29. Odd integers starting from 1 are grouped as follows: (1), $(3,5),(7,9,11),(13,15,17,19), \ldots$. where the $n$-th group consists of $n$ odd integers. How many odd integers are in the same group which 2007 belongs to?
29. Ans: 45 .
2007 is the 1004 -th odd number. If 2007 is in the group $k+1$, then $1+2+\cdots+k<1004 \leq$ $1+2+\ldots(k+1)$. Thus
$$
\frac{k(k+1)}{2}<1004 \leq \frac{(k+1)(k+2)}{2} .
$$

We get $k=44$. So 2007 is in group 45 which has 45 odd integers.