3. Write $\mathbf{2 0 1 2}$ as the sum of $N$ distinct positive integers, the maximum value of $N$ is $\qquad$
【Answer】62
【Analysis】Key points: Arithmetic sequence, maximum value
$1+2+\cdots+63=(63+1) \times 63 \div 2=2016>2012$, i.e., $N<63$
$1+2+\cdots+62=(62+1) \times 62 \div 2=1953<2012$, thus $N=62$