# 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 $2+3+...+100=5049.$