Lại một bài toán đếm trong APMOPS 2004


Question:

How many digits are there before the hundredth 9 in the following number?
9797797779777797777797777779…

Solution:

The number before the hundredth 9 in this number sequence is

97977977797777977777...9\underbrace{77...77}_{99}.

Hence, the number of numbers of this number is 2+3+...+100=5049.



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