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Number Theory Level 3

I am thinking of some number n n .

On subtracting the sum of digits of number n n from n n , I get some number s s .

Here are the digits of s s (in no specific order) -

1 , 0 , 1 , 7 , 7 , 2 , 6 , 9 , 7 , 7 1, 0, 1, 7, 7, 2, 6, 9, 7, 7

However, one digit is missing. Which digit is missing?

Details and Assumptions

  • Sum of digit refers to the digital sum of a number. For eg, sum of digits of 1997 is 1 + 9 + 9 + 7 = 26 1 + 9 + 9 + 7 = 26 .

  • s = n − sum of digits of n s = n - \text{sum of digits of n}

7 1 6 2 8 4 5 3

Arulx Z by Arulx Z , 20, India

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1 solution

Arulx Z
Dec 26, 2015

Here's a hint -

n − sum of digits of n n - \text{sum of digits of n}

will always be a multiple of 9.

Can you prove the general statement and find out the answer?

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