# Understand the problem

**k**digits, is an integer whose digits have a sum of \\(1000\\). What is

**k**?

##### Source of the problem

##### Topic

Number Theory

##### Difficulty Level

7/10

##### Suggested Book

Problem Solving Strategies Excursion In Mathematics

# Start with hints

After having a long look into this problem you can first make attempt by listing the first few numbers of the given form.Give it a try!!!!!

So we can do it like this **8*(8)=64** **8*(88)=704** **8*(888)=7104** **8*(8888)=71104** **8*(88888)=711104** Now try to observe the pattern in the above table because here lies the main insight of this problem . Come on cook it up!!!!!!

So form the table you can observe the terms are following a pattern that’s is The first number is 7 Then k-2 number of 1 Then the last two digits are 04

Now try to make the sum to 1000

So now you are in the final part so you can easily find 7+04+(k-2)=1000

implies 11+(k-2)=1000 . Solving this equation we get the value of K is 991 which is the required answer.

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#### Math Olympiad Program

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