1. Divide a circular piece of paper into several smaller pieces of any size using straight lines. If the number of smaller pieces is no less than 2004, then the minimum number of straight lines needed is ( ).
(A) 61
(B) 62
(C) 63
(D) 64
Hint: First归纳出induce that $k$ lines can divide a circle into at most $f(k)=\frac{k(k+1)}{2}+1$ pieces of paper, and $f(62)<2004<f(63)$. Answer: $\mathrm{C}$.

Note: The word "induce" in the translation should be "induce that" to better fit the context in English. Here is the corrected version:

Hint: First induce that $k$ lines can divide a circle into at most $f(k)=\frac{k(k+1)}{2}+1$ pieces of paper, and $f(62)<2004<f(63)$. Answer: $\mathrm{C}$.