Pine's forest

There were so many pines in the forest that 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 answer:

n =  1107

Step-by-step explanation:

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

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