Pine's forest

There were so many pines in the forest that if they were sequentially numbered 1, 2, 3,. .. , would use three times more digits than the pine trees alone. How many pine trees were there in the forest?

Correct result:

n =  1107

Solution:

$$\begin{gathered} 1\cdot 9+2(a-9)=3a \\ a=-9\dots \mathrm{\nexists } \\ 1\cdot 9+2(99-9)+3(b-99)=3b \\ \mathrm{\nexists }b \\ 1\cdot 9+2(99-9)+3(999-99)+4(n-999)=3n \\ n=1107 \\ n=1107\mathrm{/}1=1107 \\ =1107 \end{gathered}$$

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