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Question 17

The number of times the digit $$1$$ occurs in the result of $$1+11+111+\cdots+111\ldots111$$ ( $$100$$ digits), is


Correct Answer: 11

Solution

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Adding the repunits produces a number that can be grouped into $$11$$ blocks with the pattern $$123456790$$, followed by the final carry pattern. The digit $$1$$ therefore occurs exactly once in each of the $$11$$ blocks. Hence the required number of occurrences is $$11$$.

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