Mathematics 7775

A total of 3389 digits were needed to number all the sheets of the mathematics textbook. Assume that in a book, every leaf outside the plates is numbered.
How many pages does this textbook have if it is:
a) single-volume
b) two-volume (with both parts having roughly the same number of pages)?

Correct answer:

a =  1124

Step-by-step explanation:

$$\begin{gathered} a_1=9 \\ {a}_2=2\cdot 90=180 \\ {a}_3=3\cdot 900=2700 \\ {a}_4=4\cdot (a-999) \\ {a}_1+a_2+a_3+a_4=3389 \\ 9+2\cdot 90+3\cdot 900+4\cdot (a-999)=3389 \\ 4a=4496 \\ a=\frac{4496}{4}=1124 \\ a=1124 \\ {a}_4=4\cdot (a-999)=4\cdot (1124-999)=500 \end{gathered}$$

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