basha
Dec 12, 2015

9997 ( 3 × 9 + 7 = 34 ) + 9995 ( 3 × 9 + 5 = 32 ) = 19992 ( 1 + 27 + 2 = 30 ) 9997 (3×9+7=34) + 9995 (3×9+5=32) = 19992 (1+27+2=30)

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